In recent years, there has been an interesting new trend to apply modern robotics, information technology and artificial intelligence (AI) to restaurants. Tablet computers for food ordering have been widely utilized in many countries (1–3). Robotic restaurants without human waiters and waitresses have been in operation, such as those in Canada (4), Japan (5), and Singapore (6). Although these trends have great potential in improving restaurant service, reducing cost, and enhancing customer satisfaction, the reduction or elimination of human interaction with customers on food choices significantly increases the problem in selecting a dish from a long restaurant menu. Although food flavor and appearance have been important features for consumers choosing their favorite foods (7–10), for meal ordering service in restaurants, it is also very important to understand what drives consumers' food choices and give recommendations through computational analysis of the variables collected both historically and at the tableside. Personalized recommendation systems using information and communication technologies (ICT) have been reported (11, 12). At present, these systems mainly satisfy specific needs expressed by consumers (13), such as healthy diet (14), balanced nutrition (15), and food taste (16). With the recent developments of machine learning, artificial intelligence, and cloud computing technologies, the development of smart food recommender systems for the general customers has been reported. For instance, a cloud-based smart restaurant management system (17) can provide easy-to-use interfaces to its users for food menu recommendation. Using advanced algorithms and Amazon Web Services (AWS), not only consumers can easily find their favorite food, but also restaurants can improve service, productivity and profits. Therefore, developing an intelligent menu recommender engine is an important task with promising applications to the enormous food service industry.

Beyond the field of dietary recommendation, many systems have been developed to predict people's interests (18). Personalized recommender engines play an increasingly important role in helping people make selections from overwhelming numbers of choices. For example, online stores such as Amazon, Netflix, and Pandora can recommend books, digital products, and other commodities. There have also been considerable recommenders in the academic field for students to choose schools, majors and classes (19–21). Regardless applications, existing recommender systems can typically be classified into three categories (22): (1) content-based, (2) collaborative, and (3) hybrid systems. The first category makes recommendations by matching item features; the second category makes predictions by analyzing rating data; and the last category possesses both content-based and collaborative features. Among different recommendation algorithms, the collaborative filtering (CF) algorithm and its variants have been used most widely (23). The CF-based algorithms can be further divided into memory-based and model-based algorithms (22, 24). It has been reported that, using a hybrid content-based collaborative filtering (CCF), the recommendation performance can be improved (25, 26). Recently, there has been a new progress in using matrix-factorization (MF)-based methods with high performance and scalability (27). The earliest version of the MF approach was based on singular value decomposition (SVD) (28). Lately, MF-based methods employed customer rating data to extract features and train a recommender based on predicted user preferences (29). There have also been cross integrations of CF recommender systems with regularized MF which have appeared at the Netflix prize competition (30). CF and MF based methods, along with their variations, have found various industrial applications (31–37). Relative to other fields, restaurant menu recommenders are less developed but some works have been reported. A real-time system was developed to monitor dining activity by videos (38). The system recommends additional dishes when the customers finish the existing ones and want more. Tan et al. (13) utilized the radio frequency identification (RFID) technology to improve food service. Elahi et al. (39) used tags and latent factors to design an interactive food recommendation system. Shaikh et al. (40) described a mobile recommendation system using context and user-profile information.

Some dietary recommendation systems pay special attention to the needs of customers who are patients. A system was developed to recommend foods based on user's illness and demographic information (41). Achieving a balanced nutrition was the focus of the recommender established using consumers' dietary records (42). Similarly, a recipe recommendation system was developed to help customers achieve fitness goals (43).

There were other recommender studies focusing on ingredients. Freyne et al. (44) and Feng et al. (45) extracted ingredients, which were individually rated by users, from menus. Recommendations were produced by weighting each ingredient. He et al. (46) used tastes (sour, sweet, bitter, spicy, and salty) to compose a vector of flavors for each dish. Then, customers' food ordering records and the established flavor vectors were used to make recommendations.

Incorporating other content information from recipes, MF-based recommenders generally achieved better preference prediction for users. Forbes and Zhu (47) proposed an algorithm incorporating the ingredient information into the MF method and improved the recipe recommendation performance. Lin et al. (48) employed main ingredients, courses, cuisines, etc. to obtain a recommender model. Although these food recommendation systems enhanced prediction accuracy, they directly incorporated the content information into item vectors for matrix factorization without revealing the hidden associations among these factors. As a result, these systems can only exploit explicit information about users' preferences. In order to reveal associations of food components, consumers' needs, and other related factors to produce better recommendations, we present a multi-attribute relation matrix tri-factorization (MARMTF) technique in this work. We first represent heterogeneous information as multi-type relation matrices. In addition to including users' ordering record and ratings for the dishes, we construct a set of relationship matrices, which reflects ingredients, spicy level, and price and integrate it into the recommendation framework. The multi-variant matrices are then integrated by data fusion using an advanced MF algorithm (49).

This paper is organized as follows. We introduce the recommendation strategies and methods in section Recommendation Strategies and Methods, where attribute relations for the food recommendation system are described. In section Experimental Studies, our experimental studies are presented which employ the multi-attribute relation matrix tri-factorization (MARMTF) framework to produce menu recommendation. Then, the performance of our recommendation system is discussed in section Results and Discussion. Finally, we draw conclusions in section Conclusion.

Using the optimally determined parameters, we constructed our recommendation system using the training set, which was composed of 83.3% of the total data. Once constructed, we utilized the test set, composed of the rest of collected data, to evaluate performance based on the RMSE and MAE metrics. For reliability of the output, the test procedure was repeated 10 times, and we took the average of the evaluation results.

Additionally, we compared our method with several commonly used methods, including projected gradient NMF (pgNMF) (66), classical matrix factorization (MF) (29), and SVD++ (67). Furthermore, we compared our current use of 3-factor matrix factorization (MARMTF) with an alternative of using 2-factor matrix factorization based on the same multi-type relation dataset. Finally, in order to validate our approach of using multi-type relation data, we performed the matrix tri-factorization using only the user-dish rating matrix. The comparison results can be observed in Figure 5. The MARMTF model achieve the best prediction rating accuracy.

For more details, our results are listed in Table 5. It can be observed that the RMSE and MAE have the minimum values at 0.1693 and 0.1342, respectively, indicating that the MARMTF method outperformed other algorithms. The next performers are the rating matrix tri-factorization (RMTF) and multi-attribute relation matrix factorization (MARMF) methods which are better than the traditional methods, including SVD++, classical MF, and pgNMF.

In this comparison, the recommendation models utilize different amounts of information and/or treated the information differently. For example, the projected gradient NMF model assumes that an absence of rating implies an unfavored item, and the classical MF model only utilizes the rating matrix (68). In contrast, the SVD++ is a matrix factorization model that can combine mean rating, user-item bias, and implicit feedback information (69). As a result, the prediction accuracies of the SVD++ and other multi-attribute methods are higher than those of the projected gradient NMF and Classical MF. Thus, our results agree with a previous report that a recommendation model generally achieves a better performance if it incorporates more background information (67). However, it is difficult for the existing techniques to fuse a large number of attributes from a wide variety of resources.

With regard to making dish recommendations for consumers in restaurants, the relation matrices must be constructed with multiple attributes. Therefore, it is important to integrate and fuse the information from different sources. Our MARMTF model decomposes all the relation matrices systematically for the reconstruction of the rating prediction matrix. In addition, this model achieves a better clustering accuracy by simultaneously co-clustering multiple attributes simultaneously. Due to these valuable properties, the prediction accuracy of the MARMTF overperforms the MARMF which adopts 2-factor matrix decomposition. Overall, the MARMTF can better “understand” complex underlying relationships from different sources to produce more relevant recommendations for consumers.

Despite the advantages, we point out that the current version of the MARMTF has certain limitations. The evaluation was performed in a particular region (Chongqing) where foods tend to be spicy. As a result, there is a tendency that our food choice preferences are biased toward spicy foods and our results are subject to regional limitations. Additionally, we adopted only food ingredients, spicy levels, and price levels as the factors to help consumers choose food. Therefore, the attributes utilized are limited. In future studies, we plan to enhance our recommendation model by considering additional attributes, such as time of meal, season of the year, native region of the consumer, etc., under the MARMTF framework. Finally, food recommendations for healthy diet and balanced nutrition are of great interests for people with chronic diseases or being overweight. In order to produce health-awareness recommendations, we plan to use both food preference and demographic/medical data [e.g., age, body mass index (BMI), existing chronic conditions, etc.] and apply the MARMTF model to make dietary recommendations.

With improvements in food production and services, consumers are facing with increased food products and diverse eating environments which make food-choice decisions more complex (70). In order to provide an effective meal selection tool for consumers in restaurants, we have developed a food recommendation system incorporating the information about eating behaviors and food attributes. A multi-attribute relation matrix tri-factorization framework has been presented. Based on the user-dish rating matrix, our relation-driven recommendation model utilizes other dish attribute relation matrices, including dish-ingredients, dish-spices, and dish-price, as the input data to predict consumers' food choices. Experimental results using real-world data have shown that the MARMTF model achieved better performance than existing recommendation methods. In the future work, we will incorporate more information and attributes, not only for choosing favorable food, but also for healthy eating and balanced nutrition.

All of the authors contributed to the study conception and design, data collection, and interpretation of findings. XL conducted the statistical analyses and drafted the manuscript. MS performed the study design, interpretation of findings, and revised the manuscript. WJ advised on the statistical analysis and reviewed drafts of the manuscript.