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Feature selection is an important problem for pattern classification systems. We study how to select good features according to the maximal statistical dependency criterion based on mutual information. Because of the difficulty in directly implementing the maximal dependency condition, we first derive an equivalent form, called(More)
How to selecting a small subset out of the thousands of genes in microarray data is important for accurate classification of phenotypes. Widely used methods typically rank genes according to their differential expressions among phenotypes and pick the top-ranked genes. We observe that feature sets so obtained have certain redundancy and study methods to(More)
MOTIVATION Protein fold recognition is an important approach to structure discovery without relying on sequence similarity. We study this approach with new multi-class classification methods and examined many issues important for a practical recognition system. RESULTS Most current discriminative methods for protein fold prediction use the(More)
We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X = FG<sup>T</sup>, we focus on algorithms in which G is restricted to containing nonnegative entries, but allowing the data matrix X to have mixed signs, thus extending the applicable range of NMF methods. We also consider(More)
Currently, most research on nonnegative matrix factorization (NMF)focus on 2-factor $X=FG^T$ factorization. We provide a systematicanalysis of 3-factor $X=FSG^T$ NMF. While it unconstrained 3-factor NMF is equivalent to it unconstrained 2-factor NMF, itconstrained 3-factor NMF brings new features to it constrained 2-factor NMF. We study the orthogonality(More)
Current nonnegative matrix factorization (NMF) deals with X = F G T type. We provide a systematic analysis and extensions of NMF to the symmetric W = HH T , and the weighted W = HSH T. We show that (1) W = HH T is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X = F G T is equivalent to simultaneous clustering of(More)
Feature selection is an important component of many machine learning applications. Especially in many bioinformatics tasks, efficient and robust feature selection methods are desired to extract meaningful features and eliminate noisy ones. In this paper, we propose a new robust feature selection method with emphasizing joint 2,1-norm minimization on both(More)
Principal component analysis (PCA) minimizes the sum of squared errors (<i>L</i><inf>2</inf>-norm) and is sensitive to the presence of outliers. We propose a <i>rotational invariant L</i><inf>1</inf>-norm PCA (<i>R</i><inf>1</inf>-PCA). <i>R</i><inf>1</inf>-PCA is similar to PCA in that (1) it has a unique global solution, (2) the solution are principal(More)