Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes

Alternating Direction Method of Multipliers for Convolutive Non-Negative Matrix Factorization

Non-negative matrix factorization (NMF) has become a popular method for learning interpretable patterns from data. As one of the variants of standard NMF, convolutive NMF (CNMF) incorporates an extra time dimension to each basis, known as convolutive bases, which is well suited for representing sequential patterns. Previously proposed algorithms for solving CNMF use multiplicative updates which can be derived by either heuristic or majorization-minimization (MM) methods. However, these algorithms suffer from problems, such as low convergence rates, difficulty to reach exact zeroes during iterations and prone to poor local optima. Inspired by the success of alternating direction method of multipliers (ADMMs) on solving NMF, we explore variable splitting (i.e., the core idea of ADMM) for CNMF in this article. New closed-form algorithms of CNMF are derived with the commonly used β -divergences as optimization objectives. Experimental results have demonstrated the efficacy of the proposed algorithms on their faster convergence, better optima, and sparser results than state-of-the-art baselines.

Simultaneous Dimensionality Reduction and Classification via Dual Embedding Regularized Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a well-known paradigm for data representation. Traditional NMF-based classification methods first perform NMF or one of its variants on input data samples to obtain their low-dimensional representations, which are successively classified by means of a typical classifier [e.g., k -nearest neighbors (KNN) and support vector machine (SVM)]. Such a stepwise manner may overlook the dependency between the two processes, resulting in the compromise of the classification accuracy. In this paper, we elegantly unify the two processes by formulating a novel constrained optimization model, namely dual embedding regularized NMF (DENMF), which is semi-supervised. Our DENMF solution simultaneously finds the low-dimensional representations and assignment matrix via joint optimization for better classification. Specifically, input data samples are projected onto a couple of low-dimensional spaces (i.e., feature and label spaces), and locally linear embedding is employed to preserve the identical local geometric structure in different spaces. Moreover, we propose an alternating iteration algorithm to solve the resulting DENMF, whose convergence is theoretically proven. Experimental results over five benchmark datasets demonstrate that DENMF can achieve higher classification accuracy than state-of-the-art algorithms.

Adapting Stochastic Block Models to Power-Law Degree Distributions

Stochastic block models (SBMs) have been playing an important role in modeling clusters or community structures of network data. But, it is incapable of handling several complex features ubiquitously exhibited in real-world networks, one of which is the power-law degree characteristic. To this end, we propose a new variant of SBM, termed power-law degree SBM (PLD-SBM), by introducing degree decay variables to explicitly encode the varying degree distribution over all nodes. With an exponential prior, it is proved that PLD-SBM approximately preserves the scale-free feature in real networks. In addition, from the inference of variational E-Step, PLD-SBM is indeed to correct the bias inherited in SBM with the introduced degree decay factors. Furthermore, experiments conducted on both synthetic networks and two real-world datasets including Adolescent Health Data and the political blogs network verify the effectiveness of the proposed model in terms of cluster prediction accuracies.

Improving the Accuracy in Sentiment Classification in the Light of Modelling the Latent Semantic Relations

The research presents the methodology of improving the accuracy in sentiment classification in the light of modelling the latent semantic relations (LSR). The objective of this methodology is to find ways of eliminating the limitations of the discriminant and probabilistic methods for LSR revealing and customizing the sentiment classification process (SCP) to the more accurate recognition of text tonality. This objective was achieved by providing the possibility of the joint usage of the following methods: (1) retrieval and recognition of the hierarchical semantic structure of the text and (2) development of the hierarchical contextually-oriented sentiment dictionary in order to perform the context-sensitive SCP. The main scientific contribution of this research is the set of the following approaches: at the phase of LSR revealing (1) combination of the discriminant and probabilistic models while applying the rules of adjustments to obtain the final joint result; at all SCP phases (2) considering document as a complex structure of topically completed textual components (paragraphs) and (3) taking into account the features of persuasive documents’ type. The experimental results have demonstrated the enhancement of the SCP accuracy, namely significant increase of average values of recall and precision indicators and guarantee of sufficient accuracy level.