Linear discriminant analysis

About: Linear discriminant analysis is a research topic. Over the lifetime, 18361 publications have been published within this topic receiving 603195 citations. The topic is also known as: Linear discriminant analysis & LDA.

Emotion recognition based on physiological changes in music listening

Abstract: Little attention has been paid so far to physiological signals for emotion recognition compared to audiovisual emotion channels such as facial expression or speech. This paper investigates the potential of physiological signals as reliable channels for emotion recognition. All essential stages of an automatic recognition system are discussed, from the recording of a physiological data set to a feature-based multiclass classification. In order to collect a physiological data set from multiple subjects over many weeks, we used a musical induction method that spontaneously leads subjects to real emotional states, without any deliberate laboratory setting. Four-channel biosensors were used to measure electromyogram, electrocardiogram, skin conductivity, and respiration changes. A wide range of physiological features from various analysis domains, including time/frequency, entropy, geometric analysis, subband spectra, multiscale entropy, etc., is proposed in order to find the best emotion-relevant features and to correlate them with emotional states. The best features extracted are specified in detail and their effectiveness is proven by classification results. Classification of four musical emotions (positive/high arousal, negative/high arousal, negative/low arousal, and positive/low arousal) is performed by using an extended linear discriminant analysis (pLDA). Furthermore, by exploiting a dichotomic property of the 2D emotion model, we develop a novel scheme of emotion-specific multilevel dichotomous classification (EMDC) and compare its performance with direct multiclass classification using the pLDA. An improved recognition accuracy of 95 percent and 70 percent for subject-dependent and subject-independent classification, respectively, is achieved by using the EMDC scheme.

Discriminant adaptive nearest neighbor classification

Abstract: Nearest neighbour classification expects the class conditional probabilities to be locally constant, and suffers from bias in high dimensions. We propose a locally adaptive form of nearest neighbour classification to try to ameliorate this curse of dimensionality. We use a local linear discriminant analysis to estimate an effective metric for computing neighbourhoods. We determine the local decision boundaries from centroid information, and then shrink neighbourhoods in directions orthogonal to these local decision boundaries, and elongate them parallel to the boundaries. Thereafter, any neighbourhood-based classifier can be employed, using the modified neighbourhoods. The posterior probabilities tend to be more homogeneous in the modified neighbourhoods. We also propose a method for global dimension reduction, that combines local dimension information. In a number of examples, the methods demonstrate the potential for substantial improvements over nearest neighbour classification.

Benchmarking state-of-the-art classification algorithms for credit scoring

Abstract: In this paper, we study the performance of various state-of-the-art classification algorithms applied to eight real-life credit scoring data sets. Some of the data sets originate from major Benelux and UK financial institutions. Different types of classifiers are evaluated and compared. Besides the well-known classification algorithms (eg logistic regression, discriminant analysis, k-nearest neighbour, neural networks and decision trees), this study also investigates the suitability and performance of some recently proposed, advanced kernel-based classification algorithms such as support vector machines and least-squares support vector machines (LS-SVMs). The performance is assessed using the classification accuracy and the area under the receiver operating characteristic curve. Statistically significant performance differences are identified using the appropriate test statistics. It is found that both the LS-SVM and neural network classifiers yield a very good performance, but also simple classifiers such as logistic regression and linear discriminant analysis perform very well for credit scoring.

A Unifying Tool for Linear Multivariate Statistical Methods: The RV-Coefficient

Abstract: Consider two data matrices on the same sample of n individuals, X(p x n), Y(q x n). From these matrices, geometrical representations of the sample are obtained as two configurations of n points, in Rp and Rq It is shown that the RV‐coefficient (Escoufier, 1970, 1973) can be used as a measure of similarity of the two configurations, taking into account the possibly distinct metrics to be used on them to measure the distances between points. The purpose of this paper is to show that most classical methods of linear multivariate statistical analysis can be interpreted as the search for optimal linear transformations or, equivalently, the search for optimal metrics to apply on two data matrices on the same sample; the optimality is defined in terms of the similarity of the corresponding configurations of points, which, in turn, calls for the maximization of the associated RV‐coefficient. The methods studied are principal components, principal components of instrumental variables, multivariate regression, canonical variables, discriminant analysis; they are differentiated by the possible relationships existing between the two data matrices involved and by additional constraints under which the maximum of RV is to be obtained. It is also shown that the RV‐coefficient can be used as a measure of goodness of a solution to the problem of discarding variables.