David Becerra-Alonso

Magnetization Dynamics Under a Quasiperiodic Magnetic Field

In the present work, we study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a time dependent magnetic field using the Landau-Lifshitz-Gilbert equation. In particular, we study the case when the magnetic field consists in two terms. One is perpendicular to the anisotropy direction and has quasiperiodic time dependence, while the other term is constant and parallel to the anisotropy direction. We numerically characterize the dynamical behavior of the system by monitoring the Lyapunov exponents, and by calculating Poincaré sections and Fourier spectra. In addition, we calculate analytically the corresponding Melnikov function which gives us the bifurcations of the homoclinic orbits. We find a rather complicated landscape of sometimes closely intermingled chaotic and non-chaotic areas in parameters space. Finally, we show that the system exhibits strange nonchaotic attractors.

Toward a study of gene regulatory constraints to morphological evolution of the Drosophila ocellar region

The morphology and function of organs depend on coordinated changes in gene expression during development. These changes are controlled by transcription factors, signaling pathways, and their regulatory interactions, which are represented by gene regulatory networks (GRNs). Therefore, the structure of an organ GRN restricts the morphological and functional variations that the organ can experience—its potential morphospace. Therefore, two important questions arise when studying any GRN: what is the predicted available morphospace and what are the regulatory linkages that contribute the most to control morphological variation within this space. Here, we explore these questions by analyzing a small “three-node” GRN model that captures the Hh-driven regulatory interactions controlling a simple visual structure: the ocellar region of Drosophila. Analysis of the model predicts that random variation of model parameters results in a specific non-random distribution of morphological variants. Study of a limited sample of drosophilids and other dipterans finds a correspondence between the predicted phenotypic range and that found in nature. As an alternative to simulations, we apply Bayesian networks methods in order to identify the set of parameters with the largest contribution to morphological variation. Our results predict the potential morphological space of the ocellar complex and identify likely candidate processes to be responsible for ocellar morphological evolution using Bayesian networks. We further discuss the assumptions that the approach we have taken entails and their validity.

A two dimensional accuracy-based measure for classification performance

Abstract Accuracy has been used traditionally to evaluate the performance of classifiers. However, it is well known that accuracy is not able to capture all the different factors that characterize the performance of a multiclass classifier. In this manuscript, accuracy is studied and analyzed as a weighted average of the classification rate of each class. This perspective allows us to propose the dispersion of the classification rate of each class as its complementary measure. In this sense, a graphical performance metric, which is defined in a two dimensional space composed by accuracy and dispersion, is proposed to evaluate the performance of classifiers. We show that the combined values of accuracy and dispersion must fall within a clearly bounded two dimensional region, different for each problem. The nature of this region depends only on the a priori probability of each class, and not on the classifier used. Thus, the performance of multiclassifiers is represented in a two dimensional space where the models can be compared in a more fair manner, providing greater awareness of the strategies that are more accurate when trying to improve the performance of a classifier. Furthermore we experimentally analyze the behavior of seven different performance metrics based on the computation of the confusion matrix values in several scenarios, identifying clusters and relationships between measures. As shown in the experimentation, the graphical metric proposed is specially suitable in challenging, highly imbalanced and with a high number of classes datasets. The approach proposed is a novel point of view to address the evaluation of multiclassifiers and it is an alternative to other evaluation measures used in machine learning.

Evolutionary extreme learning machine for ordinal regression

This paper presents a novel method for generally adapting ordinal classification models. We essentially rely on the assumption that the ordinal structure of the set of class labels is also reflected in the topology of the instance space. Under this assumption, this paper proposes an algorithm in two phases that takes advantage of the ordinal structure of the dataset and tries to translate this ordinal structure in the total ordered real line and then to rank the patterns of the dataset. The first phase makes a projection of the ordinal structure of the feature space. Next, an evolutionary algorithm tunes the first projection working with the misclassified patterns near the border of their right class. The results obtained in seven ordinal datasets are competitive in comparison with state-of-the-art algorithms in ordinal regression, but with much less computational time in datasets with many patterns.

A Preliminary Study of Diversity in Extreme Learning Machines Ensembles

In this paper, the neural network version of Extreme Learning Machine (ELM) is used as a base learner for an ensemble meta-algorithm which promotes diversity explicitly in the ELM loss function. The cost function proposed encourages orthogonality (scalar product) in the parameter space. Other ensemble-based meta-algorithms from AdaBoost family are used for comparison purposes. Both accuracy and diversity presented in our proposal are competitive, thus reinforcing the idea of introducing diversity explicitly.

Gene regulatory constraints to morphological evolution of the Drosophila ocellar region

The morphology and function of organs depend on coordinated changes in gene expression during development. These changes are controlled by transcription factors, signaling pathways and their regulatory interactions, which are represented by gene regulatory networks (GRNs). Therefore, the structure of an organ GRN restricts the morphological and functional variations that the organ can experience –its potential morphospace. Therefore, two important questions arise when studying any GRN: what is the predicted available morphospace and what are the regulatory linkages that contribute the most to control morphological variation within this space. Here, we explore these questions by analyzing a small “3-node” GRN model that captures the Hh-driven regulatory interactions controlling a simple visual structure: the ocellar region of Drosophila. Analysis of the model predicts that random variation of model parameters results in a specific non-random distribution of morphological variants. Study of a limited sample of Drosophilids and other dipterans finds a correspondence between the predicted phenotypic range and that found in nature. As an alternative to simulations, we apply Bayesian Networks methods in order to identify the set of parameters with the largest contribution to morphological variation. Our results predict the potential morphological space of the ocellar complex, and identify likely candidate processes to be responsible for ocellar morphological evolution using Bayesian networks. We further discuss the assumptions that the approach we have taken entails and their validity.

Feature Grouping and Selection on High-Dimensional Microarray Data

In classification tasks, as the dimensionality increases, the performance of the classifier improves until an optimal number of features is reached. Further increases of the dimensionality without increasing the number of training samples results in a degradation in classifier performance. This fact, called the curse of dimensionality, has become more relevant with the advent of larger datasets and the demands of Knowledge Discovery from Big Data. In this context, feature grouping has become an effective approach to provide additional information about relationships between features. In this work, we propose a greedy strategy, called GreedyPGG, that groups features based on the concept of Markov blankets. To such aim, we introduce the idea of predominant group of features. We also present an adaptation of the Variable Neighborhood Search (VNS) to high-dimensional feature selection that uses the GreedyPGG to reduce the search space. We test the effectiveness of the GreedyPGG on synthetic datasets and the VNS on microarray datasets. We compare VNS with popular and competitive strategies. Results show that GreedyPGG groups correlated features in an efficient way and that VNS is a competitive strategy, capable of finding a small number of features with high predictive power.

Stochastic Sensitivity Analysis Using Extreme Learning Machine

The Extreme Learning Machine classifier is used to perform the perturbative method known as Sensitivity Analysis. The method returns a measure of class sensitivity per attribute. The results show a strong consistency for classifiers with different random input weights. In order to present the results obtained in an intuitive way, two forms of representation are proposed and contrasted against each other. The relevance of both attributes and classes is discussed. Class stability and the ease with which a pattern can be correctly classified are inferred from the results. The method can be used with any classifier that can be replicated with different random seeds.

Numerical variable reconstruction from ordinal categories based on probability distributions

Ordinal classification problems are an active research area in the machine learning community. Many previous works adapted state-of-art nominal classifiers to improve ordinal classification so that the method can take advantage of the ordinal structure of the dataset. However, these method improvements often rely upon a complex mathematical basis and they usually are attached to the training algorithm and model. This paper presents a novel method for generally adapting classification and regression models, such as artificial neural networks or support vector machines. The ordinal classification problem is reformulated as a regression problem by the reconstruction of a numerical variable which represents the different ordered class labels. Despite the simplicity and generality of the method, results are competitive in comparison with very specific methods for ordinal regression.