Deep semi-nonnegative matrix factorization with elastic preserving for data representation
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Deep semi-nonnegative matrix factorization with elastic preserving for data representation Zhen-qiu Shu 1,2 & Xiao-jun Wu 2 & Cong Hu 2 & Cong-zhe You 1 & Hong-hui Fan 1 Received: 6 April 2020 / Revised: 30 July 2020 / Accepted: 28 August 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
Deep matrix factorization methods can automatically learn the hidden representation of high dimensional data. However, they neglect the intrinsic geometric structure information of data. In this paper, we propose a Deep Semi-Nonnegative Matrix Factorization with Elastic Preserving (Deep Semi-NMF-EP) method by adding two graph regularizers in each layer. Therefore, the proposed Deep Semi-NMF-EP method effectively preserves the elasticity of data and thus can learn a better representation of high-dimensional data. In addition, we present an effective algorithm to optimize the proposed model and then provide its complexity analysis. The experimental results on the benchmark datasets show the excellent performance of our proposed method compared with other state-of-the-art methods. Keywords Deep matrix factorization . Geometric structure . Elasticity . High dimensional data . Clustering
1 Introduction Data representation techniques play a fundamental role in machine learning and pattern recognition fields. Generally, a suitable representation of high dimensional data needs to reveal the intrinsic structure of data. Over the past few decades, data representation based on matrix factorization has shown their superiority in various problems, such as face recognition, object tracking, image processing, etc. [1, 8–11, 19, 22–24]. Up to now, several variants of matrix factorization have been developed by imposing different constraints on the basis matrix or the coefficient matrix [5, 15, 17]. Nonnegative matrix factorization (NMF) method is a well-known data representation method by incorporating the non-negativity constraint [7]. Therefore, it only allows the additive combination of
* Zhen-qiu Shu [email protected]
1
School of Computer Engineering, Jiangsu University of Technology, Changzhou, China
2
Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Jiangnan University, Wuxi, China
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the basis vectors, and thus is interpreted as a parts-based representation. Recently, a graph regularized NMF (GNMF) [2] method was proposed to model the local geometric manifold embedded in data using the nearest neighbor graph. Li et al. [12] put forward to a structure preserving NMF method for data representation. It explores the structure information of data by imposing structure graph constraint on the model of NMF. Shu et al. [18] proposed a local and global regularizer and then incorporated it into the model of sparse coding. This regularizer aims to preserve the structure information of data. Liu et al. [14] put forward to a semi-supervised learning method, called Constrained Nonnegative Matrix Factorization (CNMF), with resort to
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