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Non-negative Matrix Factorisation (NMF) is a popular tool in which a ‘parts-based’ representation of a non-negative matrix is sought. NMF tends to produce sparse decompositions. This sparsity is a desirable property in many applications, and Sparse NMF (S-NMF) methods have been proposed to enhance this feature. Typically these enforce sparsity through use of a penalty term, and a ℓ1 norm penalty term...
This paper focuses on web pages clustering as a tool for typical Web patterns searching and using. Traditional methods of cluster analysis, self-organizing map and nonnegative matrix factorization were applied. Web pages on products sale and automatically detected Web patterns were used as a testing data. The application of GD-CLS (gradient descent constrained least squares) which combines some of...
Non-negative matrix factorization (NMF) is an algorithm for decomposing multivariate data into a signal dictionary and its corresponding activations. When applied to experimental data, NMF has to cope with noise, which is often highly correlated. We show that correlated noise can break the Donoho and Stodden separability conditions of a dataset and a regular NMF algorithm will fail to decompose it,...
A variety of smells can be realized by blending multiple odor components using an olfactory display. Since a set of odor components to cover the entire range of smells has not yet been known, we studied a method of selecting odor components using a large-scale mass spectrum database. Basis vectors corresponding to odor components were extracted by the NMF (nonnegative matrix factorization) method...
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