12 accepted papers
Matrix tri-factorizations (MTFs) aim to decompose an input matrix X into the product of three factor matrices, instead of only two as in standard matrix factorization (MF). In contrast to MF, MTF is able to cluster both rows and columns of X while quantifying the relationship among these two groups…
Mixture models are traditionally represented and learned by adding several distributions as components. Allowing mixtures to subtract probability mass or density can drastically reduce the number of components needed to model complex distributions. However, learning such subtractive mixtures while e…
Semi-binary matrix factorization (semi-BMF) is a matrix decomposition model where the elements of one factor are binary. Semi-BMF can be interpreted as a generalization of k - means, and can be employed in clustering problems such as community detection. In the absence of noise, Kueng and Tropp (SIA…
In this paper, we propose a new low-rank matrix factorization model, dubbed bounded simplex-structured matrix factorization (BSSMF). Given an input matrix X and a factorization rank r, BSSMF looks for a matrix W with r columns and a matrix H with r rows such that X ≈ W H where the entries in each co…
Subspace clustering is an unsupervised approach for determining the union of multiple subspaces that best fits a collection of high-dimensional samples. Self-expressive representation, that is, expressing samples as linear combination of other samples, is the core of most state-of-the-art subspace c…
We introduce a new Nonnegative Matrix Factorization (NMF) model called Nonnegative Unimodal Matrix Factorization (NuMF), which adds on top of NMF the unimodal condition on the columns of the basis matrix. NuMF finds applications for example in analytical chemistry. We propose a simple but naive brut…
We propose a novel approach to solve exactly the sparse nonnegative least squares problem, under hard ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> sparsity constraints. This approach is based on a dedicated branch-and-bound algorithm. This…
Tensor decompositions have become a central tool in machine learning to extract interpretable patterns from multiway arrays of data. However, computing the approximate Canonical Polyadic Decomposition (aCPD), one of the most important tensor decomposition model, remains a challenge. In this work, we…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order methods: (1) they allow using two different extrapolation points…
In recent years, nonnegative matrix factorization (NMF) with volume regularization has been shown to be a powerful identifiable model; for example for hyperspectral unmixing, document classification, community detection and hidden Markov models. In this paper, we show that minimum-volume NMF (min-vo…
In this paper we consider a variant of the dictionary learning problem where the dictionary has full rank, the coefficients have a fixed sparsity level, and both the coefficients and the dictionary are nonnegative. It is equivalent to k-sparse nonnegative matrix factorization (K-NMF). This model is…
In this paper, we consider the following low-rank matrix approximation problem, referred to as separable simplex-structured matrix factorization: given an input matrix X, find W and H such that X ≈ WH where the columns of W are chosen among the columns of X and where the entries of each column of H…