Graph Scaling Cut with L1-Norm for Classification of Hyperspectral Images

In this paper, we propose an L1 normalized graph based dimensionality reduction method for Hyperspectral images, called as L1-Scaling Cut (L1-SC). The underlying idea of this method is to generate the optimal projection matrix by retaining the original distribution of the data. Though L2-norm is generally preferred for computation, it is sensitive to noise and outliers. However, L1-norm is robust to them. Therefore, we obtain the optimal projection matrix by maximizing the ratio of between-class dispersion to within-class dispersion using L1-norm. Furthermore, an iterative algorithm is described to solve the optimization problem. The experimental results of the HSI classification confirm the effectiveness of the proposed L1-SC method on both noisy and noiseless data.Comment: European Signal Processing Conference 201

Discriminant Analysis via Joint Euler Transform and ℓ2, 1-Norm

Linear discriminant analysis (LDA) has been widely used for face recognition. However, when identifying faces in the wild, the existence of outliers that deviate significantly from the rest of the data can arbitrarily skew the desired solution. This usually deteriorates LDA’s performance dramatically, thus preventing it from mass deployment in real-world applications. To handle this problem, we propose an effective distance metric learning method-based LDA, namely, Euler LDA-L21 (e-LDA-L21). e-LDA-L21 is carried out in two stages, in which each image is mapped into a complex space by Euler transform in the first stage and the ℓ2,1 -norm is adopted as the distance metric in the second stage. This not only reveals nonlinear features but also exploits the geometric structure of data. To solve e-LDA-L21 efficiently, we propose an iterative algorithm, which is a closed-form solution at each iteration with convergence guaranteed. Finally, we extend e-LDA-L21 to Euler 2DLDA-L21 (e-2DLDA-L21) which further exploits the spatial information embedded in image pixels. Experimental results on several face databases demonstrate its superiority over the state-of-the-art algorithms

Semi-supervised tensor-based graph embedding learning and its application to visual discriminant tracking

An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a 2-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learningbased semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object’s appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm

Linear discriminant analysis using rotational invariant L-1 norm

Linear discriminant analysis (LDA) is a well-known scheme for supervised subspace learning. It has been widely used in the applications of computer vision and pattern recognition. However, an intrinsic limitation of LDA is the sensitivity to the presence of outliers, due to using the Frobenius norm to measure the inter-class and intra-class distances. In this paper, we propose a novel rotational invariant L-1 norm (i.e., R-1 norm) based discriminant criterion (referred to as DCL1), which better characterizes the intra-class compactness and the inter-class separability by using the rotational invariant L-1 norm instead of the Frobenius norm. Based on the DCL1, three subspace learning algorithms (i.e., 1DL(1), 2DL(1), and TDL1) are developed for vector-based, matrix-based, and tensor-based representations of data, respectively. They are capable of reducing the influence of outliers substantially, resulting in a robust classification. Theoretical analysis and experimental evaluations demonstrate the promise and effectiveness of the proposed DCL1 and its algorithms. (C) 2010 Elsevier B.V. All rights reserved

Principal Component Analysis

This book is aimed at raising awareness of researchers, scientists and engineers on the benefits of Principal Component Analysis (PCA) in data analysis. In this book, the reader will find the applications of PCA in fields such as image processing, biometric, face recognition and speech processing. It also includes the core concepts and the state-of-the-art methods in data analysis and feature extraction