Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence
Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model and algorithm for ONMF that minimizes the Kullback-Leibler (KL) divergence. As opposed to the Frobenius norm which assumes Gaussian noise, the KL divergence is the maximum likelihood estimator for Poisson-distributed data, which can model better sparse vectors of word counts in document data sets and photo counting processes in imaging. We develop an algorithm based on alternating optimization, KL-ONMF, and show that it performs favorably with the Frobenius-norm based ONMF for document classification and hyperspectral image unmixing.
Code (1)
Tasks
Document ClassificationSimilar Papers 제목 키워드 기반
Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence
Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction technique for nonnegative data sets. In order to measure the discrepancy between the input data and the low-rank approximation, the Kul…
Dimensionality ReductionWasserstein Nonnegative Tensor Factorization with Manifold Regularization
Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the origi…
Deep Nonnegative Matrix Factorization with Beta Divergences
Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have …
Probabilistic semi-nonnegative matrix factorization: a Skellam-based framework
We present a new probabilistic model to address semi-nonnegative matrix factorization (SNMF), called Skellam-SNMF. It is a hierarchical generative model consisting of prior components, Skellam-distributed hidden variable…
Bayesian InferenceAutomatic Relevance Determination in Nonnegative Matrix Factorization with the β-Divergence
This paper addresses the estimation of the latent dimensionality in nonnegative matrix factorization (NMF) with the \beta-divergence. The \beta-divergence is a family of cost functions that includes the squared Euclidean…
Stock Price Prediction