Efficient algorithm for sparse symmetric nonnegative matrix factorization

Belachew, Melisew Tefera

doi:10.1016/j.patrec.2019.07.026

Cited by 13 publications

(3 citation statements)

References 2 publications

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“…In this section, we provide the derivation of the proposed algorithm by using the concept of the block coordinate descent (BCD) method which is popular for providing closed form solutions. This concept is interesting in the sense that it enables breaking down a given matrix-based nonconvex optimization problem into convex subproblems (based on blocks of columns) which are easier to solve [22,24,25].…”

Section: Methodsmentioning

confidence: 99%

Coordinate Descent-Based Sparse Nonnegative Matrix Factorization for Robust Cancer-Class Discovery and Microarray Data Analysis

Belachew

2021

Journal of Applied Mathematics

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Determining the number of clusters in high-dimensional real-life datasets and interpreting the final outcome are among the challenging problems in data science. Discovering the number of classes in cancer and microarray data plays a vital role in the treatment and diagnosis of cancers and other related diseases. Nonnegative matrix factorization (NMF) plays a paramount role as an efficient data exploratory tool for extracting basis features inherent in massive data. Some algorithms which are based on incorporating sparsity constraints in the nonconvex NMF optimization problem are applied in the past for analyzing microarray datasets. However, to the best of our knowledge, none of these algorithms use block coordinate descent method which is known for providing closed form solutions. In this paper, we apply an algorithm developed based on columnwise partitioning and rank-one matrix approximation. We test this algorithm on two well-known cancer datasets: leukemia and multiple myeloma. The numerical results indicate that the proposed algorithm performs significantly better than related state-of-the-art methods. In particular, it is shown that this method is capable of robust clustering and discovering larger cancer classes in which the cluster splits are stable.

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Section: Methodsmentioning

confidence: 99%

Coordinate Descent-Based Sparse Nonnegative Matrix Factorization for Robust Cancer-Class Discovery and Microarray Data Analysis

Belachew

2021

Journal of Applied Mathematics

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“…Additionally, Symmetric NMF [12]- [14] and typical NMF were both based on L 2 norms. Subsequent research included [15]- [17], where various updates of matrix factors were examined in order to provide rapid computation, but they were still based on L 2 norms. To further enhance the symmetric factorization capability, more research concentrated on modifying the original model by incorporating constraints into Symmetric NMF, such as graph constraints [18], predefined instance-affinity (i.e., within/between groups) constraints [19], [20], and learnt similarity constraints [21], [22].…”

Section: Introductionmentioning

confidence: 99%

Symmetric Nonnegative Matrix Factorization Based on Box-Constrained Half-Quadratic Optimization

Chen

2020

IEEE Access

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Nonnegative Matrix Factorization (NMF) based on half-quadratic (HQ) functions was proven effective and robust when dealing with data contaminated by continuous occlusion according to the half-quadratic optimization theory. Nonetheless, state-of-the-art HQ NMF still cannot handle symmetric data matrices, and this caused problems when applications require processing symmetric matrices, e.g., similarity matrices. In view of such, this study presents HQ Symmetric NMF along with HQ optimization algorithms that can solve symmetric matrix decomposition and avoid oscillations during alternating updates. Moreover, variants of HQ Symmetric NMF are proposed and examined in this study -The direct method and the asymmetry penalty constrained method. Both show their distinct advantages. Experiments on open datasets were conducted for comparison with other methods. Experimental results showed that the proposed HQ Symmetric NMF was more robust against continuous occlusion than the baselines. Both root-mean-squared errors and coefficients of determination were better than those of the baselines, thereby demonstrating effectiveness of the proposed method.INDEX TERMS Half-quadratic optimization, symmetric nonnegative matrix factorization, similarity matrix.

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“…The first algorithm to compute NMF was proposed under the name of multiplicative updating rule in [3], but its slow convergence suggested looking for more efficient algorithms. Many of them belong to the class of Block Coordinate Descent (BCD) methods [4][5][6][7][8], but other iterative methods for nonlinear optimization have also been suggested, based on some gradient descent procedure. To improve the convergence rate, a quasi-Newton strategy has also been considered, coupled with nonnegativity (see, for example, the Newton-like algorithm of [9]).…”

Section: Introductionmentioning

confidence: 99%

Adaptive Clustering via Symmetric Nonnegative Matrix Factorization of the Similarity Matrix

et al. 2019

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The problem of clustering, that is, the partitioning of data into groups of similar objects, is a key step for many data-mining problems. The algorithm we propose for clustering is based on the symmetric nonnegative matrix factorization (SymNMF) of a similarity matrix. The algorithm is first presented for the case of a prescribed number k of clusters, then it is extended to the case of a not a priori given k. A heuristic approach improving the standard multistart strategy is proposed and validated by the experimentation.

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Efficient algorithm for sparse symmetric nonnegative matrix factorization

Cited by 13 publications

References 2 publications

Coordinate Descent-Based Sparse Nonnegative Matrix Factorization for Robust Cancer-Class Discovery and Microarray Data Analysis

Coordinate Descent-Based Sparse Nonnegative Matrix Factorization for Robust Cancer-Class Discovery and Microarray Data Analysis

Symmetric Nonnegative Matrix Factorization Based on Box-Constrained Half-Quadratic Optimization

Adaptive Clustering via Symmetric Nonnegative Matrix Factorization of the Similarity Matrix

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