arXiv subjects

Nicolas Paul

Publications and source records attributed to Nicolas Paul.

3 recordsLinked to original sources

arXiv2022

New penalized criteria for smooth non-negative tensor factorization with missing entries

Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we focus in understanding how this issue should be dealt with for nonnegative tensor factorization. We investigate several criteria used for non-negative tensor factorization in the case where some entries are missing. In particular we show how smoothness penalties can compensate the presence of missing values in order to ensure the existence of an optimum. This lead us to propose new criteria with efficient numerical optimization algorithms. Numerical experiments are conducted to support our claims.

eess.SP↗

arXiv2021

Smooth nonnegative tensor factorization for multi-sites electrical load monitoring

The analysis of load curves collected from smart meters is a key step for many energy management tasks ranging from consumption forecasting to customers characterization and load monitoring. In this contribution, we propose a model based on a functional formulation of nonnegative tensor factorization and derive updates for the corresponding optimization problem. We show on the concrete example of multi-sites load curves disaggregation how this formulation is helpful for 1) exhibiting smooth intraday consumption patterns and 2) taking into account external variables such as the outside temperature. The benefits are demonstrated on simulated and real data by exhibiting a meaningful clustering of the observed sites based on the obtained decomposition.

eess.SP↗

arXiv2006

A non-iterative algorithm to estimate the modes of univariate mixtures with well separated components

This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we introduced in a previous work. In this paper we show that the global minimum of this criterion can be reached with a linear least square minimization followed by a roots finding algorithm. This is a major advantage compared to classical iterative algorithms such as K-means or EM which suffer from the potential convergence to some local extrema of the cost function they use. Our algorithm performances are finally illustrated through simulations of a five components mixture.

physics.data-an↗