Sparse Graph-Based Discriminant Analysis for Hyperspectral Imagery

Recently, sparse graph-based discriminant analysis (SGDA) and collaborative graph-based discriminant analysis (CGDA) have been developed for dimensionality reduction of hyperspectral imagery. In SGDA or CGDA, a graph is constructed by -norm minimization-based representation or -norm minimization-based representation, respectively, based on labeled samples. These two methods have shown success over traditional methods by reinforcing discriminative power, but are limited in within-class representation and distribution of representation coefficients. In order to preserve intrinsic geometrical structure of original data and improve the interpretability of the underlying graph, we propose an adaptive collaborative graph for discriminant analysis (ACGDA), which explicitly models the internal relationship among within-class pixels during graph construction. The proposed method couples distance-weighted Tikhonov regularization with -norm minimization-based representation, of which the coefficients are solutions to a closed-form expression. The graph adaptively adjusts the collaborative representation by using distance-weighted measurement, which produces stronger ability of discrimination. In addition, the graph weight matrix is designed in the form of a block-diagonal structure, reducing the computational cost and further improving discriminative power. The proposed approach is compared with several traditional and state-of-the-art methods on two benchmark datasets. Experimental results demonstrate that the proposed approach can yield superior classification performance.

Nonnegative matrix factorization (NMF), which can lead to nonsubtractive parts-based representation, has been demonstrated to be effective for dimensionality reduction of hyperspectral imagery (HSI). However, existing NMF methods applied to HSI use only a single spectral feature and do not take into consideration spatial information, such as texture or morphological features, while it has been widely acknowledged that exploiting multiple features can improve performance. Consequently, a variant of orthogonal NMF, which can not only achieve a nonnegative factorization but also exploit the complementary information that arises among heterogeneous features, is proposed for hyperspectral dimensionality reduction. The proposed method, which couples orthogonal NMF with a previous multiple-features-combining algorithm, yields a discriminative low-dimensional feature representation that matches the intuition that parts should sum to produce a whole. An efficient multiplicative updating procedure is derived, and its local convergence is guaranteed theoretically. Experimental results on two hyperspectral data sets demonstrate the effectiveness of the proposed method.

Dimensionality reduction is of great importance which aims at reducing the spectral dimensionality while keeping the desirable intrinsic structure information of hyperspectral images. Tensor analysis which can retain both spatial and spectral information of hyperspectral images has caused more and more concern in the field of hyperspectral images processing. In general, a desirable low dimensionality feature representation should be discriminative and compact. To achieve this, a tensor discriminant analysis model via compact feature representation (TDA-CFR) was proposed in this paper. In TDA-CFR, the traditional linear discriminant analysis was extended to tensor space to make the resulting feature representation more informative and discriminative. Furthermore, TDA-CFR redefines the feature representation of each spectral band by employing the tensor low rank decomposition framework which leads to a more compact representation.

Structural health monitoring has been increasingly used due to the advances in sensing technology and data analysis, facilitating the shift from time-based to condition-based maintenance. This work is part of the efforts which have applied structural health monitoring to the Sydney Harbour Bridge – one of Australia’s iconic structures. It combines dimensionality reduction and pattern recognition techniques to accurately and efficiently distinguish faulty components from well-functioning ones. Specifically, random projection is used for dimensionality reduction on the vibration feature data. Then, healthy and damaged patterns of bridge components are learned in the lower dimensional projected space using supervised and unsupervised machine learning methods, namely, support vector machine and one-class support vector machine. The experimental results using data from a laboratory-based building structure and the Sydney Harbour Bridge showed high feasibility of applying machine learning techniques to dimensionality reduction and damage detection in structural health monitoring. Random projection combined with support vector machine significantly reduces the computational time while maintaining the detection accuracy. The proposed method also outperformed popular dimensionality reduction techniques. The computational time of the method using random projection can be more than 200 times faster than that without using dimensionality reduction while still achieving similar detection accuracy.

Recently, a high dimensional classification framework has been proposed to introduce spatial and anatomical priors in support vector machine (SVM) optimization scheme for brain image analysis. However, classical SVM has to convert 3D discrete brain images naturally represented by higher-order tensors to one-dimensional vectors in order to meet the input requirements. This traditional method destroys the natural structure and correlation in the original data, and generates high dimensional vectors. In this manuscript, the method is improved by a modified support tensor machine (STM) algorithm to make full use of spatial prior and the inherent information of tensor. The new approach reduces memory requirements and computational complexity significantly, and it is comparably demonstrated by experimental results on classification of Alzheimer patients and elderly controls. Introduction Alzheimer disease (AD) is the most prevalent neurodegenerative dementia in worldwide, and thus prevention and early accurate diagnosis of AD is increasingly crucial. In the last few years, support vector machine (SVM) methods for AD subject classification have become an incredibly active research topic. In the related work, SVM approach, as same as feature selection and extraction, has been taking the specificity of neuroimaging data into account. As an example, a frame work is proposed in [1] to include spatial and anatomical priors into SVM by using regularization operators, and it indicates a flexible way to model various types of proximity. However, for the purpose of satisfying the input requirements of classical SVM, 3D discrete brain images naturally represented by higher-order tensors have to convert to vectors in advance. This conversion breaks the inherent structure and correlation in the original data, and easily produces high dimensional vectors and leads to a poor performance in time complexity and space complexity. In order to improve above method including spatial prior of 3D discrete brain images in SVM, a new method is proposed in this manuscript to maintain the natural structure in the original tensor data and include spatial prior of all frontal slices of the tensors in STM [2]. To illustrate the improvement, we apply the proposed method to classification of 299 subjects, 137 AD patients and 162 cognitively normal (CN) controls, as the same study population in [3]. It can be observed that the proposed method reduces size of memory requested and the time complexity significantly and produces better classification performances. Spatial prior in SVM SVM is a supervised learning algorithm introduced by Vapnik and performs classification by mapping the data into higher dimensional space [4]. Let (xs, ys), s∈1,...,S be a training set of instance-labeled pairs, xs∈Ω, ys∈{-1,1} and Ω is the input space, then SVM optimization problem can be written as:

Laplacian Eigenmaps (LE) and Schroedinger Eigenmaps (SE) are effective dimensionality reduction algorithms that are capable of integrating both the spatial and spectral information inherent in a hyperspectral image. In this paper, we consider how to extend LE- and SE-based spatial-spectral dimensionality reduction algorithms to situations where partial knowledge of class labels exists, for example, when a subset of pixels has been manually labeled by an expert user. This partial knowledge is incorporated through the use of cluster potentials, turning each underlying algorithm into an instance of SE. Using publicly available data, we show that incorporating this partial knowledge improves the performance of subsequent classification algorithms.

Dimensionality reduction is a key step in hyperspectral image processing. Recent investigations are looking into nonlinear manifold learning for dimensionality reduction in hyperspectral imagery. Nonlinear manifold learning methods such as Isomap, and Local Linear Embedding are use to recover the low dimensional representation of an unknown nonlinear manifold for high dimensional data where it is important to retain the neighborhood structure of the manifold. Although these algorithms use different philosophies for recovering the nonlinear manifold, they all incorporate neighborhood information from each data point to construct a weighted graph having the data points as vertices. Thus the performance of these methods highly depends on how well these neighborhoods are selected, since all subsequent steps rely on it. The k -NN algorithm is the most widely used technique for neighbor selection in manifold learning. However, it can result in a disconnected graph and it does not fully exploit spatial neighborhood information from the image in selecting points to form the neighborhoods. In this paper, recently proposed methods for constructing the weighted graph in manifold learning are studied: k -VC, k -EC and k -MST, which have the advantage of creating connected graphs and have performed well in artificial data sets. Spatial information of the hyperspectral images is included in the manifold learning process by using spatial coherence. Experiments are conducted with artificial data and hyperspectral images. For hyperspectral images, classification accuracy was used as an indirect measure to understand how the low dimensional embedding of the data reduces dimensionality while still maintaining good discrimination performance.

In this paper, we study the Locally Linear Embedding (LLE) for nonlinear dimen- sionality reduction of hyperspectral data. We improve the existing LLE in terms of both compu- tational complexity and memory consumption by introducing a spatial neighbourhood window for calculating the k nearest neighbours. The improved LLE can process larger hyperspectral images than the existing LLE and it is also faster. We conducted experiments of endmember extraction to assess the effectiveness of the dimensionality reduction methods. Experimental results show that the improved LLE is better than PCA and the existing LLE in identifying endmembers. It finds more endmembers than PCA and the existing LLE when the Pixel Purity Index (PPI) based endmember extraction method is used. Also, better results are obtained for detection.

Marginal Fisher analysis (MFA) exploits the margin criterion to compact the intraclass data and separate the interclass data, and it is very useful to analyze the high-dimensional data. However, MFA just considers the structure relationships of neighbor points, and it cannot effectively represent the intrinsic structure of hyperspectral imagery (HSI) that possesses many homogenous areas. In this paper, we propose a new dimensionality reduction (DR) method, termed local geometric structure Fisher analysis (LGSFA), for HSI classification. Firstly, LGSFA uses the intraclass neighbor points of each point to compute its reconstruction point. Then, an intrinsic graph and a penalty graph are constructed to reveal the intraclass and interclass properties of hyperspectral data. Finally, the neighbor points and corresponding intraclass reconstruction points are used to enhance the intraclass-manifold compactness and the interclass-manifold separability. LGSFA can effectively reveal the intrinsic manifold structure and obtain the discriminating features of HSI data for classification. Experiments on the Salinas, Indian Pines, and Urban data sets show that the proposed LGSFA algorithm achieves the best classification results than other state-of-the-art methods.

In this paper we examine how the projection of hyperspectral data into smaller dimensional subspaces can effect the propagation of error. In particular, we show that the nonorthogonality of endmembers in the linear mixing model can cause small changes in band space (as, for example, from the addition of noise) to lead to relatively large changes in the estimated abundance coefficients. We also show that increasing the number of endmembers can actually lead to an increase in the amount of possible error.

This book presents different types of dimensionality reduction (DR) methods and their effectiveness in hyperspectral data processing.

Flow cytometry is a technique for analyzing cells that are suspended in a buffered salt-based solution and flow past one or more lasers. Visible light scatter and one or more fluorescence characteristics are assessed for each particle. The most common use of flow cytometry is immunophenotyping. In traditional flow cytometry analysis, a region around a population of cells is manually drawn (gating) in two-dimensional scatter plots. This enables the measuring of specific groups of cells. However, manual gating could increase the overall error rate of the study and makes the analysis hardly reproducible since it is done in less controlled settings. Furthermore, it represents a bottleneck in the analysis of large amounts of data. Some processes, such as gating, have recently been automated using R packages. In addition, dimensionality reduction approaches have been developed in the flow cytometry environment to take advantage of information from several markers at once. Despite this, none of them are integrated in a harmonized way, and none of them allow back-gating to emphasize the study population and eliminate false positives. To tackle this problem, our team has developed flowTOTAL (github.com/ImmunoOncology/flowTOTAL), a user-friendly command line workflow to analyze flow cytometry data. The major attractive feature is the facility to perform with one command not only a traditional analysis, but also an unsupervised analysis. As input, the user has to indicate the folder with the .FCS files, the metadata associated with each file, and the marker to be used during back-gating. The pipeline is divided into three main sections: preprocessing, traditional analysis, and unsupervised analysis. During preprocessing each. FCS will be subjected to correcting for fluorescence spillover (compensation), detection of anomalies by checking flow rate and signal acquisition as well as removing doublets based on forward scatter (QC). For the traditional analysis, auto-gating will be performed for the identification of the target population using back-gating. For each set of given markers, the number of events obtained and the scatter plot will be generated. Finally, in the unsupervised analysis, the population of interest will be specified and the pipeline will proceed with normalization, dimensionality reduction using PCA or UMAP and finally a clustering approach for subpopulation identification. In addition, differential abundance analysis can be performed with metadata information. flowTOTAL is presented as a standardization for the analysis of flow cytometry data, comprising all the necessary steps for comprehensive analysis and allowing mass analysis. Furthermore, it goes beyond the simple quantification of particles, since the implementation of more complex methodologies allows for the discovery of subpopulations that are not present in the traditional analysis but have a significant biological role. Citation Format: Juan Luis Onieva, Patricia Cháves, Javier Oliver, María Garrido-Barros, Juan Zafra, Belén Sojo, Alfonso Sánchez, Martina Álvarez, Pedro Jiménez, Emilio Alba, Miguel Berciano, Antonio Rueda, Manuel Cobo-Dols, Elisabeth Pérez, Isabel Barragán. flowTOTAL: A comprehensive bioinformatics workflow for flow cytometry automatic analysis [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 1910.

Many state-of-the-art i-vector based voice biometric systems use linear discriminant analysis (LDA) as a post-processing stage to increase the computational efficiency in the back-end via dimensionality reduction, as well as annihilate the undesired (noisy) directions in the total variability subspace. The traditional approach for computing the LDA transform uses parametric representations for both intra- and inter-class scatter matrices that are based on the Gaussian distribution assumption. However, it is known that the actual distribution of i-vectors may not necessarily be Gaussian, and in particular, in the presence of noise and channel distortions. In addition, the rank of the LDA projection (i.e., the maximum number of available discriminant bases) is limited to the number of classes minus 1. Accordingly, language recognition tasks on noisy data that involve only a few language classes receive limited or no benefit from the LDA post-processing. Motivated by this observation, we present an alternative non-parametric discriminant analysis (NDA) technique that measures both the within- and between-language variation on a local basis using the nearest neighbor rule. The effectiveness of the NDA method is evaluated in the context of noisy language recognition tasks using speech material from the DARPA Robust Automatic Transcription of Speech (RATS) program. Experimental results indicate that NDA is more effective than the traditional parametric LDA for language recognition under noisy and channel degraded conditions.

Exploring sex classification from earprints - A comparison of supervised machine learning algorithms and conventional linear discriminant analysis.

The linear discriminant analysis (LDA) is one of the most efficient supervised dimensionality reduction technique widely used in face recognition. This paper proposed a new weighted LDA to improve the performance of the discriminant analysis. Confusable pair of classes is considered as the primary goal in our objective function. The proposed technique not only improves the minimization of the within-class scatter, but also improves the maximization of the between classes scatter to extract better discriminant feature subset. The experimental results a real word dataset demonstrate that the proposed method achieve higher recognition rate than that traditional LDA as well as other weighted LDA.