Nonnegative Matrix Factorization Algorithms using a Constraint to Increase the Discriminability of Two Classes for EEG Feature Extraction

Weighted nonnegative matrix factorization (WNMF) is a technology for feature extraction, which can extract the feature of face dataset, and then the feature can be recognized by the classifier. To improve the performance of WNMF for feature extraction, a new iteration rule is proposed in this paper. Meanwhile, the base matrix U is sparse based on the threshold, and the new method is named sparse weighted nonnegative matrix factorization (SWNMF). The new iteration rules are based on the smaller iteration steps, thus, the search is more precise, therefore, the recognition rate can be improved. In addition, the sparse method based on the threshold is adopted to update the base matrix U, which can make the extracted feature more sparse and concentrate, and then easier to recognize. The SWNMF method is applied on the ORL and JAFEE datasets, and from the experiment results we can find that the recognition rates are improved extensively based on the new iteration rules proposed in this paper. The recognition rate of new SWNMF method reached 98% for ORL face database and 100% for JAFEE face database, respectively, which are higher than the PCA method, the sparse nonnegative matrix factorization (SNMF) method, the convex non-negative matrix factorization (CNMF) method and multi-layer NMF method.

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Simultaneous feature extraction and selection of microarray data using fuzzy-rough based multiobjective nonnegative matrix factorization

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-17954 ◽

2017 ◽

Vol 33 (6) ◽

pp. 4043-4053

Author(s):

Mohamed E. Abd Elaziz

Keyword(s):

Feature Extraction ◽

Microarray Data ◽

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Feature Extraction And Selection ◽

Selection Of

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Matrix Factorization Algorithms for the Identification of Muscle Synergies: Evaluation on Simulated and Experimental Data Sets

Journal of Neurophysiology ◽

10.1152/jn.00222.2005 ◽

2006 ◽

Vol 95 (4) ◽

pp. 2199-2212 ◽

Cited By ~ 377

Author(s):

Matthew C. Tresch ◽

Vincent C. K. Cheung ◽

Andrea d'Avella

Keyword(s):

Matrix Factorization ◽

Muscle Activation ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Muscle Synergies ◽

Data Sets ◽

Data Set ◽

Activation Patterns ◽

Muscle Activation Patterns ◽

Factorization Algorithms

Several recent studies have used matrix factorization algorithms to assess the hypothesis that behaviors might be produced through the combination of a small number of muscle synergies. Although generally agreeing in their basic conclusions, these studies have used a range of different algorithms, making their interpretation and integration difficult. We therefore compared the performance of these different algorithms on both simulated and experimental data sets. We focused on the ability of these algorithms to identify the set of synergies underlying a data set. All data sets consisted of nonnegative values, reflecting the nonnegative data of muscle activation patterns. We found that the performance of principal component analysis (PCA) was generally lower than that of the other algorithms in identifying muscle synergies. Factor analysis (FA) with varimax rotation was better than PCA, and was generally at the same levels as independent component analysis (ICA) and nonnegative matrix factorization (NMF). ICA performed very well on data sets corrupted by constant variance Gaussian noise, but was impaired on data sets with signal-dependent noise and when synergy activation coefficients were correlated. Nonnegative matrix factorization (NMF) performed similarly to ICA and FA on data sets with signal-dependent noise and was generally robust across data sets. The best algorithms were ICA applied to the subspace defined by PCA (ICAPCA) and a version of probabilistic ICA with nonnegativity constraints (pICA). We also evaluated some commonly used criteria to identify the number of synergies underlying a data set, finding that only likelihood ratios based on factor analysis identified the correct number of synergies for data sets with signal-dependent noise in some cases. We then proposed an ad hoc procedure, finding that it was able to identify the correct number in a larger number of cases. Finally, we applied these methods to an experimentally obtained data set. The best performing algorithms (FA, ICA, NMF, ICAPCA, pICA) identified synergies very similar to one another. Based on these results, we discuss guidelines for using factorization algorithms to analyze muscle activation patterns. More generally, the ability of several algorithms to identify the correct muscle synergies and activation coefficients in simulated data, combined with their consistency when applied to physiological data sets, suggests that the muscle synergies found by a particular algorithm are not an artifact of that algorithm, but reflect basic aspects of the organization of muscle activation patterns underlying behaviors.

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