Dimensionality Reduction and Linear Discriminant Analysis for Hyperspectral Image Classification

Fisher linear discriminant analysis (FLDA) is a classic linear feature extraction and dimensionality reduction approach for face recognition. It is known that geometric distribution weight information of image data plays an important role in machine learning approaches. However, FLDA does not employ the geometric distribution weight information of facial images in the training stage. Hence, its recognition accuracy will be affected. In order to enhance the classification power of FLDA method, this paper utilizes radial basis function (RBF) with fractional order to model the geometric distribution weight information of the training samples and proposes a novel geometric distribution weight information based Fisher discriminant criterion. Subsequently, a geometric distribution weight information based LDA (GLDA) algorithm is developed and successfully applied to face recognition. Two publicly available face databases, namely, ORL and FERET databases, are selected for evaluation. Compared with some LDA-based algorithms, experimental results exhibit that our GLDA approach gives superior performance.

A derivative of Fisher's Linear Discriminant Analysis (FLDA), named Fisherapples for the recognition of apple lesions which is not sensitive to large variations in illumination is proposed in this paper. We make use of the linear projection that is orthogonal to the within-class scatter of the apple images from a high-dimensional image space to a considerably low-dimensional image space. It separates the data-cases well, projecting away variations in lighting. Our approach maximizes the ratio of between-class scatter to that of within-class scatter of apple lesions, i.e., we can get maximal between-class distances and minimal within-class distances after projection. This implies that the gap between the classes becomes bigger and ensures optimal separability in the new space. Besides, we take advantage of Principal Component Analysis (PCA) to project the set of apple images to a lower dimensional space in order to overcome the complication of the singular within-class scatter matrix. After that, the resulting within-class scatter becomes nonsingular and subsequently we can use standard FLDA to reduce the dimension further. Consequently, it is effortless for the computer to calculate the result. Experimental results demonstrate that Fisherapples performs better in apple lesion recognition than PCA.

The nondestructive characterization of citrus varieties (Egyptian sweet orange, Lane Late navel orange, Australian orange, and Blood orange) was developed based on near-infrared diffuse reflectance spectroscopy (NIRDRS) together with principal component analysis (PCA) and Fisher linear discriminant analysis (FLDA). An experiment for the penetration of NIRDRS into the peel was designed and the effects of different spectral acquisition points were investigated. Pretreatments were used to eliminate the spectral interferences. As an unsupervised pattern recognition method, PCA was used to establish the characterization models. Furthermore, supervised pattern recognition based on PCA and FLDA was employed to enhance the accuracy. The results of the penetration experiments show that near-infrared light enters the citrus peel and is able to characterize the internal composition. Even with the optimized spectral pretreatment, accurate characterization of citrus varieties was not achieved by PCA. However, the accurate characterization of citrus varieties was provided by PCA-FLDA. The accuracies of four spectral acquisition points are 95%, while the characterization accuracies of six spectral acquisition points are 100% combined with optimized spectral pretreatment. Therefore, NIRDRS with PCA-FLDA is suitable for the rapid and nondestructive characterization of citrus varieties.

Dimensionality reduction based on random projection (RP) includes two problems, namely, the dimensionality is limited by the data size and the class separability of the dimensionality reduction results is unstable due to the randomly generated projection matrix. These problems make the RP algorithm unsuitable for large-size hyperspectral image (HSI) classification. To solve these problems, this paper presents a new partitioned RP (PRP) algorithm and proves its rationality in theory. First, a large-size HSI is evenly divided into multiple small-size sub-HSIs. Afterwards, the projection matrix that maximizes the class separability is selected from multiple samplings in which the class dissimilarity measurement is defined as large inter-class distance and small intra-class variance. By using the same projection matrix, each small-size sub-HSI is projected to generate a low dimensional sub-HSI, thereby generating a low dimensional HSI. Next, the minimum distance (MD) classifier is utilized to classify the low dimensional HSI obtained by the PRP algorithm. Finally, four real HSIs are used for experiments, and three of the most popular classification algorithms based on RP are selected as comparison algorithms to validate the effectiveness of the proposed algorithm. The classification performance is evaluated with the kappa coefficient, overall accuracy (OA), average accuracy (AA), average precision rate (APR), and running time. Experimental results indicate that the proposed algorithm can obtain reliable classification results in a very short time.

The enhanced capabilities of the remote sensing devices lead to capture more precise and accurate spatial and spectral information about surface materials. Increased spectral resolution results in more number of spectral bands and raises the challenge of data dimensionality. This high volume data holds plenty of redundant information. This redundancy affects both the time as well as space complexity of the system. To process and analyse the hyperspectral data with less computational cost with no information loss, data dimensionality needs to be reduced. The literature shows that the traditional image processing techniques with some modifications are applied for hyperspectral dimensionality reduction, but none of the methods give specific solution. This paper evaluates the performances and limitations of the state-of-the-art dimensionality reduction techniques. The algorithms studied and evaluated are Principal Components Analysis, Independent Component Analysis, Minimum Noise Fraction, Fisher Linear Discriminant Analysis, Factor Analysis and Linear Discriminant Analysis. The experiments are performed on the Indian Pines AVIRIS & Gulbarga Subset (AVIRIS-NG) hyperspectral datasets.

Hyperspectral image based automatic target recognition (ATR) systems often project the high dimensional hyperspectral reflectance signatures onto a lower dimensional subspace using techniques such as principal components analysis (PCA), Fisher's linear discriminant analysis (LDA) and stepwise LDA. In a general classification framework, these projections are sub-optimal, and in the absence of sufficient training data, are likely to be ill conditioned. In recent work, the authors proposed a divide and conquer approach that partitions the hyperspectral space into contiguous subspaces followed by multi-classifiers and decision fusion. Although this technique alleviated the small sample size problem and provided a good recognition performance in light and moderate pixel mixing, the performance significantly decreased under severe mixing conditions, as does with conventional ATR techniques. In this work, the authors propose a kernel discriminant analysis based projection in each subspace of the partition, followed by the multi-classifier, decision fusion framework to ensure robust recognition even in severe pixel mixing conditions. The performance of the proposed system (as measured by overall target recognition accuracies) is greatly superior to conventional dimensionality reduction techniques, as well as the more recently proposed divide-and-conquer technique.

A spatial-spectral metric learning (SSML) framework for hyperspectral image (HSI) classification is proposed. SSML learns a metric by considering both the spectral characteristics and spatial features represented as the mean of neighboring pixels. It first performs the local pixel neighborhood preserving embedding (LPNPE) to reduce the dimensionality of HSI and meanwhile to preserve the spatial local similarity structure. Then, it learns a spectral and spatial distance metric, separately. Finally, the combination of the spectral and spatial metrics yields a joint spatial-spectral metric. It is followed by a nearest neighbor (NN) classifier for HSI classification. SSML shows good performance over the spectral and spatial NN and SVM on the benchmark hyperspectral data set of Indian Pines.

In this paper a novel non-linear subspace method for face verification is proposed. The problem of face verification is considered as a two-class problem (genuine versus impostor class). The typical Fisher's linear discriminant analysis (FLDA) gives only one or two projections in a two-class problem. This is a very strict limitation to the search of discriminant dimensions. As for the FLDA for N class problems (N is greater than two) the transformation is not person specific. In order to remedy these limitations of FLDA, exploit the individuality of human faces and take into consideration the fact that the distribution of facial images, under different viewpoints, illumination variations and facial expression is highly complex and non-linear, novel kernel discriminant algorithms are proposed. The new methods are tested in the face verification problem using the XM2VTS database where it is verified that they outperform other commonly used kernel approaches.

The Fisher's linear discriminant analysis (FLDA) is a successful linear feature extraction method which aims to maximize the between-class separability and to minimize the within-class variability. In order to accomplish its goal, FLDA maximizes the Fisher's linear discriminant analysis criterion given in the paper. In this paper we first address the limitations of the classical FLDA criterion and then discuss new criterion functions which were introduced to overcome those limitations. Finally, we demonstrate the capability of the new criteria both theoretically and empirically.

Subspace analysis is an effective technique for dimensionality reduction, which aims at finding a low-dimensional space of high-dimensional data. Fisher linear discriminant analysis (FLD) and Neural Networks are commonly used techniques of image processing and recognition. In this paper, a new scheme of image feature extraction namely, the FLD and Generalized Regression Neural Networks (GRNN) approach for image recognition is presented. Linear discriminant analysis is usually performed to investigate differences among multivariate classes, to determine which attributes discriminate between the classes, and to determine the most parsimonious way to distinguish among classes. Two-dimensional linear discriminative features and GRNN are used to perform the classification. Experiments on the image database (Face, Object and Character) demonstrate the effectiveness and feasibility of the proposed method.

A computer vision system for automatic recognition and classification of five varieties of plant leaves under controlled laboratory imaging conditions, comprising: 1–Cydonia oblonga (quince), 2–Eucalyptus camaldulensis dehn (river red gum), 3–Malus pumila (apple), 4–Pistacia atlantica (mt. Atlas mastic tree) and 5–Prunus armeniaca (apricot), is proposed. 516 tree leaves images were taken and 285 features computed from each object including shape features, color features, texture features based on the gray level co-occurrence matrix, texture descriptors based on histogram and moment invariants. Seven discriminant features were selected and input for classification purposes using three classifiers: hybrid artificial neural network–ant bee colony (ANN–ABC), hybrid artificial neural network–biogeography based optimization (ANN–BBO) and Fisher linear discriminant analysis (LDA). Mean correct classification rates (CCR), resulted in 94.04%, 89.23%, and 93.99%, for hybrid ANN–ABC; hybrid ANN–BBO; and LDA classifiers, respectively. Best classifier mean area under curve (AUC), mean sensitivity, and mean specificity, were computed for the five tree varieties under study, resulting in: 1–Cydonia oblonga (quince) 0.991 (ANN–ABC), 95.89% (ANN–ABC), 95.91% (ANN–ABC); 2–Eucalyptus camaldulensis dehn (river red gum) 1.00 (LDA), 100% (LDA), 100% (LDA); 3–Malus pumila (apple) 0.996 (LDA), 96.63% (LDA), 94.99% (LDA); 4–Pistacia atlantica (mt. Atlas mastic tree) 0.979 (LDA), 91.71% (LDA), 82.57% (LDA); and 5–Prunus armeniaca (apricot) 0.994 (LDA), 88.67% (LDA), 94.65% (LDA), respectively.

An algorithm for gamma-ray identification applications has been developed and evaluated. The algorithm is based on a Fisher Linear Discriminant Analysis (FLDA) technique that generates loading coefficients that maximize the separation of a particular radionuclide from all the other radionuclides in a training library. Separate experimental data sets were obtained for the algorithms training data and for the performance evaluation. The algorithm was evaluated against a range of radionuclides and acquisitions times. An inverse square root relationship between the cluster standard deviation and its gross mean counts enabled the production of an adaptable threshold. The inverse square relationship between the Mahalanobis distance metric and the 137Cs standoff distance demonstrated a means to quantify the measured number of counts. The FLDA identification performance, for a number of threat radionuclides (including special nuclear materials), exceeded that of a commercially available peak search algorithm. The high sensitivity and specificity, of the FLDA algorithm, was maintained in low count situations. The poor performance for some radionuclides was attributed to the measured number of counts being below the minimal detectable limit. The FLDA algorithm has the potential to be used in gamma-ray identification applications and, in particular, count starved situations.

This paper presents a novel method for hyperspectral image classification based on the minimum noise fraction (MNF) and an approach combining support vector machine (SVM) and linear discriminant analysis (LDA). A new SVM/LDA algorithm is used for the classification. First, we use MNF method to reduce the dimension and extract features of the image, and then use the SVM/LDA algorithm to transform the extracted features. Next, we train the result of transformation, optimize the parameters through cross-validation and grid search method, then get a optimal hyperspectral image classifier. Finally, we use this classifier to complete classification. In order to verify the proposed method, the AVIRIS Indian Pines image was used. The experimental results show that the proposed method can solve the contradiction between the small amount of samples and high dimension, improve classification accuracy compared to the classical SVM method.

Hyperspectral remote sensing image classification based on residual generative Adversarial Neural Networks

In automatic fruit harvesting system, the method of fruit identification by using machine vision has been researched underway for years. The ultimate objective of this project is to extend a ripeness study on the citrus fruit image data and the identification methodologies by multispectral analysis for fruit picking robot. To acquire the combination of the citrus fruit image data, a cold mirror acquisition system has been prototyped to align two CCD cameras with a classical cold mirror on a custom built fixture. The use of the cold mirror system is an attempt to capture both images without registration at the same view by triggering and synchronizing two cameras. With flexible interchangeability, some physical optical filters have been interchanged on the cameras to capture the combination of the citrus image data. In this part of study, Fisher linear discriminate analysis has been used on the natural citrus image data to discuss the probability of the identification on the image by modifying the image data. In the process, the component of the visible image is selected as the dominating component based on the spectral contrast between the ripe colored citrus fruit and the background. The second component from certain near infrared spectral area is selectable to be combined with the visible component by convolution. In FLDA, the major eigenvector is found as the projection direction uniquely from the data sets of the fruit and the background. On top of the information from FLDA, the classification on the fruit set and the background set is performed by the nearest neighbor estimation in the lower dimensional space on different schemes of the image data. By comparing with some other color indices methods, the overall outcome by FLDA gives a better identification result on all sampling image data with small estimation error.