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.

Using Subspace-Based Template Attacks to Compare and Combine Power and Electromagnetic Information Leakages

Abstract: The power consumption and electromagnetic radiation are among the most extensively used side-channels for analyzing physically observable cryptographic devices. This paper tackles three important questions in this respect. First, we compare the effectiveness of these two side-channels. We investigate the common belief that electromagnetic leakages lead to more powerful attacks than their power consumption counterpart. Second we study the best combination of the power and electromagnetic leakages. A quantified analysis based on sound information theoretic and security metrics is provided for these purposes. Third, we evaluate the effectiveness of two data dimensionality reduction techniques for constructing subspace-based template attacks. Selecting automatically the meaningful time samples in side-channel leakage traces is an important problem in the application of template attacks and it usually relies on heuristics. We show how classical statistical tools such as Principal Component Analysis and Fisher Linear Discriminant Analysis can be used for efficiently preprocessing the leakage traces.

Analysis of Co-Occurrence Texture Statistics as a Function of Gray-Level Quantization for Classifying Breast Ultrasound

Abstract: In this paper, we investigated the behavior of 22 co-occurrence statistics combined to six gray-scale quantization levels to classify breast lesions on ultrasound (BUS) images. The database of 436 BUS images used in this investigation was formed by 217 carcinoma and 219 benign lesions images. The region delimited by a minimum bounding rectangle around the lesion was employed to calculate the gray-level co-occurrence matrix (GLCM). Next, 22 co-occurrence statistics were computed regarding six quantization levels (8, 16, 32, 64, 128, and 256), four orientations (0° , 45° , 90° , and 135° ), and ten distances (1, 2,...,10 pixels). Also, to reduce feature space dimensionality, texture descriptors of the same distance were averaged over all orientations, which is a common practice in the literature. Thereafter, the feature space was ranked using mutual information technique with minimal-redundancy-maximal-relevance (mRMR) criterion. Fisher linear discriminant analysis (FLDA) was applied to assess the discrimination power of texture features, by adding the first m-ranked features to the classification procedure iteratively until all of them were considered. The area under ROC curve (AUC) was used as figure of merit to measure the performance of the classifier. It was observed that averaging texture descriptors of a same distance impacts negatively the classification performance, since the best AUC of 0.81 was achieved with 32 gray levels and 109 features. On the other hand, regarding the single texture features (i.e., without averaging procedure), the quantization level does not impact the discrimination power, since AUC=0.87 was obtained for the six quantization levels. Moreover, the number of features was reduced (between 17 and 24 features). The texture descriptors that contributed notably to distinguish breast lesions were contrast and correlation computed from GLCMs with orientation of 90° and distance more than five pixels.

Learning Compact and Discriminative Stacked Autoencoder for Hyperspectral Image Classification

Abstract: As one of the fundamental research topics in remote sensing image analysis, hyperspectral image (HSI) classification has been extensively studied so far. However, how to discriminatively learn a low-dimensional feature space, in which the mapped features have small within-class scatter and big between-class separation, is still a challenging problem. To address this issue, this paper proposes an effective framework, named compact and discriminative stacked autoencoder (CDSAE), for HSI classification. The proposed CDSAE framework comprises two stages with different optimization objectives, which can learn discriminative low-dimensional feature mappings and train an effective classifier progressively. First, we impose a local Fisher discriminant regularization on each hidden layer of stacked autoencoder (SAE) to train discriminative SAE (DSAE) by minimizing reconstruction error. This stage can learn feature mappings, in which the pixels from the same land-cover class are mapped as nearly as possible and the pixels from different land-cover categories are separated by a large margin. Second, we learn an effective classifier and meanwhile update DSAE with a local Fisher discriminant regularization being embedded on the top of feature representations. Moreover, to learn a compact DSAE with as small number of hidden neurons as possible, we impose a diversity regularization on the hidden neurons of DSAE to balance the feature dimensionality and the feature representation capability. The experimental results on three widely-used HSI data sets and comprehensive comparisons with existing methods demonstrate that our proposed method is effective.

Discriminatory Analysis - Nonparametric Discrimination: Small Sample Performance

Abstract: : A classification procedure is worked out for the following situations: Two large samples, one from each of two populations, have been observed. An individual of unknown origin is to be classified as belonging to the first population if the majority of a specified odd number of individuals closet to the individual in question belong to the first population. This method has optimum properties when the number of closest individuals is permitted to be very large. For certain cases involving multivariate normal distributions with the same covariance matrix, the probabilities of possible misclassification have been computed and compared with those of the discriminant function method.

Face Recognition Using Kernel Ridge Regression

Abstract: In this paper, we present novel ridge regression (RR) and kernel ridge regression (KRR) techniques for multivariate labels and apply the methods to the problem efface recognition. Motivated by the fact that the regular simplex vertices are separate points with highest degree of symmetry, we choose such vertices as the targets for the distinct individuals in recognition and apply RR or KRR to map the training face images into a face subspace where the training images from each individual will locate near their individual targets. We identify the new face image by mapping it into this face subspace and comparing its distance to all individual targets. An efficient cross-validation algorithm is also provided for selecting the regularization and kernel parameters. Experiments were conducted on two face databases and the results demonstrate that the proposed algorithm significantly outperforms the three popular linear face recognition techniques (Eigenfaces, Fisher faces and Laplacian faces) and also performs comparably with the recently developed Orthogonal Laplacian faces with the advantage of computational speed. Experimental results also demonstrate that KRR outperforms RR as expected since KRR can utilize the nonlinear structure of the face images. Although we concentrate on face recognition in this paper, the proposed method is general and may be applied for general multi-category classification problems.