Comparing Several Methods of Discriminant Analysis on the Case of Wine Data

2000 Mathematics Subject Classification: 62H30, 62J20, 62P12, 68T99

On the application of the probabilistic linear discriminant analysis to face recognition across expression

Facial expression is one of the main issues of face recognition in uncontrolled environments. In this paper, we apply the probabilistic linear discriminant analysis (PLDA) method to recognize faces across expressions. Several PLDA approaches are tested and cross-evaluated on the Cohn-Kanade and JAFFE databases. With less samples per gallery subject, high recognition rates comparable to previous works have been achieved indicating the robustness of the approaches. Among the approaches, the mixture of PLDAs has demonstrated better performances. The experimental results also indicate that facial regions around the cheeks, eyes, and eyebrows are more discriminative than regions around the mouth, jaw, chin, and nose.

Heteroscedastic probabilistic linear discriminant analysis for manifold learning in video-based face recognition

To recognize faces in video, face appearances have been widely modeled as piece-wise local linear models which linearly approximate the smooth yet non-linear low dimensional face appearance manifolds. The choice of representations of the local models is crucial. Most of the existing methods learn each local model individually meaning that they only anticipate variations within each class. In this work, we propose to represent local models as Gaussian distributions which are learned simultaneously using the heteroscedastic probabilistic linear discriminant analysis (PLDA). Each gallery video is therefore represented as a collection of such distributions. With the PLDA, not only the within-class variations are estimated during the training, the separability between classes is also maximized leading to an improved discrimination. The heteroscedastic PLDA itself is adapted from the standard PLDA to approximate face appearance manifolds more accurately. Instead of assuming a single global within-class covariance, the heteroscedastic PLDA learns different within-class covariances specific to each local model. In the recognition phase, a probe video is matched against gallery samples through the fusion of point-to-model distances. Experiments on the Honda and MoBo datasets have shown the merit of the proposed method which achieves better performance than the state-of-the-art technique.

Predicting survival of western rock lobsters Panulirus cygnus using discriminant analysis of hemolymph parameters taken immediately following simulated handling treatments

Instances of morbidity amongst rock lobsters (Panulirus cygnus) arriving at factories in Western Australia (WA) have been attributed to stress during post-harvest handling. This study used discriminant analysis to determine whether physiological correlates of stress following a period of simulated post-harvest handling had any validity as predictors of future rejection or morbidity of western rock lobsters. Groups of 230 western rock lobsters were stored for 6 h in five environments (submerged/flowing sea water, submerged/re-circulating sea water, humid air, flowing sea water spray, and re-circulated sea water spray). The experiment was conducted in late spring (ambient sea water 22°C), and repeated again in early autumn (ambient sea water 26°C). After 6 h treatment, each lobster was graded for acceptability for live export, numbered, and its hemolymph was sampled. The samples were analysed for a number of physiological and health status parameters. The lobsters were then stored for a week in tanks in the live lobster factory to record mortality. The mortality of lobsters in the factory was associated with earlier deviations in hemolymph parameters as they emerged from the storage treatments. Discriminant analysis (DA) of the hemolymph assays enabled the fate of 80-90% of the lobsters to be correctly categorised within each experiment. However, functions derived from one experiment were less accurate at predicting mortality when applied to the other experiments. One of the reasons for this was the higher mortality and the more severe patho-physiological changes observed in lobsters stored in humid air or sprays at the higher temperature. The analysis identified lactate accumulation during emersion and associated physiological and hemocyte-related effects as a major correlate of mortality. Reducing these deviations, for example by submerged transport, is expected to ensure high levels of survival. None of the indicators tested predicted mortality with total accuracy. The simplest and most accurate means of comparing emersed treatments was to count the mortality afterwards.

Incremental Linear Discriminant Analysis Using Sufficient Spanning Sets and Its Applications

This paper presents an incremental learning solution for Linear Discriminant Analysis (LDA) and its applications to object recognition problems. We apply the sufficient spanning set approximation in three steps i.e. update for the total scatter matrix, between-class scatter matrix and the projected data matrix, which leads an online solution which closely agrees with the batch solution in accuracy while significantly reducing the computational complexity. The algorithm yields an efficient solution to incremental LDA even when the number of classes as well as the set size is large. The incremental LDA method has been also shown useful for semi-supervised online learning. Label propagation is done by integrating the incremental LDA into an EM framework. The method has been demonstrated in the task of merging large datasets which were collected during MPEG standardization for face image retrieval, face authentication using the BANCA dataset, and object categorisation using the Caltech101 dataset. © 2010 Springer Science+Business Media, LLC.

Discriminant analysis for mesh selectivity studies

Discriminant analysis takes into consideration the natural correlation existing between different characteristics of fish when studying mesh selectivity. Some specimen data are presented for two different sets of fish and it is shown that the discriminant analysis shows a significant difference between the two sets where F test failed.

Discriminant analysis of selected variables in the adoption of fish curing

Discriminant functions were worked out for adoption or non-adoption of five improved practices in fish curing. Four variables measured quantitatively formed the basis for discrimination. In four out of five equations, the selected variables were found to discriminate significantly between the adopters and non-adopters.

Incremental pairwise discriminant analysis based visual tracking

The distinguishment between the object appearance and the background is the useful cues available for visual tracking in which the discriminant analysis is widely applied However due to the diversity of the background observation there are not adequate negative samples from the background which usually lead the discriminant method to tracking failure Thus a natural solution is to construct an object-background pair constrained by the spatial structure which could not only reduce the neg-sample number but also make full use of the background information surrounding the object However this Idea is threatened by the variant of both the object appearance and the spatial-constrained background observation especially when the background shifts as the moving of the object Thus an Incremental pairwise discriminant subspace is constructed in this paper to delineate the variant of the distinguishment In order to maintain the correct the ability of correctly describing the subspace we enforce two novel constraints for the optimal adaptation (1) pairwise data discriminant constraint and (2) subspace smoothness The experimental results demonstrate that the proposed approach can alleviate adaptation drift and achieve better visual tracking results for a large variety of nonstationary scenes (C) 2010 Elsevier B V All rights reserved

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.