This paper combines linear sparse coding and nonnegative matrix factorization into sparse non-negative matrix factorization. In contrast to non-negative matrix factorization, the new model can leam much sparser representation via imposing sparseness constraints explicitly; in contrast to a close model non-negative sparse coding, the new model can learn parts-based representation via fully multi...

Non-Negative Matrix Factorization (NMF) is a dimensionality reduction method that has been shown to be very useful for a variety of tasks in machine learning and data mining. One of the fastest algorithms for NMF is the Block Principal Pivoting method (BPP) of [6], which follows a block coordinate descent approach. The optimization in each iteration involves solving a large number of expensive ...

In this paper, we extend the original non-negative matrix factorization (NMF) to kernel NMF (KNMF). The advantages of KNMF over NMF are: 1) it could extract more useful features hidden in the original data through some kernel-induced nonlinear mappings; 2) it can deal with data where only relationships (similarities or dissimilarities) between objects are known; 3) it can process data with nega...

We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a multiplicative term which models exposure. This term brings a degree of freedom for controlling the dispersion, making NBMF more robust to outliers. We show th...

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in parts-based representations. In this paper, we show how explicitly incorporating the notion of ‘sparseness’ improves the found decompositions. Additionally, ...

In this study, we apply a non-negative matrix factorization approach for the extraction and detection of concepts or topics from electronic mail messages. For the publicly released Enron electronic mail collection, we encode sparse term-by-message matrices and use a low rank non-negative matrix factorization algorithm to preserve natural data non-negativity and avoid subtractive basis vector an...

Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler d...