Fabian Lecron

Olivier Vu Thanh, Nicolas Gillis, Fabian Lecron

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 $X \approx WH$ where the entries in each column of $W$ are bounded, that is, they belong to given intervals, and the columns of $H$ belong to the probability simplex, that is, $H$ is column stochastic. BSSMF generalizes nonnegative matrix factorization (NMF), and simplex-structured matrix factorization (SSMF). BSSMF is particularly well suited when the entries of the input matrix $X$ belong to a given interval; for example when the rows of $X$ represent images, or $X$ is a rating matrix such as in the Netflix and MovieLens datasets where the entries of $X$ belong to the interval $[1,5]$. The simplex-structured matrix $H$ not only leads to an easily understandable decomposition providing a soft clustering of the columns of $X$, but implies that the entries of each column of $WH$ belong to the same intervals as the columns of $W$. In this paper, we first propose a fast algorithm for BSSMF, even in the presence of missing data in $X$. Then we provide identifiability conditions for BSSMF, that is, we provide conditions under which BSSMF admits a unique decomposition, up to trivial ambiguities. Finally, we illustrate the effectiveness of BSSMF on two applications: extraction of features in a set of images, and the matrix completion problem for recommender systems.

Maxime Manderlier, Fabian Lecron, Olivier Vu Thanh et al.

We investigate whether large language models (LLMs) can generate effective, user-facing explanations from a mathematically interpretable recommendation model. The model is based on constrained matrix factorization, where user types are explicitly represented and predicted item scores share the same scale as observed ratings, making the model's internal representations and predicted scores directly interpretable. This structure is translated into natural language explanations using carefully designed LLM prompts. Many works in explainable AI rely on automatic evaluation metrics, which often fail to capture users' actual needs and perceptions. In contrast, we adopt a user-centered approach: we conduct a study with 326 participants who assessed the quality of the explanations across five key dimensions-transparency, effectiveness, persuasion, trust, and satisfaction-as well as the recommendations themselves. To evaluate how different explanation strategies are perceived, we generate multiple explanation types from the same underlying model, varying the input information provided to the LLM. Our analysis reveals that all explanation types are generally well received, with moderate statistical differences between strategies. User comments further underscore how participants react to each type of explanation, offering complementary insights beyond the quantitative results.

Maxime Manderlier, Fabian Lecron

The RecSys Challenge 2023, presented by ShareChat, consists to predict if an user will install an application on his smartphone after having seen advertising impressions in ShareChat & Moj apps. This paper presents the solution of 'Team UMONS' to this challenge, giving accurate results (our best score is 6.622686) with a relatively small model that can be easily implemented in different production configurations. Our solution scales well when increasing the dataset size and can be used with datasets containing missing values.

Sarah Itani, Fabian Lecron, Philippe Fortemps

One-class Classification (OCC) is an area of machine learning which addresses prediction based on unbalanced datasets. Basically, OCC algorithms achieve training by means of a single class sample, with potentially some additional counter-examples. The current OCC models give satisfaction in terms of performance, but there is an increasing need for the development of interpretable models. In the present work, we propose a one-class model which addresses concerns of both performance and interpretability. Our hybrid OCC method relies on density estimation as part of a tree-based learning algorithm, called One-Class decision Tree (OC-Tree). Within a greedy and recursive approach, our proposal rests on kernel density estimation to split a data subset on the basis of one or several intervals of interest. Thus, the OC-Tree encloses data within hyper-rectangles of interest which can be described by a set of rules. Against state-of-the-art methods such as Cluster Support Vector Data Description (ClusterSVDD), One-Class Support Vector Machine (OCSVM) and isolation Forest (iForest), the OC-Tree performs favorably on a range of benchmark datasets. Furthermore, we propose a real medical application for which the OC-Tree has demonstrated its effectiveness, through the ability to tackle interpretable diagnosis aid based on unbalanced datasets.