PMC:4331678 / 6607-12566 JSONTXT

{"project":"2_test","denotations":[{"id":"25707434-18037900-14839064","span":{"begin":222,"end":224},"obj":"18037900"},{"id":"25707434-22522134-14839065","span":{"begin":240,"end":242},"obj":"22522134"},{"id":"25707434-23572412-14839066","span":{"begin":261,"end":263},"obj":"23572412"},{"id":"25707434-12015889-14839067","span":{"begin":685,"end":687},"obj":"12015889"},{"id":"25707434-15130933-14839068","span":{"begin":1350,"end":1351},"obj":"15130933"},{"id":"25707434-20507895-14839069","span":{"begin":2225,"end":2227},"obj":"20507895"},{"id":"25707434-15130933-14839070","span":{"begin":4008,"end":4009},"obj":"15130933"}],"text":"Related work\nDifferent proteomic data sources (i.e., protein sequences, PPI networks and protein domains) often capture proteins' properties in different aspects, and have different correlations with different GO terms [1,20]. Yang et al. [21] and Teng et al. [22] observed that the GO term similarities have different correlations with different proteomic data sources. Therefore, integrating these data sources can often enable a more comprehensive view of proteins and their functions. Recently, several studies have observed a significant improvement in protein function prediction when multiple heterogenous biological data sources are integrated. To name a few, Pavlidis et al. [23] integrated heterogeneous data sources in three different ways: (i) early integration concatenates all feature vectors from different data sources of a protein into a single feature vector; (ii) intermediate integration computes the functional association network for each data set separately and then combines them; (iii) late integration trains a support vector machine (SVM) on each network (or kernel) and then combines the resulting discriminant values. Their study revealed that different data sources have different qualities, and setting different weights for different networks can enhance the accuracy of protein function prediction. Lanckriet et al. [5] proposed a semi-definite programming based SVM method to get the optimal weights on individual networks. Tsuda et al. [14] constructed an optimal combination of weights on individual networks using convex optimization. Mostafavi et al. [15] determined the optimal function-specific composite network by solving a linear regression problem. These methods constructed a composite network for each functional label. Since there are often more than hundreds of functional labels, and these labels are highly unbalanced and inter-correlated, these algorithms are often confronted with the over-fitting problem and require massive computational resources.\nMore recently, some researchers advocated for the computation of optimal weights on individual networks for a group of labels, and achieved better performance than the methods operating on single labels. Mostafavi et al. [16] introduced a method, called SW, that simultaneously optimizes the weights on individual networks with respect to a group of related functional labels by solving a single-constrained linear regression problem. The optimal weights maximize a form of kernel-target alignment [24] between the composite network and the target network, which is defined based on the functional relationships implied by the functions of proteins. However, merely maximizing the kernel target alignment does not necessarily result in an optimal composite network for the network-based classifier. Yu et al. [25] proposed a method, called ProMK, that combines the composite network optimization with respect to a group of functions and the network based classifier in a unified objective function. ProMK can selectively integrate multiple networks and can construct an optimal composite network directly targeted to the network based classification, but it suffers from the parameter selection problem, and does not take into account the intrinsic unbalanced label problem in protein function prediction.\nIn this study, we build a composite network optimized for a linear neighborhood propagation classifier. The resulting method is called MNet. MNet iteratively optimizes the weights assigned to the individual networks and the loss of the classifier according to a unified objective function. We show that the unified objective function can boost the accuracy of protein function prediction according to several evaluation criteria. Furthermore, MNet is more robust than other related approaches for a wide range of parameter values.\nMNet has a close relationship with multiple kernel learning, which is a popular topic in machine learning [26], and it's also widely applied in biological data mining [5,14,25]. Wang et al. [27] introduced a method called Optimal Multiple Graphs learning (OMG) to integrate multiple graphs into a composite one for graph-based semi-supervised learning. Shiga et al. [28] proposed a method called LIG. LIG first partitions each individual graph into several locally informative subgraphs via soft spectral clustering and then integrates these subgraphs into a composite one for graph-based classification. A protein can have several different functions and these functions are inter-correlated, thus protein function prediction from multiple data sources can also be transformed into a multi-label multiple kernel learning problem [3,25]. Multi-label multiple kernel learning methods often learn a composite kernel for each binary label and thus have a complexity linear to the number of labels. Bucak et al. [29] suggested a method called multiple kernel learning by stochastic approximation, whose complexity is sub-linear to the number of labels.\nMNet is different from the aforementioned approaches to integrating multiple networks in several ways. ProMK, OMG, and LIG assign weights to the individual networks solely based on their smoothness loss: the smaller the value of the smoothness loss for a network, the larger the weight assigned to this network. However, our empirical study in this paper shows that, a smaller value of the smoothness loss on an individual network does not necessarily imply that the network is a better predictor. In contrast, MNet assigns weights to the individual networks not only based on the smoothness loss, but also on the kernel-target alignment. Therefore, MNet alleviates the drawback of the existing methods. Furthermore, MNet constructs a composite network that is coherent to all the labels, whereas most multiple kernel learning algorithms optimize a composite kernel for each binary label, or optimize the composite kernel and the classifier in two separative objectives."}