Daniel López-Montero

Daniel López-Montero, Antonio Álvarez-López, Marcos Matabuena

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse structures and data geometries, including $L^2$-functional data and random graphs in Laplacian spaces arising in modern medical applications.

Daniel López-Montero, José L. Álvarez-Aldana, Alicia Morales-Martínez et al.

This paper aims to provide an innovative machine learning-based solution to automate security testing tasks for web applications, ensuring the correct functioning of all components while reducing project maintenance costs. Reinforcement Learning is proposed to select and prioritize tools and optimize the testing path. The presented approach utilizes a simulated webpage along with its network topology to train the agent. Additionally, the model leverages Geometric Deep Learning to create priors that reduce the search space and improve learning convergence. The validation and testing process was conducted on real-world vulnerable web pages commonly used by human hackers for learning. As a result of this study, a reinforcement learning algorithm was developed that maximizes the number of vulnerabilities found while minimizing the number of steps required