Myriam Herrera

Linear dimensionality reduction by maximizing the Chernoff distance in the transformed space

Linear dimensionality reduction (LDR) techniques are quite important in pattern recognition due to their linear time complexity and simplicity. In this paper, we present a novel LDR technique which, though linear, aims to maximize the Chernoff distance in the transformed space; thus, augmenting the class separability in such a space. We present the corresponding criterion, which is maximized via a gradient-based algorithm, and provide convergence and initialization proofs. We have performed a comprehensive performance analysis of our method combined with two well-known classifiers, linear and quadratic, on synthetic and real-life data, and compared it with other LDR techniques. The results on synthetic and standard real-life data sets show that the proposed criterion outperforms the latter when combined with both linear and quadratic classifiers.

A multivariate geostatistical approach for landscape classification from remotely sensed image data

This paper proposes a methodology to address the classification of images that have been acquired from remote sensors. One common problem in classification is the high dimensionality of multivariate characteristics. The methodology we propose consists of reducing the dimensionality of the spectral bands associated with a multispectral satellite image. Such dimensionality reduction is accomplished by the use of the divergence of a modified Mahalanobis distance. Instead of using the covariance matrix of a multivariate spatial process, the codispersion matrix is considered which have some desirable asymptotic properties under very precise conditions. The consistency and asymptotic normality hold for a general class of processes that are a natural extension of the one-dimensional spatial processes for which the asymptotic properties were first established. The results allow the selection of a set of spectral bands to produce the highest value of divergence. Then, a supervised maximum likelihood method using the selected spectral bands is employed for landscape classification. An application with a real LANDSAT image is introduced to explore and visualize how our method works in practice.

A new approach to multi-class linear dimensionality reduction

Linear dimensionality reduction (LDR) is quite important in pattern recognition due to its efficiency and low computational complexity. In this paper, we extend the two-class Chernoff-based LDR method to deal with multiple classes. We introduce the criterion, as well as the algorithm that maximizes such a criterion. The proof of convergence of the algorithm and a formal procedure to initialize the parameters of the algorithm are also given. We present empirical simulations on standard well-known multi-class datasets drawn from the UCI machine learning repository. The results show that the proposed LDR coupled with a quadratic classifier outperforms the traditional LDR schemes.

A new linear dimensionality reduction technique based on chernoff distance

A new linear dimensionality reduction (LDR) technique for pattern classification and machine learning is presented, which, though linear, aims at maximizing the Chernoff distance in the transformed space. The corresponding two-class criterion, which is maximized via a gradient-based algorithm, is presented and initialization procedures are also discussed. Empirical results of this and traditional LDR approaches combined with two well-known classifiers, linear and quadratic, on synthetic and real-life data show that the proposed criterion outperforms the traditional schemes.

On the performance of chernoff-distance-based linear dimensionality reduction techniques

We present a performance analysis of three linear dimensionality reduction techniques: Fishers discriminant analysis (FDA), and two methods introduced recently based on the Chernoff distance between two distributions, the Loog and Duin (LD) method, which aims to maximize a criterion derived from the Chernoff distance in the original space, and the one introduced by Rueda and Herrera (RH), which aims to maximize the Chernoff distance in the transformed space. A comprehensive performance analysis of these methods combined with two well-known classifiers, linear and quadratic, on synthetic and real-life data shows that LD and RH outperform FDA, specially in the quadratic classifier, which is strongly related to the Chernoff distance in the transformed space. In the case of the linear classifier, the superiority of RH over the other two methods is also demonstrated.

Tipología influyente en el rendimiento académico de alumnos universitarios

The present work addresses a statistical report focused on characterizing the academic performance of university students, from the determination of associated variables, applying statistical techniques of Multivariate Analysis. The analyzes performed are based on data from a survey conducted in 2015, among the students of the Faculty of Exact, Physical and Natural Sciences and the Faculty of Philosophy, Humanities and Arts of the National University of San Juan. Through a Factorial Analysis of Multiple Correspondences, Cluster Analysis and Logistic Discrimination Analysis, it was possible to identify types of students and infl uential variables that diff erentiate the students according to their performance. The results contribute to bring tools that allow a valid diagnosis to eff ectively guide the interventions made by the educational institution.

A theoretical comparison of two-class Fisher's and heteroscedastic linear dimensionality reduction schemes

We present a theoretical analysis for comparing two linear dimensionality reduction (LDR) techniques for two classes, a homoscedastic LDR scheme, Fishers discriminant (FD), and a heteroscedastic LDR scheme, Loog-Duin (LD). We formalize the necessary and sufficient conditions for which the FD and LD criteria are maximized for the same linear transformation. To derive these conditions, we first show that the two criteria preserve the same maximum values after a diagonalization process is applied. We derive the necessary and sufficient conditions for various cases, including coincident covariance matrices, coincident prior probabilities, and for when one of the covariances is the identity matrix. We empirically show that the conditions are statistically related to the classification error for a post-processing one-dimensional quadratic classifier and the Chernoff distance in the transformed space.