A novel dictionary learning method based on total least squares approach with application in high dimensional biological
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A novel dictionary learning method based on total least squares approach with application in high dimensional biological data Parvaneh Parvasideh1 · Mansoor Rezghi1 Received: 20 March 2019 / Revised: 5 June 2020 / Accepted: 18 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In recent years dictionary learning has become a favorite sparse feature extraction technique. Dictionary learning represents each data as a sparse combination of atoms (columns) of the dictionary matrix. Usually, the input data is contaminated by errors that affect the quality of the obtained dictionary and so sparse features. This effect is especially critical in applications with high dimensional data such as gene expression data. Therefore, some robust dictionary learning methods have investigated. In this study, we proposed a novel robust dictionary learning algorithm, based on the total least squares, that could consider the inexactness of data in modeling. We confirm that standard and some robust dictionary learning models are the particular cases of our proposed model. Also, the results on various data indicate that our method performs better than other dictionary learning methods on high dimensional data. Keywords Dictionary learning · Sparse learning · Total least squares · High dimensional data
1 Introduction Sprse representation has recently become a favorite method in many applications, especially for biological data (Fan et al. 2015; Zhanga et al. 2018; Liu and Zhang 2016; Yang et al. 2010). This approach represents the data as a sparse linear combination of a matrix called dictionary (Khademlou and Rezghi 2015; Yin et al. 2016). In the machine learning viewpoint, sparse representation is a sparse feature extraction method, which its quality directly affected by the dictionary matrix Chang et al. (2016). The process of finding a data-dependent dictionary matrix is referred to as dictionary learning
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Mansoor Rezghi [email protected] Department of Computer Science, Tarbiat modares university, Tehran, Iran
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P. Parvasideh, M. Rezghi
and used in many applications like image processing Yang et al. (2010), machine learning Luh and Vu (2016), and Bioinformatics Li and Ngom (2013). Dictionary learning problem seeks to find the following decomposition D ≈ AX , for a given data matrix D, where A and X are the dictionary and sparse feature matrices, respectively. In some cases, if the dictionary matrix has further properties such as orthogonality and positivity, then matrix decompositions like NMF can be viewed as a particular case of dictionary learning (Kim and Park 2007; Zhai et al. 2019). For example, the authors in Zhai et al. (2019) investigated some interesting properties of the complete and orthogonal dictionary matrix. Although this is not in the scope of this paper, our method can be applied as well. KSVD Aharon et al. (2006) and MOD (Method of Optimal Directions ) Engan et al. (2000), are well-known dictionary learning methods. In the real world applications, the measured data may b
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