María Florencia Acosta

arXiv2026

Value-Aware Product Recommendation by Customer Segmentation using a suitable High-Dimensional Similarity Measure

This paper presents a novel value-aware approach to product recommendation that simultaneously addresses the high dimensionality and sparsity of user-item data while explicitly incorporating the contribution of each product and user to overall sales revenue. The proposed framework encodes revenue contributions in the user-item matrix and computes customer similarity directly on this basis using suitable distance measures. This enables the segmentation of users according to the revenue-based similarity of their purchase baskets and supports recommendations aligned with profitability objectives. We compare conventional similarity metrics with a novel alternative tailored to high-dimensional contexts and propose three recommendation strategies based on revenue share, product popularity, and expected profit generation. The effectiveness of the proposed method is validated through simulation experiments and a real-world application using the UCI Online Retail dataset.

cs.IR↗

arXiv2023

On the structure of the diffusion distance induced by the fractional dyadic Laplacian

In this note we explore the structure of the diffusion metric of Coifman-Lafon determined by fractional dyadic Laplacians. The main result is that, for each ${t>0}$, the diffusion metric is a function of the dyadic distance, given in $\mathbb{R}^+$ by $δ(x,y) = \inf\{|I|: I \text{ is a dyadic interval containing } x \text{ and } y\}$. Even if these functions of $δ$ are not equivalent to $δ$, the families of balls are the same, to wit, the dyadic intervals.

math.AP↗

arXiv2020

On Frink's type metrization of weighted graphs

Using the technique of the metrization theorem of uniformities with countable bases, in this note we provide, test and compare an explicit algorithm to produce a metric $d(x,y)$ between the vertices $x$ and $y$ of an affinity weighted undirected graph.

math.DS↗