Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 29, Issue 5, Pages 1947-1960Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2017.2691725
Keywords
Nonnegative matrix factorization (NMF); representation learning; semisupervised; structure
Categories
Funding
- 973 Program [2014CB347600]
- National Natural Science Foundation of China [61522203, 61402228]
- Natural Science Foundation of Jiangsu Province [BK20140058]
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Dimensionality reduction has attracted increasing attention, because high-dimensional data have arisen naturally in numerous domains in recent years. As one popular dimensionality reduction method, nonnegative matrix factorization (NMF), whose goal is to learn parts-based representations, has been widely studied and applied to various applications. In contrast to the previous approaches, this paper proposes a novel semisupervised NMF learning framework, called robust structured NMF, that learns a robust discriminative representation by leveraging the block-diagonal structure and the l(2), p-norm (especially when 0 < p <= 1) loss function. Specifically, the problems of noise and outliers are well addressed by the l(2), p-norm (0 < p <= 1) loss function, while the discriminative representations of both the labeled and unlabeled data are simultaneously learned by explicitly exploring the block-diagonal structure. The proposed problem is formulated as an optimization problem with a well-defined objective function solved by the proposed iterative algorithm. The convergence of the proposed optimization algorithm is analyzed both theoretically and empirically. In addition, we also discuss the relationships between the proposed method and some previous methods. Extensive experiments on both the synthetic and real-world data sets are conducted, and the experimental results demonstrate the effectiveness of the proposed method in comparison to the state-of-the-art methods.
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