Adaptive collaborative graph for discriminant analysis of hyperspectral imagery

Sparsity-preserving graph construction is investigated for the dimensionality reduction of hyperspectral imagery. In particular, a sparse graph-based discriminant analysis is proposed when labeled samples are available. By forcing the projection to be along the direction where a sample is clustered with within-class samples that best represented it, the discriminative power can be enhanced. The proposed method has no requirement on the number of labeled samples as in traditional linear discriminant analysis, and it can be solved by a simple generalized eigenproblem. The quality of the dimensionality reduction is evaluated by a support vector machine with a composite spatial-spectral kernel. Experimental results demonstrate that the proposed sparse graph-based discriminant analysis can yield superior classification performance with much lower dimensionality as compared to performance on the original data or on data transformed with other dimensionality-reduction approaches.

Graph Convolutional Neural Networks with Geometric and Discrimination information

Local and global regularized sparse coding for data representation

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.

Classical linear regression not only lacks of the flexibility in fitting the label, but also ignores to preserve the intrinsic local geometric structure of data, which leads to overfitting. In this paper, we propose a novel discriminative regression method, called adaptive locality preserving based discriminative regression (ALPDR), to address these problems. Firstly, a locality preserving constraint regularized by the adaptive weight is introduced to preserve the intrinsic geometric structures of data, in which the similar points of the same class are adaptively pulled together by the projection. Secondly, ALPDR directly learns the discriminative target matrix from data based on the given label information, which allows more freedom in label fitting and simultaneously enlarges the margins between different classes. Thirdly, ALPDR imposes a row-sparsity constraint on the projection, which enables the method to adaptively select the most discriminative features from data such that the negative influence of noises and redundant features can be eliminated. Finally, an efficient iterative algorithm is provided to optimize the model. Extensive experiments show that the proposed method outperforms the other state-of-art methods, which proves the effectiveness of the proposed method.

Low-rank representation (LRR) has received considerable attention in subspace segmentation due to its effectiveness in exploring low-dimensional subspace structures embedded in data. To preserve the intrinsic geometrical structure of data, a graph regularizer has been introduced into LRR framework for learning the locality and similarity information within data. However, it is often the case that not only the high-dimensional data reside on a non-linear low-dimensional manifold in the ambient space, but also their features lie on a manifold in feature space. In this paper, we propose a dual graph regularized LRR model (DGLRR) by enforcing preservation of geometric information in both the ambient space and the feature space. The proposed method aims for simultaneously considering the geometric structures of the data manifold and the feature manifold. Furthermore, we extend the DGLRR model to include non-negative constraint, leading to a parts-based representation of data. Experiments are conducted on several image data sets to demonstrate that the proposed method outperforms the state-of-the-art approaches in image clustering.

In multimedia applications, dimension reduction is essential to the effectiveness and efficiency of an algorithm due to the curse of dimensionality. Recently, its adaptive variants have received considerable attention in unsupervised learning since a single pass without label information often fails to guarantee an optimal representation, especially when the parameters are not set properly. However, most such methods are basically linear, therefore unable to consider the geometrical structure of the data space. In this paper, we propose a novel algorithm called Nonlinear Adaptive Dimension Reduction (NADR), which adaptively learns the optimal low-dimensional coordinates that preserve the intrinsic geometric structure of the original data. Moreover, the incorporation of K-means enables NADR to be a powerful alternative for cluster analysis. Experiments on benchmark image data sets illustrate that NADR outperforms the state-of-the-art adaptive dimension reduction methods.

Hyperspectral imagery contains hundreds of contiguous bands with a wealth of spectral signatures, making it possible to distinguish materials through subtle spectral discrepancies. Because these spectral bands are highly correlated, dimensionality reduction, as the name suggests, seeks to reduce data dimensionality without losing desirable information. This article reviews discriminant analysisbased dimensionality-reduction approaches for hyperspectral imagery, including typical linear discriminant analysis (LDA), state-of-the-art sparse graph-based discriminant analysis (SGDA), and their extensions.

Graphia is an open-source platform created for the graph-based analysis of the huge amounts of quantitative and qualitative data currently being generated from the study of genomes, genes, proteins metabolites and cells. Core to Graphia’s functionality is support for the calculation of correlation matrices from any tabular matrix of continuous or discrete values, whereupon the software is designed to rapidly visualise the often very large graphs that result in 2D or 3D space. Following graph construction, an extensive range of measurement algorithms, routines for graph transformation, and options for the visualisation of node and edge attributes are available, for graph exploration and analysis. Combined, these provide a powerful solution for the interpretation of high-dimensional data from many sources, or data already in the form of a network or equivalent adjacency matrix. Several use cases of Graphia are described, to showcase its wide range of applications in the analysis biological data. Graphia runs on all major desktop operating systems, is extensible through the deployment of plugins and is freely available to download from https://graphia.app/.

Linear discriminant analysis (LDA) aims to find a low-dimensional space in which data points in the same class are to be close to each other while keeping data points from different classes apart. To improve the robustness of LDA to non-Gaussian distribution data, most existing discriminant analysis methods extend LDA by approximating the underlying manifold of data. However, these methods suffer from the following problems: 1) local affinity or reconstruction coefficients are learned on the basis of the relationships of all data pairs, which would lead to a sharp increase in the amount of computation and 2) they learn the manifold information in the original space, ignoring the interference of the noise and redundant features. Motivated by these challenges, this article represents a novel discriminant analysis model, called fast and adaptive locality discriminant analysis (FALDA), to improve the efficiency and robustness. First, with the anchor-based strategy, a bipartite graph of each class is constructed to characterize the local structure of data. Since the number of anchor points is far less than that of data points, learning of fuzzy membership relationships between data points and anchor points within each class can save training time. Second, a maximum entropy regularization is introduced to control the uniformity of the weights of graphs and avoid the trivial solution. Third, the above relationships are updated adaptively in the process of dimensionality reduction, which can suppress the interference of the noise and redundant features. Fourth, the whitening constraint is imposed on the projection matrix to remove the relevance between features and restrict the total scatter of data in the subspace. Last but not the least, data with complex distribution can be explicitly divided into sub-blocks according to the learned anchor points (or subclass center points). We test our proposed method on synthetic data, benchmark datasets, and imbalanced datasets. Promising experimental results demonstrate the success of this novel model.

In order to find a compact representation which uncovers the hidden topics and simultaneously respects the intrinsic geometric structure of hyperspectral data, a novel algorithm, named GLNMF (Globally maximizing, Locally minimizing, regularized Nonnegative Matrix Factorization) feature extraction algorithm, is proposed. The proposed algorithm is a linear approximation of a multi-manifolds-based learning framework which imposes an additional constraint on NMF that both the local and non-local quantities are considered. GLNMF characterizes the local scatter as well as the non-local scatter, seeking to find a projection that simultaneously maximizes the non-local scatter and minimizes the local scatter. This characteristic makes GLNMF more intuitive and more powerful than some up-to-date methods. An iterative multiplicative updating algorithm is proposed to optimize the objective. Experiments on a benchmark hyperspectral dataset demonstrate that the proposed method outperforms NMF as well as a few current dimensionality reduction methods.

Non-negative matrix decomposition (NMF) has been widely used for sample clustering and feature selection in the field of bioinformatics. However, the existing methods based on NMF cannot effectively deal with the problem of intrinsic geometrical structure, noise, and outliers in gene expression data. In this paper, a novel method called Robust Hypergraph regularized Non-negative Matrix Factorization (RHNMF) is proposed to solve the above problem. Firstly, the hypergraph Laplacian regularization is introduced to consider the intrinsic geometrical structure of the high dimension data. Secondly, the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm is applied in the error function to reduce effects of the noise and outliers, which may improve the robustness of the algorithm. Finally, we perform clustering and common abnormal expression genes (com-abnormal expression genes) selection on multi-view gene expression data to verify the rationality and validity of the RHNMF method. Extensive experimental results demonstrate that our proposed RHNMF method has better performance than other state-of-the-art methods.

In this paper, we propose a new dimension reduction (DR) algorithm called ensemble graph-based locality preserving projections (EGLPP); to overcome the neighborhood size k sensitivity in locally preserving projections (LPP). EGLPP constructs a homogeneous ensemble of adjacency graphs by varying neighborhood size k and finally uses the integrated embedded graph to optimize the low-dimensional projections. Furthermore, to appropriately handle the intrinsic geometrical structure of the multi-view data and overcome the dimensionality curse, we propose a generalized multi-manifold graph ensemble embedding framework (MLGEE). MLGEE aims to utilize multi-manifold graphs for the adjacency estimation with automatically weight each manifold to derive the integrated heterogeneous graph. Experimental results on various computer vision databases verify the effectiveness of proposed EGLPP and MLGEE over existing comparative DR methods.

Our aim in the present research is to investigate the diagnostic performance of artificial neural networks (ANNs) applied to multispectral images of cutaneous pigmented skin lesions as well as to compare this approach to a standard traditional linear classification method, such as discriminant function analysis. This study involves a series of 534 patients with 573 cutaneous pigmented lesions (132 melanomas and 441 nonmelanoma lesions). Each lesion was analyzed by a telespectrophotometric system (TS) in vivo, before surgery. The system is able to acquire a set of 17 images at selected wavelengths from 400 to 1040 nm. For each wavelength, five lesion descriptors were extracted, related to the criteria of the ABCD (for asymmetry, border, color, and dimension) clinical guide for melanoma diagnosis. These variables were first reduced in dimension by the use of factor analysis techniques and then used as input data in an ANN. Multivariate discriminant analysis (MDA) was also performed on the same dataset. The whole dataset was split into two independent groups: i.e., train (the first 400 cases, 95 melanomas) and verification set (last 173 cases, 37 melanomas). Factor analysis was able to summarize the data structure into ten variables, accounting for at least 90% of the original parameters variance. After proper training, the ANN was able to classify the population with 80% sensitivity, 72% specificity, and 78% sensitivity, 76% specificity for the train and validation set, respectively. Following ROC analysis, area under curve (AUC) was 0.852 (train) and 0.847 (verify). Sensitivity and specificity values obtained by the standard discriminant analysis classifier resulted in a figure of 80% sensitivity, 60% specificity and 76% sensitivity, 57% specificity for the train and validation set, respectively. AUC for MDA was 0.810 and 0.764 for the train and verify set, respectively. Classification results were significantly different between the two methods both for diagnostic scores and model stability, which was worse for MDA.

Adaptive graph construction using data self-representativeness for pattern classification