Search

Networks are commonly used to model complex systems. The different entities in the system are represented by nodes of the network and their interactions by edges. In most real life systems, the different entities may interact in different ways necessitating the use of multiplex networks where multiple links are used to model the interactions. One of the major tools for inferring network topology is community detection. Although there are numerous works on community detection in single-layer networks, existing community detection methods for multiplex networks mostly learn a common community structure across layers and do not take the heterogeneity across layers into account. In this paper, we introduce a new multiplex community detection method that identifies communities that are common across layers as well as those that are unique to each layer. The proposed method, Multiplex Orthogonal Nonnegative Matrix Tri-Factorization, represents the adjacency matrix of each layer as the sum of two low-rank matrix factorizations corresponding to the common and private communities, respectively. Unlike most of the existing methods which require the number of communities to be pre-determined, the proposed method also introduces a two stage method to determine the number of common and private communities. The proposed algorithm is evaluated on synthetic and real multiplex networks, as well as for multiview clustering applications, and compared to state-of-the-art techniques.

Nonnegative matrix factorization (NMF) decomposes a nonnegative matrix into the product of two lower-rank nonnegative matrices. Since NMF learns parts-based representation, it has been widely used as a feature learning component in many fields. However, standard NMF algorithms ignore the training labels as well as unlabeled data in the test domain. In this paper, we propose a transductive nonnegative matrix tri-factorization method (T-NMTF) to simultaneously exploit the label information of training examples and the statistical structure of features in the test domain. Different from standard NMF, nonnegative matrix tri-factorization (NMTF) decomposes a nonnegative matrix into the product of three lower-rank nonnegative matrices, and thus provides a flexible framework to transduce discriminative information of training examples to test examples. In particular, the proposed T-NMTF projects both training examples and test examples into a unified subspace, and expects the coefficients of training examples close to their label vectors. Since training examples and test examples are assumed to identically distributed, it is reasonable to expect the learned coefficients of test examples approximate their label vectors well. To estimate the T-NMTF parameters, we develop an efficient multiplicative update rule and prove its convergence. In addition, we propose a manifold regularized T-NMTF (MT-NMTF) algorithm that exploits the local geometry structure of the dataset to boost discriminant power. Experimental results on face recognition demonstrate the effectiveness of T-NMTF and MT-NMTF.

Due to the explosive growth of image data, image annotation has been one of the most popular research directions in computer vision. It has been widely used in image retrieval, image analysis and understanding. Because traditional manual image annotation is time consuming, more advanced automatic annotation methods are needed. A major challenge in developing an efficient image annotation method is how to effectively use all available information contained in the data. To this end, this paper proposes a novel image annotation framework that uses multiple information from data. It employs nonnegative matrix tri-factorization (NMTF) to simultaneously factorize image-to-label, image-to-feature, and feature-to-label relation matrices using their intertype relationships and incorporates the intratype information through manifold regularizations. This method can be referred to as the trigraph regularized collective matrix tri-factorization framework (TG-CMTF). TG-CMTF captures the correlations among different labels, different images and different features. By taking advantage of these relations from images, features and labels, TG-CMTF can achieve better annotation performance than most state-of-the-art methods. The promising experimental results on three standard benchmarks have shown the effectiveness of this information. Furthermore, we show the annotation process as a precise optimization problem and solve it by an iterative algorithm, which proves the correctness of the proposed method from the mathematical theory.