Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring

Schroedinger Eigenmaps for Manifold Alignment of Multimodal Hyperspectral Images

Multimodal remote sensing is an upcoming field as it allows for many views of the same region of interest. Domain adaption attempts to fuse these multimodal remotely sensed images by utilizing the concept of transfer learning to understand data from different sources to learn a fused outcome. Semisupervised Manifold Alignment (SSMA) maps multiple Hyperspectral images (HSIs) from high dimensional source spaces to a low dimensional latent space where similar elements reside closely together. SSMA preserves the original geometric structure of respective HSIs whilst pulling similar data points together and pushing dissimilar data points apart. The SSMA algorithm is comprised of a geometric component, a similarity component and dissimilarity component. The geometric component of the SSMA method has roots in the original Laplacian Eigenmaps (LE) dimension reduction algorithm and the projection functions have roots in the original Locality Preserving Projections (LPP) dimensionality reduction framework. The similarity and dissimilarity component is a semisupervised component that allows expert labeled information to improve the image fusion process. Spatial-Spectral Schroedinger Eigenmaps (SSSE) was designed as a semisupervised enhancement to the LE algorithm by augmenting the Laplacian matrix with a user-defined potential function. However, the user-defined enhancement has yet to be explored in the LPP framework. The first part of this thesis proposes to use the Spatial-Spectral potential within the LPP algorithm, creating a new algorithm we call the Schroedinger Eigenmap Projections (SEP). Through experiments on publicly available data with expert-labeled ground truth, we perform experiments to compare the performance of the SEP algorithm with respect to the LPP algorithm. The second part of this thesis proposes incorporating the Spatial Spectral potential from SSSE into the SSMA framework. Using two multi-angled HSI’s, we explore the impact of incorporating this potential into SSMA

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

Semisupervised hypergraph discriminant learning for dimensionality reduction of hyperspectral image.

Semisupervised learning is an effective technique to represent the intrinsic features of a hyperspectral image (HSI), which can reduce the cost to obtain the labeled information of samples. However, traditional semisupervised learning methods fail to consider multiple properties of an HSI, which has restricted the discriminant performance of feature representation. In this article, we introduce the hypergraph into semisupervised learning to reveal the complex multistructures of an HSI, and construct a semisupervised discriminant hypergraph learning (SSDHL) method by designing an intraclass hypergraph and an interclass graph with the labeled samples. SSDHL constructs an unsupervised hypergraph with the unlabeled samples. In addition, a total scatter matrix is used to measure the distribution of the labeled and unlabeled samples. Then, a low-dimensional projection function is constructed to compact the properties of the intraclass hypergraph and the unsupervised hypergraph, and simultaneously separate the characteristics of the interclass graph and the total scatter matrix. Finally, according to the objective function, we can obtain the projection matrix and the low-dimensional features. Experiments on three HSI data sets (Botswana, KSC, and PaviaU) show that the proposed method can achieve better classification results compared with a few state-of-the-art methods. The result indicates that SSDHL can simultaneously utilize the labeled and unlabeled samples to represent the homogeneous properties and restrain the heterogeneous characteristics of an HSI

A REVIEW ON MULTIPLE-FEATURE-BASED ADAPTIVE SPARSE REPRESENTATION (MFASR) AND OTHER CLASSIFICATION TYPES

A new technique Multiple-feature-based adaptive sparse representation (MFASR) has been demonstrated for Hyperspectral Images (HSI's) classification. This method involves mainly in four steps at the various stages. The spectral and spatial information reflected from the original Hyperspectral Images with four various features. A shape adaptive (SA) spatial region is obtained in each pixel region at the second step. The algorithm namely sparse representation has applied to get the coefficients of sparse for each shape adaptive region in the form of matrix with multiple features. For each test pixel, the class label is determined with the help of obtained coefficients. The performances of MFASR have much better classification results than other classifiers in the terms of quantitative and qualitative percentage of results. This MFASR will make benefit of strong correlations that are obtained from different extracted features and this make use of effective features and effective adaptive sparse representation. Thus, the very high classification performance was achieved through this MFASR technique

Face Recognition: Issues, Methods and Alternative Applications

Face recognition, as one of the most successful applications of image analysis, has recently gained significant attention. It is due to availability of feasible technologies, including mobile solutions. Research in automatic face recognition has been conducted since the 1960s, but the problem is still largely unsolved. Last decade has provided significant progress in this area owing to advances in face modelling and analysis techniques. Although systems have been developed for face detection and tracking, reliable face recognition still offers a great challenge to computer vision and pattern recognition researchers. There are several reasons for recent increased interest in face recognition, including rising public concern for security, the need for identity verification in the digital world, face analysis and modelling techniques in multimedia data management and computer entertainment. In this chapter, we have discussed face recognition processing, including major components such as face detection, tracking, alignment and feature extraction, and it points out the technical challenges of building a face recognition system. We focus on the importance of the most successful solutions available so far. The final part of the chapter describes chosen face recognition methods and applications and their potential use in areas not related to face recognition

Unsupervised spectral sub-feature learning for hyperspectral image classification

Spectral pixel classification is one of the principal techniques used in hyperspectral image (HSI) analysis. In this article, we propose an unsupervised feature learning method for classification of hyperspectral images. The proposed method learns a dictionary of sub-feature basis representations from the spectral domain, which allows effective use of the correlated spectral data. The learned dictionary is then used in encoding convolutional samples from the hyperspectral input pixels to an expanded but sparse feature space. Expanded hyperspectral feature representations enable linear separation between object classes present in an image. To evaluate the proposed method, we performed experiments on several commonly used HSI data sets acquired at different locations and by different sensors. Our experimental results show that the proposed method outperforms other pixel-wise classification methods that make use of unsupervised feature extraction approaches. Additionally, even though our approach does not use any prior knowledge, or labelled training data to learn features, it yields either advantageous, or comparable, results in terms of classification accuracy with respect to recent semi-supervised methods

Making Laplacians commute

In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. Our construction naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of applications in dimensionality reduction, shape analysis, and clustering, demonstrating that our method better captures the inherent structure of multi-modal data