Linear discriminant analysis with misallocation in training samples

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule

Incremental and Decremental Nonparametric Discriminant Analysis for Face Recognition

Nonparametric Discriminant Analysis (NDA) possesses inherent advantages over Linear Discriminant Analysis (LDA) such as capturing the boundary structure of samples and avoiding matrix inversion. In this paper, we present a novel method for constructing an updated Nonparametric Discriminant Analysis (NDA) model for face recognition. The proposed method is applicable to scenarios where bursts of data samples are added to the existing model in random chunks. Also, the samples which degrade the performance of the model need to be removed. For both of these problems, we propose incremental NDA (INDA) and decremental NDA (DNDA) respectively. Experimental results on four publicly available datasets viz. AR, PIE, ORL and Yale show the efficacy of the proposed method. Also, the proposed method requires less computation time in comparison to batch NDA which makes it suitable for real time applications

Colour image processing and texture analysis on images of porterhouse steak meat

This paper outlines two colour image processing and texture analysis techniques applied to meat images and assessment of error due to the use of JPEG compression at image capture. JPEG error analysis was performed by capturing TIFF and JPEG images, then calculating the RMS difference and applying a calibration between block boundary features and subjective visual JPEG scores. Both scores indicated high JPEG quality. Correction of JPEG blocking error was trialled and found to produce minimal improvement in the RMS difference. The texture analysis methods used were singular value decomposition over pixel blocks and complex cell analysis. The block singular values were classified as meat or non- meat by Fisher linear discriminant analysis with the colour image processing result used as ‘truth.’ Using receiver operator characteristic (ROC) analysis, an area under the ROC curve of 0.996 was obtained, demonstrating good correspondence between the colour image processing and the singular values. The complex cell analysis indicated a ‘texture angle’ expected from human inspection

Face recognition using nonparametric-weighted Fisherfaces

This study presents an appearance-based face recognition scheme called the nonparametric-weighted Fisherfaces (NW-Fisherfaces). Pixels in a facial image are considered as coordinates in a high-dimensional space and are transformed into a face subspace for analysis by using nonparametric-weighted feature extraction (NWFE). According to previous studies of hyperspectral image classification, NWFE is a powerful tool for extracting hyperspectral image features. The Fisherfaces method maximizes the ratio of between-class scatter to that of within-class scatter. In this study, the proposed NW-Fisherfaces weighted the between-class scatter to emphasize the boundary structure of the transformed face subspace and, therefore, enhances the separability for different persons' face. The proposed NW-Fisherfaces was compared with Orthogonal Laplacianfaces, Eigenfaces, Fisherfaces, direct linear discriminant analysis, and null space linear discriminant analysis methods for tests on five facial databases. Experimental results showed that the proposed approach outperforms other feature extraction methods for most databases. © 2012 Li et al

Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.Comment: 30 pages, 2 figure