Sparse non-negative tensor factorization using columnwise coordinate descent

• Published in: Pattern recognition Vol. 45; no. 1; pp. 649 - 656
• Main Authors: Liu, Ji, Liu, Jun, Wonka, Peter, Ye, Jieping
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2012; Elsevier
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Biological and medical sciences; Charge coupled devices; Coding, codes; Columnwise coordinate descent; Computer science; control theory; systems; Computerized, statistical medical data processing and models in biomedicine; Descent; Exact sciences and technology; Factorization; Image processing; Information, signal and communications theory; Mathematical analysis; Mathematical models; Medical management aid. Diagnosis aid; Medical sciences; Non-negative; Pattern recognition. Digital image processing. Computational geometry; Signal and communications theory; Signal processing; Sparse; Telecommunications and information theory; Tensor factorization; Tensors; Non-negative; Sparse; Columnwise coordinate descent; Tensor factorization; Computer vision; State of the art; Data compression; Updating; Factorization; Nuclear magnetic resonance imaging; Hyperspectral imaging sensor; Non negative matrix; Basis function; Data visualization; Medical imagery; Fast algorithm; Biomedical engineering
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2011.05.015

Many applications in computer vision, biomedical informatics, and graphics deal with data in the matrix or tensor form. Non-negative matrix and tensor factorization, which extract data-dependent non-negative basis functions, have been commonly applied for the analysis of such data for data compression, visualization, and detection of hidden information (factors). In this paper, we present a fast and flexible algorithm for sparse non-negative tensor factorization (SNTF) based on columnwise coordinate descent (CCD). Different from the traditional coordinate descent which updates one element at a time, CCD updates one column vector simultaneously. Our empirical results on higher-mode images, such as brain MRI images, gene expression images, and hyperspectral images show that the proposed algorithm is 1–2 orders of magnitude faster than several state-of-the-art algorithms. ► We present a columnwise coordinate descent (CCD) algorithm for sparse non-negative tensor factorization (SNTF). ► Different from the traditional coordinate descent, CCD updates one column vector simultaneously. ► The proposed algorithm is 1–2 orders of magnitude faster than several state-of-the-art algorithms.