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Nonnegative matrix factorization (NMF) is a powerful matrix decomposition technique that approximates a nonnegative matrix by the product of two low-rank nonnegative matrix factors. It has been widely applied to signal processing, computer vision, and data mining. Traditional NMF solvers include the multiplicative update rule (MUR), the projected gradient(More)
Nonnegative matrix factorization (NMF) has become a popular dimension-reduction method and has been widely applied to image processing and pattern recognition problems. However, conventional NMF learning methods require the entire dataset to reside in the memory and thus cannot be applied to large-scale or streaming datasets. In this paper, we propose an(More)
Nonnegative matrix factorization (NMF) has become a popular data-representation method and has been widely used in image processing and pattern-recognition problems. This is because the learned bases can be interpreted as a natural parts-based representation of data and this interpretation is consistent with the psychological intuition of combining parts to(More)
In this paper, we present a non-negative patch alignment framework (NPAF) to unify popular non-negative matrix factorization (NMF) related dimension reduction algorithms. It offers a new viewpoint to better understand the common property of different NMF algorithms. Although multiplicative update rule (MUR) can solve NPAF and is easy to implement, it(More)
Non-negative matrix factorization (NMF) approximates a non-negative matrix X by a product of two non-negative low-rank factor matrices W and H. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between X and W T H to model the Poisson noise or the Gaussian noise. In practice, when the noise distribution is(More)
RNA-sequencing is rapidly becoming the method of choice for studying the full complexity of transcriptomes, however with increasing dimensionality, accurate gene ranking is becoming increasingly challenging. This paper proposes an accurate and sensitive gene ranking method that implements discriminant non-negative matrix factorization (DNMF) for RNA-seq(More)
Advances in DNA microarray technologies have made gene expression profiles a significant candidate in identifying different types of cancers. Traditional learning-based cancer identification methods utilize labeled samples to train a classifier, but they are inconvenient for practical application because labels are quite expensive in the clinical cancer(More)
With accumulating public omics data, great efforts have been made to characterize the genetic heterogeneity of breast cancer. However, identifying novel targets and selecting the best from the sizeable lists of candidate targets is still a key challenge for targeted therapy, largely owing to the lack of economical, efficient and systematic discovery and(More)
Semi-supervised clustering aims at boosting the clustering performance on unlabeled samples by using labels from a few labeled samples. Constrained NMF (CNMF) is one of the most significant semi-supervised clustering methods, and it factorizes the whole dataset by NMF and constrains those labeled samples from the same class to have identical encodings. In(More)
Projective non-negative matrix factorization (P-NMF) projects a set of examples onto a subspace spanned by a non-negative basis whose transpose is regarded as the projection matrix. Since PNMF learns a natural parts-based representation, it has been successfully used in text mining and pattern recognition. However, it is non-trivial to analyze the(More)