14 accepted papers
Whitening is a classical technique in unsupervised learning that can facilitate estimation tasks by standardizing data. An important application is the estimation of latent variable models via the decomposition of tensors built from high-order moments. In particular, whitening orthogonalizes the mea…
State-of-the-art music recommendation systems are based on collaborative filtering, which predicts a user’s interest from his listening habits and similarities with other users’ profiles. These approaches are agnostic to the song content, and therefore face the cold-start problem: they cannot recomm…
Time-frequency audio source separation is usually achieved by estimating the short-time Fourier transform (STFT) magnitude of each source, and then applying a phase recovery algorithm to retrieve time-domain signals. In particular, the multiple input spectrogram inversion (MISI) algorithm has shown…
Safe screening rules are powerful tools to accelerate iterative solvers in sparse regression problems. They allow early identification of inactive coordinates (i.e., those not belonging to the support of the solution) which can thus be screened out in the course of iterations. In this paper, we exte…
This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context, we show that the corresponding optimization problem can be…
We introduce a new non-negative matrix factorization (NMF) method for ordinal data, called OrdNMF. Ordinal data are categorical data which exhibit a natural ordering between the categories. In particular, they can be found in recommender systems, either with explicit data (such as ratings) or implic…
This paper deals with positive semidefinite matrix factorization (PS-DMF). PSDMF writes each entry of a nonnegative matrix as the inner product of two symmetric positive semidefinite matrices. PS-DMF generalizes nonnegative matrix factorization. Exact PSDMF has found applications in combinatorial op…
Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to learn transforms from raw data attracts increasing attention…
Nonnegative matrix factorization (NMF) has become a method of choice for spectrogram decomposition. However, its inability to capture dependencies across columns of the input motivated the introduction of a variant, convolutive NMF. While algorithms for solving the convolutive NMF problem were previ…
Count data are often used in recommender systems: they are widespread (song play counts, product purchases, clicks on web pages) and can reveal user preference without any explicit rating from the user. Such data are known to be sparse, over-dispersed and bursty, which makes their direct use in reco…
An important task when processing dynamic PET images is to identify the time-activity curves (TACs) of the pure tissues, along with their corresponding spatial proportions. This step, often referred to as unmixing or factor analysis, is based on a loss function which measures the discrepancy between…
We present novel understandings of the Gamma-Poisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the estimation of the topic/dictionary matrix by maximum marginal likel…
Traditional NMF-based signal decomposition relies on the factorization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn a short-time orthogonal transform together with the factori…
Many spectral unmixing methods rely on the non-negative decomposition of spectral data onto a dictionary of spectral templates. In particular, state-of-the-art music transcription systems decompose the spectrogram of the input signal onto a dictionary of representative note spectra. The typical meas…