Dual local learning regularized nonnegative matrix factorization and its semi-supervised extension for clustering
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ORIGINAL ARTICLE
Dual local learning regularized nonnegative matrix factorization and its semi-supervised extension for clustering Zhenqiu Shu1,2 • Yunmeng Zhang1 • Peng Li1 • Congzhe You1 • Zhen Liu2 • Honghui Fan1 Xiao-jun Wu2
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Received: 13 March 2020 / Accepted: 24 September 2020 Ó Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Nonnegative matrix factorization (NMF) has received considerable attention in data representation due to its strong interpretability. However, traditional NMF methods neglect the discriminative information and geometric structure of both the data space and the feature space, simultaneously. In this paper, we propose a dual local learning regularized nonnegative matrix factorization (DLLNMF) method, which not only considers the geometric structure of both the data manifold and the feature manifold, simultaneously, but also takes advantage of the discriminative information of both the data space and the feature space. To make full use of the partial label information among samples, we further propose its semi-supervised extension, called dual local learning regularized nonnegative matrix factorization with label constraint (DLLNMF-LC), which imposes the label information as a hard constraint without additional parameters. Experimental results on some benchmark datasets have demonstrated the effectiveness of our proposed methods. Keywords Data representation NMF Geometric structure Manifold Dual local learning regularization Hard constraint
1 Introduction Data representation is a fundamental topic in the field of pattern recognition and computer vision [1–6]. Due to the high dimensionality of the real data, traditional pattern recognition methods not only take expensive computational costs, but also may lead to so-called dimensionality curses. Therefore, the goal of data representation methods is to effectively explore the semantic information hidden in data using a low-dimensional representation [7]. In many practical applications, it plays an important role in dealing with high-dimensional data. In the past few decades, matrix factorization methods have received a significant amount of attention in data & Zhenqiu Shu [email protected] 1
School of Computer Engineering, Jiangsu University of Technology, Changzhou 231001, China
2
Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Jiangnan University, Wuxi 231001, China
representation. Due to the plausible physical interpretation, nonnegative matrix factorization (NMF) becomes one of the most popular matrix factorization methods [8]. It aims to minimize the reconstruction error between its low-rank approximation and the original data matrix. Moreover, NMF is a parts-based representation method due to the strict nonnegative constraint and thus has been widely applied in many real applications [9–11]. Many studies have shown that the low-dimensional manifold embedding in high-dimensional samples has been attracted e
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