Isneri Talavera

Classification of three-way data by the dissimilarity representation

Representation of objects by multi-dimensional data arrays has become very common for many research areas e.g. image analysis, signal processing and chemometrics. In most cases, it is the straightforward representation obtained from sophisticated measurement equipments e.g. radar signal processing. Although the use of this complex data structure could be advantageous for a better discrimination between different classes of objects, it is usually ignored. Classification tools that take this structure into account have hardly been developed yet. Meanwhile, the dissimilarity representation has demonstrated advantages in the solution of classification problems e.g. spectral data. Dissimilarities also allow the representation of multi-dimensional objects in a way that the data structure can be used. This paper introduces their use as a tool for classifying objects originally represented by two-dimensional (2D) arrays. 2D measures can be useful to achieve this representation. A 2D measure to compute the dissimilarity representation from spectral data with this kind of structure is proposed. It is compared to existent 2D measures, in terms of the information that is taken into account and computational complexity.

Support vector regression methods for functional data

Many regression tasks in practice dispose in low gear instance of digitized functions as predictor variables. This has motivated the development of regression methods for functional data. In particular, Naradaya-Watson Kernel (NWK) and Radial Basis Function (RBF) estimators have been recently extended to functional nonparametric regression models. However, these methods do not allow for dimensionality reduction. For this purpose, we introduce Support Vector Regression (SVR) methods for functional data. These are formulated in the framework of approximation in reproducing kernel Hilbert spaces. On this general basis, some of its properties are investigated, emphasizing the construction of nonnegative definite kernels on functional spaces. Furthermore, the performance of SVR for functional variables is shown on a real world benchmark spectrometric data set, as well as comparisons with NWK and RBF methods. Good predictions were obtained by these three approaches, but SVR achieved in addition about 20% reduction of dimensionality.

Dissimilarity representation on functional spectral data for classification

In chemometrics, spectral data are typically represented by vectors of features in spite of the fact that they are usually plotted as functions of e.g. wavelengths and concentrations. In the representation, this functional information is thereby not reflected. Consequently, some characteristics of the data that can be essential for discrimination between samples of different classes or any other analysis are ignored. Examples are the continuity between measured points and the shape of curves. In the Functional Data Analysis (FDA) approach, the functional characteristics of spectra are taken into account by approximating the data by real valued functions, e.g. splines. Another solution is the Dissimilarity Representation (DR), in which classifiers are trained in a space built by dissimilarities with training examples or prototypes of each class. Functional information may be incorporated in the definition of the dissimilarity measure. In this paper we compare the feature‐based representation of chemical spectral data with three other representations: FDA, DR defined on raw data and DR defined on FDA descriptions. We analyze the classification results of these four representations for five data sets of different types, by using different classifiers. We demonstrate the importance of reflecting the functional characteristics of chemical spectral data in their representation, and we show when the presented approaches are more suitable. Copyright

The Representation of Chemical Spectral Data for Classification

The classification of unknown samples is among the most common problems found in chemometrics. For this purpose, a proper representation of the data is very important. Nowadays, chemical spectral data are analyzed as vectors of discretized data where the variables have not connection, and other aspects of their functional nature e.g. shape differences (structural), are also ignored. In this paper, we study some advanced representations for chemical spectral datasets, and for that we make a comparison of the classification results of 4 datasets by using their traditional representation and two other: Functional Data Analysis and Dissimilarity Representation. These approaches allow taking into account the information that is missing in the traditional representation, thus better classification results can be achieved. Some suggestions are made about the more suitable dissimilarity measures to use for chemical spectral data.

A non-Bayesian predictive approach for statistical calibration

A non-Bayesian predictive approach for statistical calibration is introduced. This is based on particularizing to the calibration setting the general definition of non-Bayesian (or frequentist) predictive probability density proposed by Harris [Predictive fit for natural exponential families, Biometrika 76 (1989), pp. 675–684]. The new method is elaborated in detail in case of Gaussian linear univariate calibration. Through asymptotic analysis and simulation results with moderate sample size, it is shown that the non-Bayesian predictive estimator of the unknown parameter of interest in calibration (commonly, a substance concentration) favourably compares with previous estimators such as the classical and inverse estimators, especially for extrapolation problems. A further advantage of the non-Bayesian predictive approach is that it provides not only point estimates but also a predictive likelihood function that allows the researcher to explore the plausibility of any possible parameter value, which is also briefly illustrated. Furthermore, the introduced approach offers a general framework that can be applied for calibrating on the basis of any parametric statistical model, so making it potentially useful for nonlinear and non-Gaussian calibration problems.

The dissimilarity representation as a tool for three-way data classification: a 2D measure

The dissimilarity representation has demonstrated advantages in the solution of classification problems. Meanwhile, the representation of objects by multi-dimensional arrays is necessary in many research areas. However, the development of proper classification tools that take the multi-way structure into account is incipient. This paper introduces the use of the dissimilarity representation as a tool for classifying three-way data, as dissimilarities allow the representation of multidimensional objects in a natural way. As an example, the classification of three-way seismic volcanic data is used. A comparison is made between dissimilarity measures used in different representations of the three-way data. 2D dissimilarity measures for three-way data can be useful.

Classifying Three-way Seismic Volcanic Data by Dissimilarity Representation

Multi-way data analysis is a multivariate data analysis technique having a wide application in some fields. Nevertheless, the development of classification tools for this type of representation is incipient yet. In this paper we study the dissimilarity representation for the classification of three-way data, as dissimilarities allow the representation of multi-dimensional objects in a natural way. As an example, the classification of seismic volcanic events is used. It is shown that in this application classification based on 2D spectrograms, dissimilarities perform better than on 1D spectral features.

Performance evaluation of relevance vector machines as a nonlinear regression method in real-world chemical spectroscopic data

Conventional multivariate calibration methods have been developed in chemometrics, using linear regression techniques as principal component regression (PCR) and partial least squares (PLS). Nevertheless, nonlinear methods such as neural networks have been also introduced, and more recently support vector (SVR) based methods. This paper presents the application of relevance vector machines regression method (RVMR) as an alternative regression technique based on the Bayesian theory, for the prediction of physical-chemical properties from chemical spectroscopic data of different instrumental sources. In terms of measuring the real effectiveness and generalization capability of this approach, a comparison study of its performance with other known regression techniques are presented. The good results obtained in terms of root mean square error of prediction (RMSEP) in the prediction of properties of interest, combined with the high sparseness capability exhibited, make this approach a good alternative to solve multivariate regression problems in practice.

A New Iris Recognition Approach Based on a Functional Representation

This paper proposes the introduction of annular Zernike polynomials for representing iris images data. This representation offers notables advantages like representing the images on a continuous domain that allows the application of Functional Data Analysis techniques, preserving their original nature. In addition, it provides a significant dimensionality reduction of the data, while it still has a high discriminative power. The proposed approach also deals with the occlusion problems that can be present in this type of images. In order to corroborate the effectiveness of the introduced approach, identification experiments were carried out. Iris international databases were used. Some of them are characterized by the presence of severe occlusion problems. Results have shown high recognition accuracy.

Missing Values in Dissimilarity-Based Classification of Multi-way Data

Missing values can occur frequently in many real world situations. Such is the case of multi-way data applications, where objects are usually represented by arrays of 2 or more dimensions e.g.i¾?biomedical signals that can be represented as time-frequency matrices. This lack of attributes tends to influence the analysis of the data. In classification tasks for example, the performance of classifiers is usually deteriorated. Therefore, it is necessary to address this problem before classifiers are built. Although the absence of values is common in these types of data sets, there are just a few studies to tackle this problem for classification purposes. In this paper, we study two approaches to overcome the missing values problem in dissimilarity-based classification of multi-way data. Namely, imputation by factorization, and a modification of the previously proposed Continuous Multi-way Shape measure for comparing multi-way objects.