arXiv subjects

Mauricio Soto-Gomez

Publications and source records attributed to Mauricio Soto-Gomez.

6 recordsLinked to original sources

arXiv2026

Hyperbolic Graph Representation Learning for Differential Diagnosis on Biomedical Knowledge Graphs

Biomedical knowledge graphs combine ontology-derived hierarchies with transversal associations among heterogeneous entities such as phenotypes, diseases, genes, proteins, and patients. This hybrid structure raises the question of whether hyperbolic embeddings, which naturally capture tree-like organization, remain useful beyond purely hierarchical graphs. We present a preliminary study of hyperbolic graph representation learning for Mendelian-disease differential diagnosis on a patient-integrated biomedical graph. Experiments on isolated ontology subgraphs show that hyperbolic models achieve strong performance in substantially lower dimensions than Euclidean baselines. We then evaluate the models on a link-prediction task that ranks candidate diseases for each patient. Results suggest that hyperbolic embeddings can exploit biomedical hierarchical structure while supporting diagnostic reasoning over heterogeneous patient-level graphs.

cs.AI↗

arXiv2026

T-Robinson Spaces: Structure, Recognition, and Applications to Real Data

We study \emph{$T$-Robinson spaces}, a tree-based generalization of Robinson spaces in which every path of a compatible tree induces a Robinson subspace. This framework extends the classical notion of Robinsonian representations from linear orderings to tree structures, allowing the modeling of hierarchical and branching data. We establish a complete combinatorial characterization of $T$-Robinson spaces by proving their equivalence with several graph- and hypergraph-theoretic properties. In particular, we show that a dissimilarity space is $T$-Robinson if and only if all its level graphs are dually chordal with a common compatible tree. Combined with the characterization of hypertrees established by Brucker~\cite{brucker2005hypertrees}, this yields the equivalent characterization in terms of the associated cluster, ball, and 2-ball hypergraphs being hypertrees. Building upon these structural results, we develop a recognition algorithm with complexity $O(K n^{2})$, where $K$ denotes the number of minimum spanning trees of the dissimilarity space, improving upon existing hypertree-based approaches whenever $K$ remains moderate. We further introduce a quantitative measure of $T$-Robinson structure that evaluates the extent to which an arbitrary dissimilarity space admits a tree-like representation. Finally, we discuss applications to real-world datasets, illustrating how $T$-Robinson spaces provide an interpretable framework for analyzing and organizing relational data.

cs.DM↗

arXiv2026

Robinson spaces and their representation in low-dimensional metric spaces

Robinson spaces are structures equipped with a total order that encodes comparative dissimilarity relationships. We study the problem of representing Robinson dissimilarity spaces into low-dimensional metric spaces. These representations aim to preserve the relative dissimilarity relationships between elements rather than their exact values. While low dimensional Euclidean spaces such as $\mathbb{R}^1$ and $\mathbb{R}^2$ are natural candidates for such embeddings, previous work has shown that not all Robinson spaces admit a valid embedding in the real line that respects their structural constraints. Motivated by this limitation, we explore the broader class of real trees, which retain low-dimensional interpretability while allowing greater flexibility. To address the embedding problem, we develop two key tools: a combinatorial representation of Robinson spaces and a topological characterization of caterpillars, a restricted class of real trees. These tools enable a formulation of the embedding problem as a linear program, providing both computational and theoretical insights. We prove that some subclasses of Robinson spaces always admit embeddings in a caterpillar, and we establish the existence of Robinson spaces that cannot be embedded in any real tree. These results clarify the geometric limitations of representing ordered dissimilarity structures and open new directions for studying the interaction between dissimilarity, order, and metric geometry.

math.CO↗

arXiv2025

Hybrid Quantum-Classical Walks for Graph Representation Learning in Community Detection

Graph Representation Learning (GRL) has emerged as a cornerstone technique for analysing complex, networked data across diverse domains, including biological systems, social networks, and data analysis. Traditional GRL methods often struggle to capture intricate relationships within complex graphs, particularly those exhibiting non-trivial structural properties such as power-law distributions or hierarchical structures. This paper introduces a novel quantum-inspired algorithm for GRL, utilizing hybrid Quantum-Classical Walks to overcome these limitations. Our approach combines the benefits of both quantum and classical dynamics, allowing the walker to simultaneously explore both highly local and far-reaching connections within the graph. Preliminary results for a case study in network community detection shows that this hybrid dynamic enables the algorithm to adapt effectively to complex graph topologies, offering a robust and versatile solution for GRL tasks.

quant-ph↗

arXiv2024

Het-node2vec: second order random walk sampling for heterogeneous multigraphs embedding

Many real-world problems are naturally modeled as heterogeneous graphs, where nodes and edges represent multiple types of entities and relations. Existing learning models for heterogeneous graph representation usually depend on the computation of specific and user-defined heterogeneous paths, or in the application of large and often not scalable deep neural network architectures. We propose Het-node2vec, an extension of the node2vec algorithm, designed for embedding heterogeneous graphs. Het-node2vec addresses the challenge of capturing the topological and structural characteristics of graphs and the semantic information underlying the different types of nodes and edges of heterogeneous graphs, by introducing a simple stochastic node and edge type switching strategy in second order random walk processes. The proposed approach also introduces an ''attention mechanism'' to focus the random walks on specific node and edge types, thus allowing more accurate embeddings and more focused predictions on specific node and edge types of interest. Empirical results on benchmark datasets show that Hetnode2vec achieves comparable or superior performance with respect to state-of-the-art methods for heterogeneous graphs in node label and edge prediction tasks.

cs.LG↗

arXiv2023

RNA-KG: An ontology-based knowledge graph for representing interactions involving RNA molecules

The "RNA world" represents a novel frontier for the study of fundamental biological processes and human diseases and is paving the way for the development of new drugs tailored to the patient's biomolecular characteristics. Although scientific data about coding and non-coding RNA molecules are continuously produced and available from public repositories, they are scattered across different databases and a centralized, uniform, and semantically consistent representation of the "RNA world" is still lacking. We propose RNA-KG, a knowledge graph encompassing biological knowledge about RNAs gathered from more than 50 public databases, integrating functional relationships with genes, proteins, and chemicals and ontologically grounded biomedical concepts. To develop RNA-KG, we first identified, pre-processed, and characterized each data source; next, we built a meta-graph that provides an ontological description of the KG by representing all the bio-molecular entities and medical concepts of interest in this domain, as well as the types of interactions connecting them. Finally, we leveraged an instance-based semantically abstracted knowledge model to specify the ontological alignment according to which RNA-KG was generated. RNA-KG can be downloaded in different formats and also queried by a SPARQL endpoint. A thorough topological analysis of the resulting heterogeneous graph provides further insights into the characteristics of the "RNA world". RNA-KG can be both directly explored and visualized, and/or analyzed by applying computational methods to infer bio-medical knowledge from its heterogeneous nodes and edges. The resource can be easily updated with new experimental data, and specific views of the overall KG can be extracted according to the bio-medical problem to be studied.

cs.CE↗