arXiv subjects

Linda Maria De Cave

Publications and source records attributed to Linda Maria De Cave.

2 recordsLinked to original sources

arXiv2025

Topological Data Analysis for Unsupervised Anomaly Detection and Customer Segmentation on Banking Data

This paper introduces advanced techniques of Topological Data Analysis (TDA) for unsupervised anomaly detection and customer segmentation in banking data. Using the Mapper algorithm and persistent homology, we develop unsupervised procedures that uncover meaningful patterns in customers' banking data by exploiting topological information. The framework we present in this paper yields actionable insights that combine the abstract mathematical subject of topology with real-life use cases that are useful in industry.

cs.LG↗

arXiv2017

Existence and uniqueness results for possibly singular nonlinear elliptic equations with measure data

We study existence and uniqueness of solutions to a nonlinear elliptic boundary value problem with a general, and possibly singular, lower order term, whose model is $$\begin{cases} -Δ_p u = H(u)μ& \text{in}\ Ω,\\ u>0 &\text{in}\ Ω,\\ u=0 &\text{on}\ \partialΩ. \end{cases}$$ Here $Ω$ is an open bounded subset of $\mathbb{R}^N$ ($N\ge2$), $Δ_p u:= \operatorname{div}(|\nabla u|^{p-2}\nabla u)$ ($1<p<N$) is the $p$-laplacian operator, $μ$ is a nonnegative bounded Radon measure on $Ω$ and $H(s)$ is a continuous, positive and finite function outside the origin which grows at most as $s^{-γ}$, with $γ\ge0$, near zero.

math.AP↗