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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Neurosci.</journal-id>
<journal-title>Frontiers in Neuroscience</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Neurosci.</abbrev-journal-title>
<issn pub-type="epub">1662-453X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fnins.2022.869137</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Neuroscience</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Novel Machine-Learning Based Framework Using Electroretinography Data for the Detection of Early-Stage Glaucoma</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Gajendran</surname> <given-names>Mohan Kumar</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1650148/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Rohowetz</surname> <given-names>Landon J.</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/592331/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Koulen</surname> <given-names>Peter</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/658163/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Mehdizadeh</surname> <given-names>Amirfarhang</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1661371/overview"/>
</contrib>
</contrib-group>
<aff id="aff1"><sup>1</sup><institution>Department of Civil and Mechanical Engineering, School of Computing and Engineering, University of Missouri-Kansas City</institution>, <addr-line>Kansas City, MO</addr-line>, <country>United States</country></aff>
<aff id="aff2"><sup>2</sup><institution>Vision Research Center, Department of Ophthalmology, University of Missouri-Kansas City</institution>, <addr-line>Kansas City, MO</addr-line>, <country>United States</country></aff>
<aff id="aff3"><sup>3</sup><institution>Department of Biomedical Sciences, University of Missouri-Kansas City</institution>, <addr-line>Kansas City, MO</addr-line>, <country>United States</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Rafael Linden, Federal University of Rio de Janeiro, Brazil</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: Marc Sarossy, The University of Melbourne, Australia; Flora Hui, Centre for Eye Research Australia, Australia</p></fn>
<corresp id="c001">&#x0002A;Correspondence: Amirfarhang Mehdizadeh <email>mehdizadeha&#x00040;umkc.edu</email></corresp>
<fn fn-type="other" id="fn001"><p>This article was submitted to Neurodegeneration, a section of the journal Frontiers in Neuroscience</p></fn></author-notes>
<pub-date pub-type="epub">
<day>04</day>
<month>05</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>16</volume>
<elocation-id>869137</elocation-id>
<history>
<date date-type="received">
<day>03</day>
<month>02</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>28</day>
<month>03</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2022 Gajendran, Rohowetz, Koulen and Mehdizadeh.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Gajendran, Rohowetz, Koulen and Mehdizadeh</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/"><p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p></license>
</permissions>
<abstract>
<sec>
<title>Purpose</title>
<p>Early-stage glaucoma diagnosis has been a challenging problem in ophthalmology. The current state-of-the-art glaucoma diagnosis techniques do not completely leverage the functional measures&#x00027; such as electroretinogram&#x00027;s immense potential; instead, focus is on structural measures like optical coherence tomography. The current study aims to take a foundational step toward the development of a novel and reliable predictive framework for early detection of glaucoma using machine-learning-based algorithm capable of leveraging medically relevant information that ERG signals contain.</p>
</sec>
<sec>
<title>Methods</title>
<p>ERG signals from 60 eyes of DBA/2 mice were grouped for binary classification based on age. The signals were also grouped based on intraocular pressure (IOP) for multiclass classification. Statistical and wavelet-based features were engineered and extracted. Important predictors (ERG tests and features) were determined, and the performance of five machine learning-based methods were evaluated.</p>
</sec>
<sec>
<title>Results</title>
<p>Random forest (bagged trees) ensemble classifier provided the best performance in both binary and multiclass classification of ERG signals. An accuracy of 91.7 and 80% was achieved for binary and multiclass classification, respectively, suggesting that machine-learning-based models can detect subtle changes in ERG signals if trained using advanced features such as those based on wavelet analyses.</p>
</sec>
<sec>
<title>Conclusions</title>
<p>The present study describes a novel, machine-learning-based method to analyze ERG signals providing additional information that may be used to detect early-stage glaucoma. Based on promising performance metrics obtained using the proposed machine-learning-based framework leveraging an established ERG data set, we conclude that the novel framework allows for detection of functional deficits of early/various stages of glaucoma in mice.</p>
</sec>
</abstract>
<kwd-group>
<kwd>glaucoma</kwd>
<kwd>machine learning</kwd>
<kwd>electroretinography</kwd>
<kwd>ERG</kwd>
<kwd>wavelet transform</kwd>
<kwd>early stage</kwd>
<kwd>AI</kwd>
</kwd-group>
<contract-num rid="cn002">EY031248</contract-num>
<contract-sponsor id="cn001">Vision Research Center, University of Missouri-Kansas City School of Medicine<named-content content-type="fundref-id">10.13039/100006590</named-content></contract-sponsor>
<contract-sponsor id="cn002">National Institutes of Health<named-content content-type="fundref-id">10.13039/100000002</named-content></contract-sponsor>
<counts>
<fig-count count="10"/>
<table-count count="4"/>
<equation-count count="7"/>
<ref-count count="132"/>
<page-count count="18"/>
<word-count count="12299"/>
</counts>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>1. Introduction</title>
<p>Glaucoma, a chronic neurodegenerative disease affecting the retina and optic nerve, and a leading cause of blindness, is characterized by a progressive, irreversible loss of vision. As currently available treatment paradigms focus primarily on a predisposing factor, elevated intraocular pressure (IOP), and do not allow for repair of the retina and optic nerve once the disease has progressed and damage has occurred, technologies enabling an early diagnosis of glaucoma are needed urgently. Consequently, such new diagnostic modalities enabling early therapeutic intervention would significantly improve treatment outcomes. Current methods of glaucoma diagnosis are based on psychophysical techniques and the assessment of structural changes to the retina and optic nerve (Bussel et al., <xref ref-type="bibr" rid="B18">2014</xref>). Standard automated perimetry testing, including the widely used Humphrey visual field testing, currently represents the most commonly utilized technique for glaucoma diagnosis and monitoring of disease progression and therapy outcomes (Ernest et al., <xref ref-type="bibr" rid="B35">2012</xref>; Fidalgo et al., <xref ref-type="bibr" rid="B37">2015</xref>). Recent efforts to employ machine-learning (ML) approaches to improve the analysis of behavioral psychophysical testing approaches produced moderate improvements over conventional analysis algorithms (Saeedi et al., <xref ref-type="bibr" rid="B102">2021</xref>). However, significant damage to the retina and optic nerve, including loss of retinal ganglion cells (RGCs) has often already occurred before changes can be detected with standard automated perimetry testing (Turalba and Grosskreutz, <xref ref-type="bibr" rid="B117">2010</xref>).</p>
<p>Recently, automated retinal image analysis (ARIA) systems have been developed for the diagnosis of complex diseases such as diabetic retinopathy and glaucoma (Sim et al., <xref ref-type="bibr" rid="B110">2015</xref>; Lee et al., <xref ref-type="bibr" rid="B73">2017</xref>). The development of these ARIA systems involved ML-based methods to detect structural changes determined with optical coherence tomography (OCT) imaging resulting in high analytical accuracy in automatically classifying disease phenotypes based on structural characteristics (Zhu et al., <xref ref-type="bibr" rid="B132">2014</xref>; Asaoka et al., <xref ref-type="bibr" rid="B9">2016</xref>; An et al., <xref ref-type="bibr" rid="B6">2019</xref>). Despite such significant progress, early detection of glaucoma is still a challenge (Brandao et al., <xref ref-type="bibr" rid="B16">2017</xref>), given the highly significant limitations of early detection of glaucoma based on structural methods. Systems employing the analysis of structural changes for glaucoma diagnosis are based on measuring retinal nerve fiber layer (RNFL) thickness in OCT images of the retina, which is highly variable and weakly correlated with RGC counts despite RNFL thickness being a surrogate marker of RGC degeneration and optic nerve fiber loss, hallmarks of glaucoma pathogenesis (Ledolter et al., <xref ref-type="bibr" rid="B72">2015</xref>). Further, RGC loss often occurs early during pathogenesis in the absence of measurable RNFL thinning, prompting an urgent clinical need for methods with higher sensitivity, such as functional measures including ERG (Harwerth et al., <xref ref-type="bibr" rid="B50">2002</xref>; Fortune et al., <xref ref-type="bibr" rid="B40">2003</xref>; Takagi et al., <xref ref-type="bibr" rid="B112">2012</xref>; Ledolter et al., <xref ref-type="bibr" rid="B72">2015</xref>; Brandao et al., <xref ref-type="bibr" rid="B16">2017</xref>). In contrast, functional measures such as visual field and ERG are sensitive to subtle changes in RGC function and RGC damage, which suggest a significant potential to enable early detection of glaucoma, even in the absence of elevated IOP, as seen in patients with normotensive glaucoma (Fortune et al., <xref ref-type="bibr" rid="B40">2003</xref>; Aldebasi et al., <xref ref-type="bibr" rid="B5">2004</xref>; Brandao et al., <xref ref-type="bibr" rid="B16">2017</xref>). Therefore, this study aims to investigate such potential considering ERG signals.</p>
<p>Consequently, interventions could be initiated before irreversible damage occurs, allowing for the optimization of treatment strategies based on the improvement of RGC function (Ventura and Porciatti, <xref ref-type="bibr" rid="B120">2006</xref>). This is of high clinical importance as determining the efficacy of therapies aimed at lowering IOP in open-angle glaucoma (Palmberg, <xref ref-type="bibr" rid="B98">2002</xref>; Leske et al., <xref ref-type="bibr" rid="B77">2007</xref>) requires early validation of therapy success (An et al., <xref ref-type="bibr" rid="B6">2019</xref>), but will also be of importance for the development of novel alternative and complementary glaucoma therapies based on neuroprotective strategies (Rohowetz et al., <xref ref-type="bibr" rid="B101">2018</xref>). Recently, in a study conducted by Tang et al. (<xref ref-type="bibr" rid="B113">2020</xref>) photopic negative response (PhNR) was used to assess the short-term changes in inner retinal function following intraocular pressure (IOP) decrease in glaucoma using eyedrops. Hui et al. (<xref ref-type="bibr" rid="B59">2020</xref>) showed that Nicotinamide supplementation helps improve the function of the inner retina in glaucoma.</p>
<p>Recent advances in the acquisition of complex neuroscience data have a significant innovative potential to progress toward more effective diagnostic systems (Kononenko, <xref ref-type="bibr" rid="B66">2001</xref>). The adequate, timely, and clinically relevant analysis of such data has potentially high clinical impact (Lisboa, <xref ref-type="bibr" rid="B80">2002</xref>). However, while such data sets can be readily acquired and technologies to further improve and simplify data acquisition continue to emerge (McPadden et al., <xref ref-type="bibr" rid="B88">2019</xref>), critical barriers to implement the effective use of such novel data in clinical diagnostics and therapy delivery remain (Lee and Yoon, <xref ref-type="bibr" rid="B74">2017</xref>). While the analysis of complex biomedical data is often part of medical diagnostics, current expert analysis standards and algorithms are limited by pattern recognition in few dimensions, which results in less than optimal identification or even exclusion of potentially relevant diagnostic features (Hannun et al., <xref ref-type="bibr" rid="B49">2019</xref>). Machine learning could significantly augment medical diagnostics and increase their efficacy by analyzing aspects of complex and multi-dimensional biomedical data that are either not being considered adequately or that are not accessible to current analysis methods (Holzinger, <xref ref-type="bibr" rid="B55">2014</xref>). Such machine-learning based diagnostic approaches have been developed and are being actively used for the detection of cardiovascular diseases (Al&#x00027;Aref et al., <xref ref-type="bibr" rid="B4">2019</xref>), and cancer (Cruz and Wishart, <xref ref-type="bibr" rid="B23">2006</xref>).</p>
<p>ERG data are one such type of complex and multi-dimensional biomedical data that are potentially relevant to the diagnosis of glaucoma, but are currently not considered during routine clinical practice or in clinical research. Historically, this is due to multiple barriers related to clinical ERG data acquisition, such as limitations in reproducibility, high costs of both equipment and of individual tests, long test duration and complex test administration resulting in reduced patient acceptance and compliance, and the need for highly trained experts to administer tests. With the advent of novel ERG technologies, most of these barriers related to clinical ERG data acquisition have been removed (Nakamura et al., <xref ref-type="bibr" rid="B92">2016</xref>; Asakawa et al., <xref ref-type="bibr" rid="B8">2017</xref>; Kato et al., <xref ref-type="bibr" rid="B63">2017</xref>; Hobby et al., <xref ref-type="bibr" rid="B54">2018</xref>; Liu et al., <xref ref-type="bibr" rid="B81">2018</xref>; Man et al., <xref ref-type="bibr" rid="B84">2020</xref>), opening up the possibility to effectively use ERG data for glaucoma diagnostics, calling the necessity for the development of novel approaches (e.g., M-L-based ones) that is capable to quickly and thoroughly analyze such data.</p>
<p>Machine learning is based on statistical techniques to learn from data and develop predictive models (Jordan and Mitchell, <xref ref-type="bibr" rid="B61">2015</xref>). Recently, there has been a surge of interest in machine learning as significant advancements in computational hardware (Shi et al., <xref ref-type="bibr" rid="B109">2016</xref>) facilitate the development of novel machine learning approaches as solutions to problems in various disciplines from financial forecasting to public transportation and healthcare (Trafalis and Ince, <xref ref-type="bibr" rid="B116">2000</xref>; Omrani, <xref ref-type="bibr" rid="B97">2015</xref>; Ahmad et al., <xref ref-type="bibr" rid="B3">2018</xref>). There are several predictive techniques in machine learning with various complexities, ranging from simple linear models to advanced non-linear models such as those based on deep learning algorithms (Shailaja et al., <xref ref-type="bibr" rid="B108">2018</xref>; Khan et al., <xref ref-type="bibr" rid="B65">2021</xref>; Saxe et al., <xref ref-type="bibr" rid="B106">2021</xref>). Currently, available ERG analysis methods, such as those developed by Hood et al. (<xref ref-type="bibr" rid="B56">2000</xref>); Ventura and Porciatti (<xref ref-type="bibr" rid="B120">2006</xref>), have contributed to a significantly improved understanding of the relationship between ERG signals and vision loss. These methods are limited to frequency domain analysis (Miguel-Jim&#x000E9;nez et al., <xref ref-type="bibr" rid="B89">2010</xref>; Luo et al., <xref ref-type="bibr" rid="B82">2011</xref>; Palmowski-Wolfe et al., <xref ref-type="bibr" rid="B99">2011</xref>; Ledolter et al., <xref ref-type="bibr" rid="B71">2013</xref>) and the analyses of differences in amplitude and latency of ERG (Fortune et al., <xref ref-type="bibr" rid="B39">2002</xref>; Thienprasiddhi et al., <xref ref-type="bibr" rid="B114">2003</xref>; Stiefelmeyer et al., <xref ref-type="bibr" rid="B111">2004</xref>; Chu et al., <xref ref-type="bibr" rid="B21">2007</xref>; Todorova and Palmowski-Wolfe, <xref ref-type="bibr" rid="B115">2011</xref>; Ho et al., <xref ref-type="bibr" rid="B53">2012</xref>; Hori et al., <xref ref-type="bibr" rid="B57">2012</xref>). In addition, these methods are often time-consuming, labor-intensive, and focused on parameters developed to address a small subset of mostly genetic diseases of the eye affecting predominantly pediatric patient populations (Frishman et al., <xref ref-type="bibr" rid="B41">2000</xref>; Graham et al., <xref ref-type="bibr" rid="B43">2000</xref>; Dale et al., <xref ref-type="bibr" rid="B25">2010</xref>). To achieve higher accuracy and a more detailed understanding of disease progression and of the impact of therapeutic intervention, more sophisticated features such as those obtained from wavelet analysis are required (Forte et al., <xref ref-type="bibr" rid="B38">2008</xref>; Barraco et al., <xref ref-type="bibr" rid="B12">2014</xref>). Additionally, currently available methods are often not suitable for analyzing large data sets and databases, rendering them incapable of taking advantage of complex and rich datasets (Consejo et al., <xref ref-type="bibr" rid="B22">2019</xref>; Armstrong and Lorch, <xref ref-type="bibr" rid="B7">2020</xref>). These drawbacks prompted others (Bowd et al., <xref ref-type="bibr" rid="B15">2014</xref>; Yousefi et al., <xref ref-type="bibr" rid="B127">2015</xref>; Atalay et al., <xref ref-type="bibr" rid="B11">2016</xref>; Verma et al., <xref ref-type="bibr" rid="B121">2017</xref>) and us to design and develop novel methods capable of handling complex and large datasets and ultimately to provide a unique approach for diagnosing early-stage glaucoma. However, it should be noted that early detection of glaucoma is not possible with currently available techniques during the early stages of glaucoma pathogenesis, when cellular changes occur that do not result in structural damage or visual impairment yet. Such early-onset factors predisposing to glaucoma development include processes preceding the onset of ocular hypertension, for example, the onset of iris pigment dispersion preceding IOP elevation in the DBA/2 mouse model. However, and more importantly, we identified cellular changes resulting in altered ERG signals, such as changes in oscillatory potentials, that currently cannot be detected with other functional or structural measures.</p>
<p>Boquete and colleagues developed a method to automate glaucoma diagnosis based on ERG signals using neural networks and structural pattern analysis (Boquete et al., <xref ref-type="bibr" rid="B14">2012</xref>). They utilized thirteen features (morphological and transitional characteristics) for training the model and achieved a testing accuracy of 80.7% (Boquete et al., <xref ref-type="bibr" rid="B14">2012</xref>). This study was limited to basic morphological characteristics of mfERG recordings (Boquete et al., <xref ref-type="bibr" rid="B14">2012</xref>). Miguel-Jim&#x000E9;nez et al. (<xref ref-type="bibr" rid="B90">2015</xref>) also employed neural networks for ERG-based glaucoma diagnosis but used continuous wavelet transformed coefficients and achieved a binary classification accuracy of 86.90% (Miguel-Jim&#x000E9;nez et al., <xref ref-type="bibr" rid="B90">2015</xref>). Although a higher accuracy was achieved, this analysis was limited to wavelet features only (Miguel-Jim&#x000E9;nez et al., <xref ref-type="bibr" rid="B90">2015</xref>). Nevertheless, both studies showed that machine learning-based methods trained even on compact data sets provide powerful tools to analyze ERG signals and provide potentially new information relevant for the early detection of glaucoma. Sarossy and colleagues investigated the relationship between a compact set of features and glaucoma that can be analyzed with machine learning approaches; however, the study was limited to the analysis of the photopic negative response (PhNR) and five additional features (Sarossy et al., <xref ref-type="bibr" rid="B104">2021</xref>).</p>
<p>The goal of the present study was to comprehensively assess the capability of machine-learning-based methods to detect early-stage glaucoma using time-series ERG signals. In particular, the following points are addressed during method development:</p>
<list list-type="order">
<list-item><p>Develop a framework to extract and identify important predictors (features) from ERG signals.</p></list-item>
<list-item><p>Compare the predictive capability of statistical and wavelet-based features for binary and multiclass classification.</p></list-item>
<list-item><p>Develop a robust ML-based model to diagnose glaucoma (binary classification).</p></list-item>
<list-item><p>Develop a robust ML-based model capable of distinguishing various stages of glaucoma progression (multiclass classification).</p></list-item>
<list-item><p>Develop a robust ML-based model to provide a quantitative assessment of visual function by predicting retinal ganglion cell count from ERG signals for the first time.</p></list-item>
</list>
</sec>
<sec sec-type="methods" id="s2">
<title>2. Methods</title>
<sec>
<title>2.1. Overview</title>
<p>ML based algorithms have been applied to Electrocardiogram (ECG) signals in order to develop predictive models for diagnosing heart diseases (Li et al., <xref ref-type="bibr" rid="B78">2014</xref>; Al&#x00027;Aref et al., <xref ref-type="bibr" rid="B4">2019</xref>). Recently machine learning-based Artificial Neural Networks (ANN) have been applied to ERG signals for obesity diagnosis (Yapici et al., <xref ref-type="bibr" rid="B125">2021</xref>). However, to date, machine learning-based methods have not been applied systematically to analyze ERG signals for glaucoma detection. Therefore, the potential of ERG signals in glaucoma diagnosis has not been fully utilized. The present work aims to develop a predictive model for early glaucoma diagnosis based on machine-learning algorithms by utilizing advanced features from ERG signals as predictors. The steps involved in developing a machine-learning-based predictive model for ERG analysis are shown in <xref ref-type="fig" rid="F1">Figure 1</xref>. Each of these steps is explained in detail below.</p>
<fig id="F1" position="float">
<label>Figure 1</label>
<caption><p>Machine learning workflow using ERG signals. <italic>ERG Database:</italic> the ERG database contains the input ERG data used to train the predictive model. <italic>Pre-processing of data:</italic> this step ensures data quality by transforming the data to a common baseline, accounting for missing data, and handling outliers. <italic>Feature extraction:</italic> mathematical operations are performed on the data to extract features/parameters that indicate functional deficits in the eye. <italic>Predictive Model Development:</italic> algorithms can determine trends and patterns in data from statistical analysis of extracted features during training; these models can predict either class or value from the input data are called classifier and regression models, respectively. <italic>Deployment of Model into medical devices:</italic> successful predictive models can be included with ERG testing devices to provide real-time prognosis and diagnosis.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0001.tif"/>
</fig>
</sec>
<sec>
<title>2.2. ERG: A Biomarker</title>
<p>Electroretinography measures the electrical responses of different types of cells in the retina, such as ganglion cells. These signals are usually measured in microvolts. Oscillatory Potential (OP) and Scotopic Threshold Response (STR) represent important ERG components indicative of RGC cell function (Saszik et al., <xref ref-type="bibr" rid="B105">2002</xref>; Dong et al., <xref ref-type="bibr" rid="B33">2004</xref>; Hancock and Kraft, <xref ref-type="bibr" rid="B48">2004</xref>; Lei et al., <xref ref-type="bibr" rid="B75">2006</xref>). OPs are small rhythmic wavelets superimposed on the ascending b-wave of the ERG and STR are negative corneal deflection elicited in the fully dark-adapted eye to dim stimuli. An International Society for Clinical Electrophysiology of Vision (ISCEV) standardized ERG protocol (Marmor et al., <xref ref-type="bibr" rid="B85">2009</xref>) included several tests to measure the function of various retinal cell types, including the rod response, standard rod-cone response, Hi-intensity rods, and cones response, cone response, Hi-intensity cone response, flicker, and Hi flicker (Grillo et al., <xref ref-type="bibr" rid="B46">2018</xref>). A visualization of nine ERG signals resulting from two ERG components (OP and STR) and seven ERG test responses is provided in <xref ref-type="fig" rid="F2">Figure 2</xref>. The dynamics of ERG signals vary in people with various conditions and can therefore aid in differentiating individuals with glaucoma (Grillo et al., <xref ref-type="bibr" rid="B46">2018</xref>), schizophrenia (Demmin et al., <xref ref-type="bibr" rid="B30">2018</xref>), obesity (Yapici et al., <xref ref-type="bibr" rid="B125">2021</xref>), and bipolar disorder (H&#x000E9;bert et al., <xref ref-type="bibr" rid="B51">2020</xref>). ERG can also help in evaluating the effectiveness of new or existing drugs and therapy modalities (Lai et al., <xref ref-type="bibr" rid="B70">2006</xref>, <xref ref-type="bibr" rid="B69">2009</xref>; Nebbioso et al., <xref ref-type="bibr" rid="B94">2009</xref>; da Silva et al., <xref ref-type="bibr" rid="B24">2020</xref>).</p>
<fig id="F2" position="float">
<label>Figure 2</label>
<caption><p>Visualization of ERG Signals manifesting their complex nature. The blue lines correspond to healthy and red lines correspond to glaucomatous Signals. Signals resulting from ERG tests include <italic>OP</italic> (Oscillatory Potential: small rhythmic wavelets superimposed on the ascending b-wave of the ERG), <italic>STR</italic> (Scotopic Threshold Response: negative corneal deflection elicited in the fully dark-adapted eye to dim stimuli), <italic>Rods</italic> (rod response), <italic>Rods and cones</italic> (standard rod-cone response), <italic>Hi Rods and cones</italic> (Hi-intensity rods and cones response), <italic>Cones</italic> (cone response), <italic>Hi cones</italic> (Hi-intensity cone response), <italic>Flicker</italic> (Flicker response), and <italic>Hi flicker</italic> (Hi-intensity flicker response).</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0002.tif"/>
</fig>
</sec>
<sec>
<title>2.3. Ganzfeld Flash Electroretinography</title>
<p>The development of pigmentary glaucomatous optic neuropathy in the DBA/2 mouse model had several similarities to glaucoma pathogenesis in human patients, including loss of vision and RGC (McKinnon et al., <xref ref-type="bibr" rid="B87">2009</xref>; Burroughs et al., <xref ref-type="bibr" rid="B17">2011</xref>; Grillo et al., <xref ref-type="bibr" rid="B44">2013</xref>; de Lara et al., <xref ref-type="bibr" rid="B29">2014</xref>; Kaja et al., <xref ref-type="bibr" rid="B62">2014</xref>; Grillo and Koulen, <xref ref-type="bibr" rid="B45">2015</xref>; Montgomery et al., <xref ref-type="bibr" rid="B91">2016</xref>). The Ganzfeld flash electroretinography (fERG) procedures in mice were conducted under dim red light that was followed by an overnight dark adaptation (&#x0003E;12 h). Isoflurane at 3 and 1.5% was used respectively, to anesthetize mice and maintain anesthesia. The pupils were dilated using 1 drop of 1% tropicamide and were allowed to dilate for 10 min. Rectal temperature was monitored and maintained at 37&#x000B0;C using a heating pad. Silver-embedded thread electrodes were placed over the cornea in 1% methylcellulose with mini-contact lenses fitted preventing the corneal dehydration (Ocuscience LLC, Henderson, NV). The head was placed inside the Ganzfeld dome, and fERG with 2 recording channels was performed using an HMsERG system (Ocuscience LLC) equipped with an amplifier with a band pass from 0.3 to 300 Hz. Mice were subjected to the International Society for Clinical Electrophysiology of Vision (ISCEV) standardized ERG protocol [29], whose implementation is described in detail in Marmor et al. (<xref ref-type="bibr" rid="B85">2009</xref>). ERGView 4.380V software (OcuScience LLC) was used to perform statistical analyses including averaging multiple flashes recorded at each intensity and stored for further analysis. Additionally, mice were tested using a scotopic flash intensity series in the range of &#x02212;4.5 to 1.5 log cd s/m<sup>2</sup>. Further, a 1:1,000 neutral density filter (ND3) was used to control the 7 lowest flash intensities; data were averaged from 10 flashes (&#x02212;4.5 to &#x02212;3.5 log cd s/m<sup>2</sup>), 4 flashes (&#x02212;3 to 0.5 log cd s/m<sup>2</sup>) at the lower intensities or measured from 1 flash at the 2 highest intensities (1 to 1.5 log cd s/m<sup>2</sup>). Following the light adaptation (1.5 log cd s/m<sup>2</sup> for 10 min), responses from a photopic series (&#x02212;2 to 1.5 log cd s/m<sup>2</sup>; 32 flashes per intensity) were recorded in a separate fashion. Further details about data acquisition can be found in Grillo et al. (<xref ref-type="bibr" rid="B46">2018</xref>).</p>
</sec>
<sec>
<title>2.4. ERG Dataset</title>
<p>Ganzfeld fERG tests were performed on 4 months old (<italic>n</italic> = 15) and 11 months old (<italic>n</italic> = 15) male DBA/2 mice. Each animal had two sets of test data, one for each eye. Therefore, a total of 60 data sets for individual eyes were included in this study. Each data set comprised of nine different ERG signals (OP, STR, and seven signals from ERG testing protocols), as shown in <xref ref-type="fig" rid="F2">Figure 2</xref> (OPs are small rhythmic wavelets superimposed on the ascending b-wave of the ERG and STR are negative corneal deflection elicited in the fully dark-adapted eye to dim stimuli). Therefore, 540 recordings were utilized in this study. Intraocular pressure (IOP) and retinal ganglion cell (RGC) count measurements were also utilized in this study. Although IOP data was available for all animals, RGC counts were only available for 10 (20 eyes). The animals were grouped in a binary group (healthy and glaucomatous) based on age and multiclass group based on IOP as (normal, &#x0003C;12 mm Hg; high, [&#x02265;12 mm Hg &#x0003C;17 mm Hg]; glaucomatous, &#x02265;17 mm Hg). All the data used in this study was well-balanced for respective groups.</p>
</sec>
<sec>
<title>2.5. Pre-processing of Data</title>
<p>ERG raw data may contain several anomalies such as different start times, missing data, different sampling frequencies, noise, and unequal lengths of the signal recordings. In Machine learning-based modeling, the quality of the training data can significantly impact the model performance. Therefore, pre-processing (data preparation and screening) is crucial to ensure the quality of the training dataset (Jambukia et al., <xref ref-type="bibr" rid="B60">2015</xref>). Pre-processing steps considered in the present study include,</p>
<list list-type="order">
<list-item><p>Baseline adjustment</p></list-item>
<list-item><p>Feature extraction</p></list-item>
<list-item><p>Handling missing data</p></list-item>
<list-item><p>Handling outliers</p></list-item>
<list-item><p>Feature scaling</p></list-item>
<list-item><p>Feature selection</p></list-item>
</list>
<p>The signal&#x00027;s baseline (start time) can be different for different animals and testing protocols. Therefore, all the measurements were brought to a common baseline (start time was offset to zero) during baseline adjustment (Jambukia et al., <xref ref-type="bibr" rid="B60">2015</xref>). Feature extraction involves computing a reduced set of values from a high-dimensional signal capable of summarizing most of the information contained in the signal (Khalid et al., <xref ref-type="bibr" rid="B64">2014</xref>). The missing data were replaced with mean values (Graham et al., <xref ref-type="bibr" rid="B42">2013</xref>). For handing outliers, values more than three scaled median absolute deviations (MAD) away from the median were detected as outliers and replaced with threshold values used in outlier detection (Aguinis et al., <xref ref-type="bibr" rid="B1">2013</xref>). The feature&#x00027;s values vary widely, even by orders of magnitude. Therefore, it is important to bring the feature values to a similar range (feature scaling), especially when using distance-based machine learning algorithms (Wan, <xref ref-type="bibr" rid="B122">2019</xref>). Feature selection is further dimensionality reduction from the extracted features. It is performed to reduce the computational cost of modeling, to achieve a better generalized, high-performance model that is simple and easy to understand (Aha and Bankert, <xref ref-type="bibr" rid="B2">1996</xref>). Feature extraction and selection are explained in detail in the following sections.</p>
</sec>
<sec>
<title>2.6. Feature Extraction</title>
<p>ERG signals are complex high-dimensional data, and training a model with many variables requires significant computational resources. Feature extraction reduces the dimensionality of the data by computing a reduced set of values from a high-dimensional signal capable of summarizing most of the information contained in the signal (Guyon et al., <xref ref-type="bibr" rid="B47">2008</xref>). In the present study, feature extraction was performed in two phases. First, common statistical features were extracted from the signal, followed by the extraction of advanced wavelet-based features. <xref ref-type="fig" rid="F3">Figure 3</xref> provides an overview of the feature extraction process and is explained below.</p>
<fig id="F3" position="float">
<label>Figure 3</label>
<caption><p>Feature Extraction. During this process, mathematical operations are performed on the data to extract features. This step is crucial for discovering features indicative of functional deficits in the eye. ERG test on each eye leads to nine signals, as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>. Two sets of features (Standard features and advanced features) are extracted from each of the nine signals. The standard set of features include common statistical features such as mean, quartiles, and entropies. In contrast, the advanced set of features include sophisticated features such as autoregressive coefficients, Shannon entropy, and wavelet features.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0003.tif"/>
</fig>
<sec>
<title>2.6.1. Statistical Feature Extraction</title>
<p>A total of 17 Statistical features capable of describing the general behavior of ERG signals were extracted from the signal. These features were grouped as follows.</p>
<list list-type="order">
<list-item><p>Measures of Central Tendency</p></list-item>
<list-item><p>Measures of Spread</p></list-item>
<list-item><p>Measures of Shape</p></list-item>
<list-item><p>Measures of Peaks</p></list-item>
<list-item><p>Measures of Derivatives</p></list-item>
<list-item><p>Measures of Correlation</p></list-item>
</list>
<p>Measures of central tendency included mean, median, trimmed mean. Measures of spread included range, standard deviation, variance, mean absolute deviation, and interquartile range. Measures of the shape include skewness, kurtosis, central moments of the second and third-order, and aspect ratio. Measures of peaks included the number of peaks and troughs in the signal. Measures of derivatives include the first-order derivative of the signal with respect to time. Measures of correlation included the correlation coefficient of the signal with respect to time. The equations for the computation of these quantities can be found in Asgharzadeh-Bonab et al. (<xref ref-type="bibr" rid="B10">2020</xref>); Yapici et al. (<xref ref-type="bibr" rid="B125">2021</xref>).</p>
</sec>
<sec>
<title>2.6.2. Advanced Feature Extraction</title>
<p>Advanced features capable of capturing subtle changes were extracted from the signal. Each signal was split into 32 blocks (&#x0007E; 2000 samples/block) to further capture subtle changes in the signal (Martis et al., <xref ref-type="bibr" rid="B86">2014</xref>). Daubechies least-asymmetric wavelet with four vanishing moments (Symlets 4) was used as mother wavelet to derive the wavelet coefficients (Daubechies, <xref ref-type="bibr" rid="B27">1992</xref>). The following features (190 features in total as shown in <xref ref-type="fig" rid="F3">Figure 3</xref>) were extracted from each block of the signal:</p>
<p><bold>AR coefficients:</bold> The signal <italic>x</italic>[<italic>n</italic>] at time instant n in an AR process of order p can be described as a linear combination of <italic>p</italic> earlier values of the same signal. The procedure is modeled as follows:</p>
<disp-formula id="E1"><label>(1)</label><mml:math id="M1"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mi>x</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:munderover accentunder="false" accent="false"><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:munderover></mml:mstyle><mml:mi>a</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>&#x0002B;</mml:mo><mml:mi>e</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>a</italic>[<italic>i</italic>] is the AR model&#x00027;s <italic>i</italic><sup><italic>th</italic></sup> coefficient, <italic>e</italic>[<italic>n</italic>] denotes white noise with mean zero, and <italic>p</italic> denotes the AR order. The AR coefficients for each block were estimated using the Burg method (Zhao and Zhang, <xref ref-type="bibr" rid="B130">2005</xref>); the order was determined using the ARfit model order selection method (Neumaier and Schneider, <xref ref-type="bibr" rid="B95">2001</xref>) as 4th order. Therefore a 4-order AR model is chosen to represent each of the ERG signal components.</p>
<p><bold>Wavelet based Shannon Entropy:</bold> The Shannon entropy is an information-theoretic measure of a signal. Shannon entropy (denoted as SE) values for the maximal overlap discrete wavelet packet transform (MOD- PWT) using four-level wavelet decomposition was computed on the terminal nodes of the wavelet (Li and Zhou, <xref ref-type="bibr" rid="B79">2016</xref>). Mathematical expression for Shannon entropy using wavelet packet transform is as follows:</p>
<disp-formula id="E2"><label>(2)</label><mml:math id="M2"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mi>S</mml:mi><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:munderover accentunder="false" accent="false"><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover></mml:mstyle><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>*</mml:mo><mml:mo class="qopname">log</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>N</italic> is the number of coefficients in the <italic>j</italic><sup><italic>th</italic></sup> node and <italic>p</italic><sub><italic>j,k</italic></sub> are the normalized squares of the wavelet packet coefficients in the <italic>j</italic><sup><italic>th</italic></sup> terminal node of the wavelet.</p>
<p><bold>Multifractal wavelet leader estimates and multiscale wavelet variance estimates:</bold> The multifractal measure of the ERG signal was obtained using two wavelet methods (wavelet leader and cumulant of the scaling exponents). Wavelet leaders are time/space-localized suprema of the discrete wavelet coefficients&#x00027; absolute value. These suprema are used to calculate the Holder exponents, which characterize the local regularity. In addition, second cumulant of the scaling exponents were obtained. Scaling exponents are scale-dependent exponents that describe the signal&#x00027;s power-law behavior at various resolutions. The second cumulant basically depicts the scaling exponents&#x00027; divergence from linearity (Leonarduzzi et al., <xref ref-type="bibr" rid="B76">2010</xref>). Wavelet variance of ERG signals were also obtained as features. Wavelet variance quantifies the degree of variability in a signal by scale, or more precisely, the degree of variability in a signal between octave-band frequency intervals (Maharaj and Alonso, <xref ref-type="bibr" rid="B83">2014</xref>).</p>
</sec>
</sec>
<sec>
<title>2.7. Feature Selection</title>
<p>Feature extraction discussed previously was performed in order to reduce the dimensionality of the signals; however, the resulting number of features was still higher than the number of training data. Therefore, further reduction in the dimensionality of the data was performed using the feature selection method to identify relevant features for classification and regression. It should be noted that feature selection was necessary to reduce the computational cost of modeling, prevent the generation of a complex and over-fitted model with high generalization error, and generate a high-performance model that is simple and easy to understand (Saeys et al., <xref ref-type="bibr" rid="B103">2007</xref>). In particular, the Minimum Redundancy Maximum Relevance (MRMR) sequential feature selection algorithm was used in the present study because this algorithm is specifically designed to drop redundant features [see (Darbellay and Vajda, <xref ref-type="bibr" rid="B26">1999</xref>; Ding and Peng, <xref ref-type="bibr" rid="B32">2005</xref>) for mathematical details/formulations], which was required to design a compact and efficient machine-learning-based model (Zhao et al., <xref ref-type="bibr" rid="B131">2019</xref>). It is worth noting that other available dimensionality reduction techniques such as Principal component analysis (PCA) were not considered in this study as such techniques do not allow for direct tracing and understanding the relevance of each feature (Aha and Bankert, <xref ref-type="bibr" rid="B2">1996</xref>).</p>
</sec>
<sec>
<title>2.8. Predictive Model Development</title>
<p>ML models are mathematical algorithms that provide predictions based on an inference derived from the generalizable predictive patterns of the training data (Bzdok et al., <xref ref-type="bibr" rid="B19">2018</xref>). Several machine learning models were employed and evaluated in order to identify the best one to classify the ERG signals. These included decision trees, discriminant, support vector machine, nearest neighbor, and ensemble classifiers. Most of these models can perform both classification and regression. Decision tree-based models predict the target variable by learning simple decision rules (Navada et al., <xref ref-type="bibr" rid="B93">2011</xref>). Discriminant classifiers are based on the assumption that each class has different Gaussian distributions of data, and the classification is performed based on Gaussian distribution parameters estimated by the fitting function (Cawley and Talbot, <xref ref-type="bibr" rid="B20">2003</xref>). Support vector machine (SVM) is based on Vapnik&#x02013;Chervonenkis theory, where a hyperplane separating the classes is determined. SVMs are efficient algorithms suitable for compact datasets (Noble, <xref ref-type="bibr" rid="B96">2006</xref>). The nearest neighbor algorithm is based on the assumption that similar things exist nearby. It is a simple yet versatile model with high computational cost (Zhang and Zhou, <xref ref-type="bibr" rid="B128">2007</xref>). Ensemble methods such as bagged trees (or random forest) combine the predictions of several learning algorithms with improving generalization. Although these methods are also computationally expensive, they are unlikely to over-fit (Dietterich, <xref ref-type="bibr" rid="B31">2000</xref>). Regression analysis based on the above techniques was also performed alongside classification.</p>
</sec>
<sec>
<title>2.9. Performance Evaluation</title>
<p>Various performance evaluation metrics were utilized to compare different machine learning algorithms. The metrics used in this study include accuracy, sensitivity, specificity, precision, recall, f-score, root mean squared error, and their corresponding mathematical formulations are given below.</p>
<p>The abbreviations used in the following expressions include True Positive (TP) which are the cases the model correctly predicted the positive (glaucomatous) class. True Negative (TN) are the cases the model correctly predicted the negative (non-glaucomatous) class. False Positive (FP) are the cases the model incorrectly predicted the positive (glaucomatous) class. False Negative (FN) are the cases the model incorrectly predicted the negative (non-glaucomatous) class.</p>
<sec>
<title>2.9.1. Accuracy</title>
<p>Accuracy is the percentage of correctly classified observations, as shown below.</p>
<disp-formula id="E3"><label>(3)</label><mml:math id="M3"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mtext class="textrm" mathvariant="normal">Accuracy</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>%</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mtext>TP&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mtext>&#x000A0;FP</mml:mtext></mml:mrow><mml:mrow><mml:mtext>TP&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mtext>&#x000A0;TN&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mtext>&#x000A0;FP&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mtext>&#x000A0;FN</mml:mtext></mml:mrow></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
</sec>
<sec>
<title>2.9.2. Sensitivity</title>
<p>Sensitivity/Recall estimates the proportion of actual positives (e.g., actual glaucomatous) was identified correctly.</p>
<disp-formula id="E4"><label>(4)</label><mml:math id="M4"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mtext>Sensitivity</mml:mtext><mml:mo>/</mml:mo><mml:mtext>Recall&#x000A0;</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mtext>RE</mml:mtext></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mtext>TP</mml:mtext></mml:mrow><mml:mrow><mml:mtext>TP&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mtext>&#x000A0;FN</mml:mtext></mml:mrow></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
</sec>
<sec>
<title>2.9.3. Specificity</title>
<p>Recall estimates the model&#x00027;s ability to correctly reject healthy patients without a Glaucoma.</p>
</sec>
<sec>
<title>2.9.4. Precision</title>
<p>Precision estimates the proportion of positive predictions (e.g., glaucomatous predictions) that was actually correct.</p>
<disp-formula id="E5"><label>(5)</label><mml:math id="M5"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mtext>Precision&#x000A0;</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mtext>PR</mml:mtext></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mtext>TP</mml:mtext></mml:mrow><mml:mrow><mml:mtext>TP&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mtext>&#x000A0;FP</mml:mtext></mml:mrow></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
</sec>
<sec>
<title>2.9.5. F-Score</title>
<p>The F-Score estimates the harmonic mean of the precision and recall.</p>
<disp-formula id="E6"><label>(6)</label><mml:math id="M6"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mtext>F-&#x000A0;Score</mml:mtext><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mtext>PR&#x000A0;</mml:mtext><mml:mo>&#x000D7;</mml:mo><mml:mtext>&#x000A0;RE</mml:mtext></mml:mrow><mml:mrow><mml:mtext>PR&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mtext>&#x000A0;RE</mml:mtext></mml:mrow></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
</sec>
<sec>
<title>2.9.6. Root Mean Square Error (RMSE)</title>
<p>The Root Mean Square Error (RMSE) was used as the performance evaluation metric for regression analysis. RSME is the standard deviation of the prediction errors (residuals).</p>
<disp-formula id="E7"><label>(7)</label><mml:math id="M7"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mtext>RMSE</mml:mtext><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mfrac><mml:mrow><mml:mstyle displaystyle="true"><mml:msubsup><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msubsup></mml:mstyle><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mstyle class="mbox"><mml:mtext>Actual&#x000A0;</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mstyle class="mbox"><mml:mtext>Predicted&#x000A0;</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:msqrt></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>Where <italic>N</italic> is the number of observations.</p>
</sec>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>3. Results</title>
<p>A machine learning-based approach was developed and trained using the balanced ERG data previously published by Grillo et al. (<xref ref-type="bibr" rid="B46">2018</xref>). Although a compact dataset of 60 observations and 540 signals was used in this study, the current framework was able to consistently detect features (<xref ref-type="fig" rid="F6">Figures 6</xref>, <xref ref-type="fig" rid="F9">9</xref>) that are known to be medically relevant such as OP, STR, Flicker reported in various studies (Tyler, <xref ref-type="bibr" rid="B118">1981</xref>; Saszik et al., <xref ref-type="bibr" rid="B105">2002</xref>; de Lara et al., <xref ref-type="bibr" rid="B29">2014</xref>, <xref ref-type="bibr" rid="B28">2015</xref>; Porciatti, <xref ref-type="bibr" rid="B100">2015</xref>; Grillo et al., <xref ref-type="bibr" rid="B46">2018</xref>). In particular, studies conducted by Wilsey and Fortune (<xref ref-type="bibr" rid="B123">2016</xref>); Hermas (<xref ref-type="bibr" rid="B52">2019</xref>); Beykin et al. (<xref ref-type="bibr" rid="B13">2021</xref>) investigating the variability of PhNR in glaucomatous and healthy subjects in PERG and fERG have found that PhNR to be an important biomarkers for detection of glaucoma. It is worth noting that in fERG analysis (ERG protocol for this study), pSTR, nSTR, PhNR are extracted from STR.</p>
<p>Therefore, we were able to demonstrate that the proposed framework for early-stage glaucoma diagnosis can be reproducibly evaluated and validated even on such a compact database. Furthermore, we would like to note that there are other investigations that successfully applied ML-based method in different fields, including biomedical (Seo et al., <xref ref-type="bibr" rid="B107">2020</xref>) and material science (Zhang and Ling, <xref ref-type="bibr" rid="B129">2018</xref>) using compact datasets. The procedure employed for the development of the predictive modeling framework is summarized below.</p>
<list list-type="bullet">
<list-item><p><bold>Data Split:</bold> Hold out (80% training, k-fold cross-validation, 20% testing).</p></list-item>
<list-item><p><bold>Dimensionality reduction:</bold> Feature Extraction.</p></list-item>
<list-item><p><bold>Feature selection:</bold> MRMR.</p></list-item>
<list-item><p><bold>Hyper-parameter tuning:</bold> k-fold cross-validation (<italic>k</italic> = 10).</p></list-item>
<list-item><p><bold>Model Evaluation:</bold> Performance metrics evaluated on the unseen testing set.</p></list-item>
</list>
<p>The dataset was divided into two parts; 80% of the data was used for training and validation, and the remaining 20% was set aside for testing. The hold-out testing strategy ensured that the test data was never a part of the training process (Yadav and Shukla, <xref ref-type="bibr" rid="B124">2016</xref>). Dimensionality reduction was performed using feature extraction and feature selection. MRMR feature selection algorithm was used to identify the important predictors. K-fold (<italic>K</italic> = 10) cross-validation was used for training and hyper-parameter tuning (Duan et al., <xref ref-type="bibr" rid="B34">2003</xref>). The cross-validation technique significantly reduces bias when working with small datasets (Varma and Simon, <xref ref-type="bibr" rid="B119">2006</xref>). The loss function was the objective minimization function for both classification regressions during hyper-parameter optimization. The hyper-parameters associated with corresponding ML algorithms (Feurer and Hutter, <xref ref-type="bibr" rid="B36">2019</xref>), as shown in <xref ref-type="table" rid="T1">Table 1</xref>, were optimized through nested cross-validation. Next, the trained model with optimized hyper-parameters was evaluated using test data that was not a part of training. To further ensure that the machine learning models compared in this investigation were not over-fitted, given the compact dataset used in the present study, the behavior of training and testing error vs. training cycles was monitored. Different techniques, including Tree, Discriminant, SVM, Naive Bayes, Tree Ensemble, and KNN, were applied, and their performances were assessed. The performance of each technique was assessed based on the accuracy (discussed in section 2.9) is tabulated in <xref ref-type="table" rid="T2">Table 2</xref>. Considering binary and multiclass classifications, it can be seen that the Ensemble-based technique (bagged tree) was consistently outperforming other techniques. Additionally, other performance metrics for ensemble bagged trees (discussed in section 2.9) are summarized in <xref ref-type="table" rid="T3">Table 3</xref>.</p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>Hyperparameters tested/optimized.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Method</bold></th>
<th valign="top" align="left"><bold>Hyperparameter search range</bold></th>
<th valign="top" align="left"><bold>Optimized hyperparameters</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Ensemble</td>
<td valign="top" align="left"><bold>Ensemble method:</bold> Bag, GentleBoost,<break/> LogitBoost, AdaBoost, RUSBoost<break/> <bold>Number of learners:</bold> 10&#x02013;500<break/> <bold>Learning rate:</bold> 0.001-1<break/> <bold>Maximum number of splits:</bold> 1&#x02013;47<break/> <bold>Number of predictors to sample:</bold> 1&#x02013;5</td>
<td valign="top" align="left"><bold>Ensemble method:</bold> Bag<break/> <bold>Maximum number of splits:</bold> 1<break/> <bold>Number of learners:</bold> 52<break/> <bold>Number of predictors-</bold><break/> <bold>to sample:</bold> 1</td>
</tr>
<tr>
<td valign="top" align="left">Knn</td>
<td valign="top" align="left"><bold>Number of neighbors:</bold> 1-24<break/> <bold>Distance metric:</bold> City block, Chebyshev,<break/> Correlation, Cosine, Euclidean, Hamming,<break/> Jaccard, Mahalanobis, Minkowski (cubic),<break/> Spearman<break/> <bold>Distance weight:</bold> Equal, Inverse,<break/> Squared inverse<break/> <bold>Standardize data:</bold> true, false</td>
<td valign="top" align="left"><bold>Number of neighbors:</bold> 24<break/> <bold>Distance metric:</bold> Correlation<break/> <bold>Distance weight:</bold> Inverse<break/> <bold>Standardize data:</bold> true</td>
</tr>
<tr>
<td valign="top" align="left">NaiveBayes</td>
<td valign="top" align="left"><bold>Distribution names:</bold> Gaussian,<break/> Kernel<break/> <bold>Kernel type:</bold> Gaussian, Box,<break/> Epanechnikov, Triangle</td>
<td valign="top" align="left"><bold>Distribution names:</bold> Gaussian<break/> <bold>Kernel type:</bold> Epanechnikov</td>
</tr>
<tr>
<td valign="top" align="left">Discriminant</td>
<td valign="top" align="left"><bold>Discriminant type:</bold> Linear, Quadratic,<break/> Diagonal Linear, Diagonal Quadratic</td>
<td valign="top" align="left"><bold>Discriminant type:</bold><break/> Diagonal Linear</td>
</tr>
<tr>
<td valign="top" align="left">SVM</td>
<td valign="top" align="left"><bold>Multiclass method:</bold><break/> One-vs-All, One-vs.-One<break/> <bold>Box constraint level:</bold> 0.001-1000<break/> <bold>Kernel scale:</bold> 0.001&#x02013;1000<break/> <bold>Kernel function:</bold> Gaussian, Linear,<break/> Quadratic,<break/> <bold>Cubic Standardize data:</bold> true, false</td>
<td valign="top" align="left"><bold>Kernel function:</bold> Linear<break/> <bold>Box constraint level:</bold> 2.4185<break/> <bold>Multiclass method:</bold> One-vs.-All<break/> <bold>Standardize data:</bold> false</td>
</tr>
<tr>
<td valign="top" align="left">Tree</td>
<td valign="top" align="left"><bold>Maximum number of splits:</bold> 1&#x02013;47<break/> <bold>Split criterion:</bold> Gini&#x00027;s diversity index,<break/> Maximum deviance reduction</td>
<td valign="top" align="left"><bold>Maximum number of splits:</bold> 5<break/> <bold>Split criterion:</bold><break/> Maximum deviance reduction</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap position="float" id="T2">
<label>Table 2</label>
<caption><p>Testing accuracy obtained using various machine learning techniques.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th/>
<th/>
<th valign="top" align="center"><bold>Tree</bold></th>
<th valign="top" align="center"><bold>Discriminant</bold></th>
<th valign="top" align="center"><bold>SVM</bold></th>
<th valign="top" align="center"><bold>Naive Bayes</bold></th>
<th valign="top" align="center"><bold>Ensemble (Bagged)</bold></th>
<th valign="top" align="center"><bold>KNN</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left"><bold>Binary</bold></td>
<td valign="top" align="center"><bold>Statistical</bold></td>
<td valign="top" align="center">75</td>
<td valign="top" align="center">80</td>
<td valign="top" align="center"><bold>83.33</bold></td>
<td valign="top" align="center">80</td>
<td valign="top" align="center"><bold>83.33</bold></td>
<td valign="top" align="center">66.70</td>
</tr>
<tr>
<td/>
<td valign="top" align="center"><bold>Wavelet</bold></td>
<td valign="top" align="center">83.33</td>
<td valign="top" align="center">83.33</td>
<td valign="top" align="center"><bold>91.70</bold></td>
<td valign="top" align="center">83.33</td>
<td valign="top" align="center"><bold>91.70</bold></td>
<td valign="top" align="center">75</td>
</tr>
<tr>
<td valign="top" align="left"><bold>Multiclass</bold></td>
<td valign="top" align="center"><bold>Statistical</bold></td>
<td valign="top" align="center">33.33</td>
<td valign="top" align="center">41.70</td>
<td valign="top" align="center">50</td>
<td valign="top" align="center">16.70</td>
<td valign="top" align="center"><bold>53.33</bold></td>
<td valign="top" align="center">33.33</td>
</tr>
<tr>
<td/>
<td valign="top" align="center"><bold>Wavelet</bold></td>
<td valign="top" align="center">41.70</td>
<td valign="top" align="center">50</td>
<td valign="top" align="center">64.66</td>
<td valign="top" align="center">33.33</td>
<td valign="top" align="center"><bold>80</bold></td>
<td valign="top" align="center">50</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p><italic>Values in bold font indicate the accuracies of best-performing classifier</italic>.</p>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="T3">
<label>Table 3</label>
<caption><p>Performance metrics for ensemble classifier.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th/>
<th/>
<th valign="top" align="center"><bold>Accuracy</bold></th>
<th valign="top" align="center"><bold>F-measure</bold></th>
<th valign="top" align="center"><bold>Precision</bold></th>
<th valign="top" align="center"><bold>Sensitivity</bold></th>
<th valign="top" align="center"><bold>Specificity</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left"><bold>Binary</bold></td>
<td valign="top" align="center"><bold>Statistical</bold></td>
<td valign="top" align="center">80</td>
<td valign="top" align="center">80</td>
<td valign="top" align="center">80.36</td>
<td valign="top" align="center">80.36</td>
<td valign="top" align="center">80.36</td>
</tr>
<tr>
<td/>
<td valign="top" align="center"><bold>Wavelet</bold></td>
<td valign="top" align="center">91.67</td>
<td valign="top" align="center">91.61</td>
<td valign="top" align="center">92.86</td>
<td valign="top" align="center">91.67</td>
<td valign="top" align="center">91.67</td>
</tr>
<tr>
<td valign="top" align="left"><bold>Multi-class</bold></td>
<td valign="top" align="center"><bold>Statistical</bold></td>
<td valign="top" align="center">53.33</td>
<td valign="top" align="center">50.74</td>
<td valign="top" align="center">53.18</td>
<td valign="top" align="center">51.67</td>
<td valign="top" align="center">75.48</td>
</tr>
<tr>
<td/>
<td valign="top" align="center"><bold>Wavelet</bold></td>
<td valign="top" align="center">80</td>
<td valign="top" align="center">79.63</td>
<td valign="top" align="center">83.81</td>
<td valign="top" align="center">83.333</td>
<td valign="top" align="center">90.30</td>
</tr>
</tbody>
</table>
</table-wrap>
<sec>
<title>3.1. Binary Classification</title>
<p>For binary classification (classifying animals with/without glaucoma) based on statistical features, the correlation of cones, mean of flicker, median, and skewness of Hi Rods and cones, and standard deviation of cones were identified as important among the statistical features as shown in <xref ref-type="fig" rid="F4">Figure 4</xref>. Moreover, the box plot demonstrates variations of each feature for each class (with/without glaucoma), respectively. Several models, including SVM and ensemble-based classifiers were used for training, and their performances were assessed. It turned out that the SVM and ensemble bagged tree provide the best performance with a testing accuracy of 83.33%, as shown in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<fig id="F4" position="float">
<label>Figure 4</label>
<caption><p>Boxplot of statistical features selected by Minimum Redundancy and Maximum Relevance (MRMR) feature selection algorithm for binary classification (Std D, Standard Deviation). On each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the &#x0201C;&#x0002B;&#x0201D; marker symbol.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0004.tif"/>
</fig>
<p>Next, the binary classification was performed using wavelet-based features. Among the extracted wavelet features, Shannon Entropy Values for Maximal Overlap Discrete Wavelet Packet Transform (MOD-PWT) were identified as important features from Rods and cones, Rods, STR, and OP, as shown in <xref ref-type="fig" rid="F5">Figure 5</xref>. The utilization of the selected advanced features improved the accuracy to 91.70% by the ensemble bagged tree algorithm.</p>
<fig id="F5" position="float">
<label>Figure 5</label>
<caption><p>Box plot of wavelet-based features selected by Minimum Redundancy and Maximum Relevance (MRMR) feature selection algorithm for binary classification (W-SE, Wavelet based Shannon Entropy; AR-COEF, Autoregressive Coefficient). On each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the &#x0201C;&#x0002B;&#x0201D; marker symbol.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0005.tif"/>
</fig>
<p>It should be noted that the MRMR method selects features based on statistical relevance while dropping redundant features and thus, is computationally efficient (Darbellay and Vajda, <xref ref-type="bibr" rid="B26">1999</xref>; Ding and Peng, <xref ref-type="bibr" rid="B32">2005</xref>). <xref ref-type="fig" rid="F6">Figure 6</xref> demonstrates this for binary classification. It can be observed that correlation feature from cones, Moment of order three and trimmed mean feature from Oscillatory Potentials (OP) and Range and aspect ratio from Scotopic Threshold Response (STR) are highly correlated; Therefore, only the feature cones correlation was picked by the MRMR algorithm as inclusion of the other three did not increase/decrease the models predictability.</p>
<fig id="F6" position="float">
<label>Figure 6</label>
<caption><p>Boxplot of statistically important features for binary classification. The important features capable of distinguishing healthy and glaucomatous are correlated feature from Cones, third order Moment and trimmed mean feature from Oscillatory Potentials (OP) and Range and aspect ratio from Scotopic Threshold Response (STR). However, the high similarity between these features quantified by the correlation scores in the scatter plot create redundancy (inclusion cones(correlation) feature alone vs inclusion all five features does not improve accuracy). Therefore, utilizing the cones correlation feature alone captures the behavior of the other four features. This dropping of redundant features and choosing Cones (correlation) feature alone is achieved by using Minimum Redundancy and Maximum Relevance (MRMR) algorithm (On each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the &#x0201C;&#x0002B;&#x0201D; marker symbol.).</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0006.tif"/>
</fig>
<p><xref ref-type="fig" rid="F7">Figure 7</xref> compares the predictive importance scores obtained based on the statistical and wavelet-based features. Predictive importance scores describe the predictive capability of selected features (Kuhn and Johnson, <xref ref-type="bibr" rid="B67">2013</xref>). It can be observed that wavelet-based features can distinguish healthy and glaucomatous animals suggesting that they are more sensitive to subtle changes in ERG signals due to glaucoma. It should be noted that the feature selection algorithm MRMR (Maximum Relevance and Minimum Redundancy) ignores highly correlated features for model simplicity. Therefore, only uncorrelated sets of features that improved predictability across the animals were chosen, i.e., for a set of correlated features, one representing the correlated set gets picked by the algorithm. <xref ref-type="fig" rid="F6">Figure 6</xref> demonstrates the list of important but highly correlated features that were dropped. The scatter plot inside the <xref ref-type="fig" rid="F6">Figure 6</xref> shows the correlation coefficients confirming the high degree of the correlation between them.</p>
<fig id="F7" position="float">
<label>Figure 7</label>
<caption><p>Comparison of predictive importance scores for binary classification using <bold>(A)</bold> statistical features and <bold>(B)</bold> wavelet-based features. This bar chart illustrates the superior predictive capability of wavelet-based features. Std D, Standard Deviation; W-SE, Wavelet based Shannon entropy; AR-COEF, Autoregressive coefficient.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0007.tif"/>
</fig>
</sec>
<sec>
<title>3.2. Multiclass Classification</title>
<p>For multiclass classification (classifying animals to different stages, normal, high, and glaucomatous as mentioned in section 2.4) based on statistical features, the correlation of cones, number of troughs in Hi cones, kurtosis of STR and mean of flicker were identified as important among the statistical features as shown in <xref ref-type="fig" rid="F8">Figure 8</xref>. Several models, including SVM and ensemble-based classifiers, were used for training, and their performances were assessed. It turned out that the ensemble-based classifiers, specifically the bagged trees model, provided the best performance with a testing accuracy of 53.33%, as shown in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<fig id="F8" position="float">
<label>Figure 8</label>
<caption><p>Boxplot of statistical features selected by Minimum Redundancy and Maximum Relevance (MRMR) feature selection algorithm for multiclass classification. STR, Scotopic Threshold Response. On each box, the central mark corresponds to the median, and the bottom and top edges of the box correspond to the 25th and 75th percentiles, respectively. The dashed lines (whiskers) extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the &#x0201C;&#x0002B;&#x0201D; marker symbol.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0008.tif"/>
</fig>
<p>Next, the multiclass classification was performed using wavelet-based features. Among the extracted wavelet features, Wavelet variance of rods and Shannon Entropy Values and AR coefficients for Maximal Overlap Discrete Wavelet Packet Transform (MOD-PWT) were identified as important features from Hi-Flicker, Flicker, Hi-cones, and STR as shown in <xref ref-type="fig" rid="F9">Figure 9</xref>. The identification of flicker as an important distinguishing feature in diagnosing early-stage glaucoma was consistent with previous studies (Tyler, <xref ref-type="bibr" rid="B118">1981</xref>; Lachenmayr and Drance, <xref ref-type="bibr" rid="B68">1992</xref>; Horn et al., <xref ref-type="bibr" rid="B58">1997</xref>; Yoshiyama and Johnson, <xref ref-type="bibr" rid="B126">1997</xref>). In fact, flicker measurements in eyes with early-stage glaucoma exhibited a loss in sensitivity around 30&#x02013;40 Hz (Tyler, <xref ref-type="bibr" rid="B118">1981</xref>). It is worth noting that the flicker measurements used in this study were recorded using flashes at 30 Hz. The identification of the flicker ERG test and the corresponding features, among other tests, reconfirmed the capability of the current approach in identifying the relevant features. Training the ensemble bagged trees model, utilizing the selected advanced features, improved the multiclass classification accuracy to 80%, as shown in <xref ref-type="table" rid="T2">Table 2</xref>. This improvement in accuracy indicated that wavelet-based features can distinguish healthy and glaucomatous animals suggesting that they are more sensitive to subtle changes in ERG signals due to glaucoma. The multiclass classification ability of this framework reaffirmed the rich and complex nature of ERG signals in assessing the disease progression.</p>
<fig id="F9" position="float">
<label>Figure 9</label>
<caption><p>Boxplot of wavelet-based features selected by Minimum Redundancy and Maximum Relevance (MRMR) feature selection algorithm for multiclass classification. STR, Scotopic Threshold Response; W-SE, Wavelet based Shannon Entropy; AR-COEF, Autoregressive Coefficient. On each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the &#x0201C;&#x0002B;&#x0201D; marker symbol.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0009.tif"/>
</fig>
</sec>
<sec>
<title>3.3. RGC Regression</title>
<p>Regression analysis was performed to predict retinal ganglion cell count from ERG signals. Feature selection for regression was performed using MRMR sequential feature selection. RGC values of the animals ranged between 8 and 120. RSME for RGC regression was 15.64 and 11.20 for models trained with statistical features and wavelet-based features, respectively. Regression results using wavelet-based features are shown in <xref ref-type="fig" rid="F10">Figure 10</xref>. The results in Grillo et al. (<xref ref-type="bibr" rid="B46">2018</xref>) indicate that RGC counts had a strong correlation with STR and OPs. The dominant features selected for RGC regression (from STR and OP) were in agreement with the findings in Grillo et al. (<xref ref-type="bibr" rid="B46">2018</xref>). <xref ref-type="table" rid="T4">Table 4</xref> compares performance of various ML based regression models in predicting retinal ganglion cells (RGCs) counts: The higher error (RSME) with statistical features compared with the wavelet-based advanced features emphasized the need for sophisticated features to predict RGC count accurately. SVM- and GPR-based models provided the most accurate prediction of RGC numbers from ERG signals. Specifically, squared exponential and rational quadratic models of GPR provided the least error.</p>
<fig id="F10" position="float">
<label>Figure 10</label>
<caption><p>RGC count regression plot. This plot contains the ground truth and predicted response of RGC count predicted using Gaussian Process Regression (GPR). The squared exponential GPR model was trained using both standard and advanced features. The RGC count of the animals ranged between 8 and 120, and the root mean squared error in the prediction of RGC was 11.2. The line in this plot denotes when the predicted values are equal to ground truth values.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fnins-16-869137-g0010.tif"/>
</fig>
<table-wrap position="float" id="T4">
<label>Table 4</label>
<caption><p>Performance metrics for retinal ganglion cells (RGCs) Regression.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Machine learning algorithm</bold></th>
<th valign="top" align="center" colspan="2" style="border-bottom: thin solid #000000;"><bold>RSME</bold></th>
</tr>
<tr>
<th/>
<th valign="top" align="center"><bold>Statistical</bold></th>
<th valign="top" align="center"><bold>Wavelet</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Tree</td>
<td valign="top" align="center">31.716</td>
<td valign="top" align="center">17.852</td>
</tr>
<tr>
<td valign="top" align="left">SVM</td>
<td valign="top" align="center">17.177</td>
<td valign="top" align="center">13.82</td>
</tr>
<tr>
<td valign="top" align="left">Ensemble (Bagged)</td>
<td valign="top" align="center">29.129</td>
<td valign="top" align="center">24.387</td>
</tr>
<tr>
<td valign="top" align="left">Logistic regression</td>
<td valign="top" align="center">44.622</td>
<td valign="top" align="center">24.873</td>
</tr>
<tr>
<td valign="top" align="left"><bold>Gaussian process regression</bold></td>
<td valign="top" align="center"><bold>15.644</bold></td>
<td valign="top" align="center"><bold>11.201</bold></td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p><italic>Bold font indicate the best performing regression model and its corresponding RSME</italic>.</p>
</table-wrap-foot>
</table-wrap>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>4. Discussion</title>
<p>Our goal was to determine the feasibility of applying ML-based methods to the analysis of ERG signals for glaucoma detection at different stages of the disease. In the present study, we systematically applied machine-learning-based methods for the first time to detect glaucoma and predict RGC loss based on ERG signals. The present study utilized ERGs measured in mice rather than from human patients, because the use of data from a preclinical model allowed us to validate &#x0201C;ground truth&#x0201D; data sets with a range of complimentary and alternative experimental strategies, which is not possible in human clinical studies. These include histology, biochemical, and immunochemical assays, as well as optomotor reflex measurements. We were able to determine for the first time that advanced features (wavelet-based features) are capable of detecting subtle changes in the ERG signal and perform multiclass classification based on the progression level of the disease with 80% accuracy. In particular, we found that Shannon Entropy Values for Maximal Overlap Discrete Wavelet Packet Transform (MOD-PWT) and AR coefficients represent important features capable of detecting early-stage glaucoma. Among the nine available ERG signals, Flicker, STR, OP, and Rod-Cone appear integral for such successful detection. This is in agreement with the results published in Lei et al. (<xref ref-type="bibr" rid="B75">2006</xref>). However, given that these features are highly correlated, the ML-based algorithm picks only one for each set of highly correlated features to reduce the model complexity as shown in <xref ref-type="fig" rid="F6">Figure 6</xref>.</p>
<p>In addition, the method proposed here performs ERG analysis in a wavelet domain instead of a frequency domain, which allows to capture subtle changes in the signals. In addition, various intricate features such as multiscale wavelet variance estimates, Shannon entropy, and autoregressive coefficients are incorporated in the method, compared to basic features such as differences in amplitude and latency in previous studies (Hood et al., <xref ref-type="bibr" rid="B56">2000</xref>; Fortune et al., <xref ref-type="bibr" rid="B39">2002</xref>; Thienprasiddhi et al., <xref ref-type="bibr" rid="B114">2003</xref>; Stiefelmeyer et al., <xref ref-type="bibr" rid="B111">2004</xref>; Ventura and Porciatti, <xref ref-type="bibr" rid="B120">2006</xref>; Chu et al., <xref ref-type="bibr" rid="B21">2007</xref>; Miguel-Jim&#x000E9;nez et al., <xref ref-type="bibr" rid="B89">2010</xref>; Luo et al., <xref ref-type="bibr" rid="B82">2011</xref>; Palmowski-Wolfe et al., <xref ref-type="bibr" rid="B99">2011</xref>; Todorova and Palmowski-Wolfe, <xref ref-type="bibr" rid="B115">2011</xref>; Ho et al., <xref ref-type="bibr" rid="B53">2012</xref>; Hori et al., <xref ref-type="bibr" rid="B57">2012</xref>; Ledolter et al., <xref ref-type="bibr" rid="B71">2013</xref>; Consejo et al., <xref ref-type="bibr" rid="B22">2019</xref>). The results strongly suggest that such advanced features in the wavelet domain are necessary for detection of early-stage glaucoma. Moreover, in contrast to the recent study that leverages ML-based technique to analyze ERG using solely the photopic negative response (PhNR) component (Armstrong and Lorch, <xref ref-type="bibr" rid="B7">2020</xref>), the current method uses all ERG components in the analysis to fully utilize the capability of the ML-based technique to crunch large data sets and draw complicated relationships. Therefore, the proposed framework is not limited to a small subset of genetic eye diseases like previous studies (Fortune et al., <xref ref-type="bibr" rid="B39">2002</xref>; Thienprasiddhi et al., <xref ref-type="bibr" rid="B114">2003</xref>; Stiefelmeyer et al., <xref ref-type="bibr" rid="B111">2004</xref>; Chu et al., <xref ref-type="bibr" rid="B21">2007</xref>; Miguel-Jim&#x000E9;nez et al., <xref ref-type="bibr" rid="B89">2010</xref>; Luo et al., <xref ref-type="bibr" rid="B82">2011</xref>; Palmowski-Wolfe et al., <xref ref-type="bibr" rid="B99">2011</xref>; Todorova and Palmowski-Wolfe, <xref ref-type="bibr" rid="B115">2011</xref>; Ho et al., <xref ref-type="bibr" rid="B53">2012</xref>; Hori et al., <xref ref-type="bibr" rid="B57">2012</xref>; Ledolter et al., <xref ref-type="bibr" rid="B71">2013</xref>; Consejo et al., <xref ref-type="bibr" rid="B22">2019</xref>); instead, it is capable of mapping ERG signals to various eye diseases.</p>
</sec>
<sec sec-type="conclusions" id="s5">
<title>5. Conclusion</title>
<p>Results obtained in the present study strongly suggest that the methods employed can reproducibly identify dominant features for classification and regression from STR, Oscillatory potentials (OPs), and other ERG tests consistent with the results reported in previously published work on the sensitivity of and OPs and flicker to subtle changes in RGC function and viability (Tyler, <xref ref-type="bibr" rid="B118">1981</xref>; Brandao et al., <xref ref-type="bibr" rid="B16">2017</xref>). Further, our approach identified additional dominant distinguishing features such as Shannon Entropy Values for Maximal Overlap Discrete Wavelet Packet Transform (MOD-PWT) and AR coefficients, which are not distinguishable by traditional methods used in Grillo et al. (<xref ref-type="bibr" rid="B46">2018</xref>). This strongly suggests that the current machine-learning-based algorithm has significant potential in distinguishing subtle changes in ERG signals corresponding to different stages of glaucoma disease development. This capability of the technique could be used as a foundational step to create a reliable framework for the early detection of glaucoma and to monitor efficacy of therapeutic intervention in both clinical practice and novel drug development for glaucoma. In addition, the inclusion of various ERG protocols in this framework, such as cones, rods and cones, STR, and oscillatory potentials, represent responses from different cell types in the eye. Therefore, ERG response can be mapped to diseases specific to those cell types. It should be noted that this study was based on mice and with 12 h of dark adaptation. The promising results obtained here suggest the great potential for this method to help detect early stage, pre-symptomatic glaucoma. However, an additional study on adaptation requirements would be required before extending this framework to humans.</p>
</sec>
<sec sec-type="data-availability" id="s6">
<title>Data Availability Statement</title>
<p>The datasets generated for this study are available on request to the corresponding author. Requests to access these datasets should be directed to <email>mehdizadeha&#x00040;umkc.edu</email>.</p>
</sec>
<sec id="s7">
<title>Author Contributions</title>
<p>MG contributed in machine learning framework development, formal analysis, investigation, validation, visualization, and writing&#x02014;original draft. LR contributed in writing&#x02014;review and editing. PK contributed in providing the data, conceptualization, supervision, and writing&#x02014;review and editing. AM contributed in conceptualization, supervision, and writing&#x02014;review and editing. All authors contributed to the article and approved the submitted version.</p>
</sec>
<sec sec-type="funding-information" id="s8">
<title>Funding</title>
<p>Research reported in this publication was supported by the Felix and Carmen Sabates Missouri Endowed Chair in Vision Research, the Vision Research Foundation of Kansas City, and in part by National Eye Institute grant EY031248 of the National Institutes of Health (PK). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The publication cost was covered by PK.</p>
</sec>
<sec id="s9">
<title>Author Disclaimer</title>
<p>The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.</p>
</sec>
<sec sec-type="COI-statement" id="conf1">
<title>Conflict of Interest</title>
<p>PK, AM, and MG have a patent-pending based on this study. The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x00027;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
</body>
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