In our experiments, we use the data sets listed in Table 1 to build a tripartite heterogeneous network model. Table 1 shows the exactly biologic data sets we used during the experiments (Yamanishi et al., 2008; Zheng and Wu, 2021). Especially, the main resource of the data set for the disease layer is from DisGeNET. This paper also uses a data set called DisGeNET approved, which contains FDA-approved drugs and their corresponding protein targets in the DisGeNET.

We will evaluate the performance of THNCDF on benchmark data sets. The benchmark data sets used in many DTI predictions were originally proposed by Y. Yamanishi, which have been considered as the golden data sets for comparing various DTI prediction methods. The benchmark data sets are listed in Table 2, which are downloaded from http://web.kuicr.kyotou.ac.jp/supp/yoshi/drugtarget/. The data sets include four subsets grouped by target classification: Enzyme, ion channel, GPCR (G protein-coupled receptor), and nuclear receptor. The largest subset, Enzyme, includes 445 drugs and 664 targets with 2,926 known DTI between them. Another NR, the smallest subset includes only 54 drugs and 26 targets with 90 known interactions. The other two subsets, IC and GPCR, consist of 210 and 223 drugs, 204 and 95 targets, and 1,476 and 635 known interactions, respectively.

Based on the related ideas of pharmacology, the therapeutic effect of a single drug is relatively limited for diseases that are complex multiple pathological (Zamami et al., 2017; Zhu et al., 2020). Recently, the development of high-throughput biotechnology has produced a large amount of data. However, one of the main difficulties is how to collect and analyze the required biomedical data because they are heterogeneous and the data generated from different experiments include different types of information, such as nucleotide sequences and protein–protein interactions (Luo et al., 2020).

In this paper, we integrate the composition of many different heterogeneous networks and construct our novel tripartite heterogeneous network model according to different types of data. Figure 1A is the part of visualization of the Enzyme in benchmark data sets, in which the red nodes are drugs and the green nodes are targets. Figure 1B is the bipartite graph model of a part of Figure 1A; the red nodes are drugs, and the green nodes are targets in the same.

We construct a tripartite network that includes three layers: drugs, targets, and diseases. Correspondingly, two types of interactions, drug–target interactions and target–disease interactions, are interpreted as edges to connect nodes in these layers. We mainly focus on constructing the similarity matrix and feature information of the tripartite heterogeneous network.

To ensure that the features in the network model are distinguishable, the similarity of the medicinal chemical structure is a relatively objective feature (Zheng and Wu, 2021). In particular, the chemical structure of various drugs under the same standard can be obtained through the simplified molecular-input line-entry system (SIMILES), and then converted into 166-bits string of a certain length fingerprint. Thus, each fingerprint represents a unique drug. Through the calculation of Tanimoto’s coefficient, the similarity matrix of medicinal chemical structure among all drugs is obtained. The formula for calculating Tanimoto’s coefficient is shown in Equation (1).

where f_(dx) is the binary chemical fingerprint of drug x. According to Equation (1), a matrix of chemical structure similarity is constructed.

The Gaussian kernel is defined as the unimodal of the Euclidean distance between any two points in the network (Zheng and Wu, 2021). In THNCDF method, the Gaussian kernel is mainly used to calculate the feature of the connection between two layers, like the edge between the drug layer and the target layer or between the target layer and the disease layer. Also, for drug–drug interactions and target–target interactions, the Gaussian Kernel can calculate the edges in the same layer. Therefore, the calculation formula is commonly used to construct various types of matrices, such as the drug–drug interactions similarity matrix, target–target interactions similarity matrix, and target–disease interactions similarity matrix. The calculation formula is as follows:

where D_i is defined as the i-th drug in the drug set, T_i represents the i-th target in the target set, while ts_i represents the i-th target in the target–disease interactions set. m is the size of drug set, while n and k represent the size of target set and the size of target–disease interactions set, respectively. The adjacency matrix Y ∈ mn represents the known drug–target interactions. If the drug and the target have an existing interaction, the value is 1; otherwise, the value is 0. yd_i{y_i1,y_i2,…,y_in} is defined as the correlation vector between the drug d_i and all targets; meanwhile, yts_i{y_i1,y_i2,…,y_in} is defined as the correlation vector between the target ts_i and all diseases. γ_d, γ_t, and γ_ts are adjustment parameters that control the width of the kernel, whereγd′, γt′, and γt⁢s′ are set to 1 by using Gaussian kernels.

According to the above multiple similarity matrices, we construct a kernel containing the spatial information of drugs and targets (Ding et al., 2018, 2020a,b; Zheng and Wu, 2021). Since the similarity matrix is not a positive definite matrix, predictions are ultimately required. We linearly fit the similarity matrix of drug chemical structure, the drug Gaussian kernel, the target Gaussian kernel, and the disease Gaussian kernel. We also set the weighted factors in the following equations empirically.

The result of similarity matrices is used as the original input of the next step. In the latter experiments, in order to balance the constructed similarity matrix, the ratio of 0.5:0.5 is used with parameter setting.

Random forest, developed by Bermain and Culter (Breiman, 2001), is widely used due to its excellent stability and resistance to overfitting. Nowadays, random forest has been successfully applied to the analysis of multiple biological and pharmacological contexts, such as Diabetic Retinopathy screening procedure (Alabdulwahhab et al., 2021) and detection of copy number variations for uncovering genetic factors (Zhuang et al., 2020). But in novel review by Zhou et al., deep learning based on non-differentiable modules exhibits the possibility of constructing deep models without using backpropagation. They have proposed the gcForest approach, which has generated three characteristics: layer-by-layer processing, in-model feature transformation, and sufficient model complexity. It provides an alternative methods to deep neural networks (DNNs) to learn hyper-level representations at a low computational cost. gcForest is a novel decision tree ensemble, with a cascade structure. It has much fewer hyper-parameters than DNNs, which the training process does not rely on backpropagation. In fact, the most important value of gcForest approach is it may open a door for non-NN style deep learning, or deep models based on non-differentiable modules. An extended depiction and the study of the theory on random forest or gcForest can be referred to the Web site of Bremain or the paper of Zhou et al.

Based on the advantage of random forest and characteristics of gcForest, we construct the THNCDF method, which includes the similarity matrices described above and utilizes improved gcForest approach for prediction. First, the fusion similarity matrix is the origin input for cascade structure of deep forest. Each level of cascade receives the feature information processed by its previous level and outputs its processing result to the next level. All level is an ensemble of decision tree forest. For example, each forest will count the percentages of different classes of training examples at the leaf node, and then average all trees in the same forest to obtain an estimate of the class distribution.

Secondly, we use three random forests: (a) two completely random tree forests, (b) two gradient boosting tree forests, and (c) two extra randomized tree forests. Each forest contains 1,000 trees, and there are 6,000 trees in total. Each node selects a feature randomly as the judgment condition and generates leaf nodes according to the condition. Stop until each leaf node contains only instances of the same class.

To compare with other results, we use 10-fold cross validation (Liu et al., 2016). It means that class vectors produced by each forest are generated by 10-fold cross validation to reduce the risk of overfitting. Finally, if there is no significant performance gain, the training process will terminate. The number of cascade levels is automatically determined.

In order to evaluate the performance of our method, we mainly introduce DTI prediction results compared with baseline methods on the benchmark data sets that are proposed by Y. Yamanishi. The following are the state-of-the-art methods made in comparison with the same standard criteria:

RLS-KF (Hao et al., 2016): A regularized least squares combining with nonlinear kernel fusion method is developed.

RF (Cao et al., 2014): A computational method integrated the information from network, chemical, and biological properties. This method is developed based on the random forest combining with integrated features.

DTiGEMS (Thafar et al., 2020): A computational method using graph embedding, graph mining, and similarity properties techniques. DTiGEMS firstly applies a similarity selection procedure and a similarity fusion algorithm. Then, it integrates multiple drug–drug similarities and target–target similarities into the final heterogeneous graph structure after.

iDTI-ESBoost (Rayhan et al., 2017): A prediction model uses evolutionary and structural features. The method uses a new data balancing and boosting technique to make prediction.

Two quality measures are commonly used to evaluate the performance of these methods: AUC and AUPR. Specifically, we calculate the receiver operating characteristic curve (ROC) of true positive as a function of false positive, and use the area under the ROC curve (AUC) value as a quality measure. In addition, we also calculate the precision–recall curve (P–R), which is the chart of true positive rate between all positive predictions of each given recall rate. The area under the P–R curve (AUPR) provides a quantitative assessment. These two kinds of quality measures have become the standard criteria for evaluating methods.

To provide a fair comparison of DTI prediction performances, we apply these methods on the same benchmark data sets. We also use 10-fold cross-validation random setting, the same evaluation criteria, and optimal parameters of each method.

From the results reported in Table 3 and Figure 3, THNCDF algorithm still maintains a high performance, especially for the AUPR values. For example, in the enzyme data set (Figure 3A), the ion channel data set (Figure 3B), and the GPCR data set (Figure 3C), THNCDF outperforms all other methods by achieving the best performance for AUPR values. On the other hand, for the AUC values, THNCDF still maintains the high performance. It is well known that the training of DNN usually requires a large amount of training data; hence, its implementation on tasks with small-scale data is not suitable. This is the inherently unavoidable characteristic of the method we use. Thus, it is reflected in the correlation between the size of the benchmark data sets and the AUC values obtained.

In addition, the number of positive samples and negative samples in each data set is highly imbalanced. The fact that few positive samples make THNCDF cannot exert its advantages, which is based on a large amount of training data. For benchmark data set, the feature dimension used in this method is low, and cascade deep forest has great advantages in the representation learning of ultra-high-dimensional data.

As shown in Figure 3, it is found that the prediction accuracy is approximately equal to each other. It also shows that the THNCDF preserves the best performance on all data sets so that it can be migrated to other predictions. The experiment procedure shows that THNCDF is not very sensitive to parameter settings. Therefore, it does not need large-scale parameter adjustment, especially the selection of the optimal combination of base classifiers. Comparing with DNN, THNCDF is more stable and easier.

It is worth mentioning that for the two commonly used evaluation metrics, more and more authors think that AUPR provides more informative assessment than AUC for highly imbalanced data sets. They argue in favor of AUPR values as a key standard of evaluating the performance for skewed data sets, especially the data sets with more negative samples than positive samples. In fact, all of the four subsets in the benchmark data sets possess the imbalanced characteristic, which means that the number of known drug–target interactions is far less than the number of pairs with no interaction evidence. So a more sensitive AUPR metric is generally preferred for assessing the prediction results for those imbalanced datasets. From this perspective, the result clearly shows that THNCDF outperforms the prediction in terms of AUPR as well.