Javier Díaz-Rozo

Cristian Puerto-Santana, Javier Diaz-Rozo, Carlos Puerto-Santana et al.

This article proposes a novel methodology for the classification of transient and stationary regimes in dynamic systems. Several sensor-based solutions for regime classification in the literature require the setting of several parameters, or are not suitable for scenarios involving multivariate systems that may contain periodic signals. The proposed method introduces a spatial curve representation of the considered system based on its sample mathematical moments. Then, by connecting concepts of stability theory, geometrical properties of spatial curves and stationary stochastic processes, two regime classifiers are designed using the arc length and the curvatures of the proposed curve. Both classifiers are capable of describing and detecting transient regimes, considering behaviors such as: multivariate asymptotically, marginally stability, and cyclostationarity. Furthermore, a quantitative comparison in performance and computation resources of the proposed classifiers against existing classifiers in the literature illustrates that the proposed regime classifier based on the arc length outperforms other techniques in classifying transient regimes for simulated linear, non-linear, and discontinuous multivariate systems under the specified studied conditions.

Rafael Sojo, Javier Díaz-Rozo, Concha Bielza et al.

This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability distributions are developed for the new binned semiparametric Bayesian networks, the sparse binned kernel density estimation and the Fourier kernel density estimation. These two probability distributions address the curse of dimensionality, which typically impacts binned models, by using sparse tensors and restricting the number of parent nodes in conditional probability calculations. To evaluate the proposal, we perform a complexity analysis and conduct several comparative experiments using synthetic data and datasets from the UCI Machine Learning repository. The experiments include different binning rules, parent restrictions, grid sizes, and number of instances to get a holistic view of the model's behavior. As a result, our binned semiparametric Bayesian networks achieve structural learning and log-likelihood estimations with no statistically significant differences compared to the semiparametric Bayesian networks, but at a much higher speed. Thus, the new binned semiparametric Bayesian networks prove to be a reliable and more efficient alternative to their non-binned counterparts.