Tensor-Based Low-Rank Graph With Multimanifold Regularization for Dimensionality Reduction of Hyperspectral Images

In this paper, we proposed a new semi-supervised multi-manifold learning method, called semi- supervised sparse multi-manifold embedding (S3MME), for dimensionality reduction of hyperspectral image data. S3MME exploits both the labeled and unlabeled data to adaptively find neighbors of each sample from the same manifold by using an optimization program based on sparse representation, and naturally gives relative importance to the labeled ones through a graph-based methodology. Then it tries to extract discriminative features on each manifold such that the data points in the same manifold become closer. The effectiveness of the proposed multi-manifold learning algorithm is demonstrated and compared through experiments on a real hyperspectral images.

Hyperspectral image (HSI) has shown promising results in many fields because of its high spectral resolution. However, redundancy and noise in spectral dimension seriously affect the classification of HSI. For this reason, many popular dimensionality reduction (DR) methods are proposed to solve the problem. The local discriminant embedding (LDE) as an effective non-linear method for DR can be more discriminative by constructing two neighborhood graphs. However, HSI is very easy influenced by noise, and the LDE algorithm based on K nearest neighborhood is highly susceptible to interference from extreme point, which may lead to inaccurate graph construction and poor performance of classification. To overcome the problem and retain the advantages of LDE, a modified local discriminant embedding (MLDE) is firstly applied on HSI by constructing neighborhood graphs on a new spectral feature space instead of the original space. We use variance to characterize the pixels similarity of the same class and use covariance to characterize the separation of different classes of pixels. The combination of variance and covariance makes pixels in the same class to be closer and makes greater separation of pixels from different classes, which enhances classification performance of HSI. The way of representing data by using variance and covariance can attenuate the effects of noise. The Log-Euclidean metric is used to capture the similarity between spectral vectors, which can provide a more accurate similarity evaluation than euclidean distance. The experimental results of two hyperspectral datasets demonstrate the effectiveness of our proposed MLDE method.

A method fusing spectral and image information with a one-dimensional convolutional neural network(1D-CNN) for the detection of moisture content in Orah mandarin (Citrus reticulata Blanco) was proposed. The 1D-CNN model integrated with three different attention modules (SEAM, ECAM, CBAM) and machine learning models were applied to individual spectrum and fused information by passing the traditional feature extraction stage. Additionally, the dimensionality reduction of hyperspectral images and extraction of one-dimensional color and textural features from the reduced images were performed, thus avoiding the large parameter volumes and efficiency decline inherent in the direct modeling of two-dimensional images. The results indicated that the 1D-CNN model with integrated attention modules exhibited clear advantages over machine learning models in handling multi-source information. The optimal machine learning model was determined to be the random forest (RF) model under the fusion information, with a correlation coefficient (R) of 0.8770 and a root mean square error (RMSE) of 0.0188 on the prediction set. The CBAM-1D-CNN model under the fusion information exhibited the best performance, with an R of 0.9172 and an RMSE of 0.0149 on the prediction set. The 1D-CNN models utilizing fusion information exhibited superior performance compared to single spectrum, and 1D-CNN with the fused information based on SEAM, ECAM, and CBAM respectively improved Rp by 4.54%, 0.18%, and 10.19% compared to the spectrum, with the RMSEP decreased by 11.70%, 14.06%, and 31.02%, respectively. The proposed approach of 1D-CNN integrated attention can obtain excellent regression results by only using one-dimensional data and without feature pre-extracting, reducing the complexity of the models, simplifying the calculation process, and rendering it a promising practical application.

An important solution to the curse of dimensionality problem in large-volume, multi-band hyperspectral data is to perform the dimensionality reduction (DR) through graph embedding (GE) techniques. In this paper, a novel DR method called tensor-based multigraph structure preserving embedding (TMSPE) is proposed for HSI classification. At first, TMSPE defines a multi-graph structure with pixel-sharing weights, which can integrate the spatial-spectral information within the tensor samples. Then, it selects effective neighbor points for multigraph construction based on the probability distribution of different samples, which ensures than all nodes in the multigraph structure have correct connection relationships. Finally, the spatial coordinate relationships between pixels are introduced to adjusts the connection weights between different pixels adaptively, which can enhance the effectiveness of manifold reconstruction for HSI data. The performance of TMSPE is evaluated on PaviaU dataset, and experimental comparisons with several classical algorithms demonstrate the superiority of the proposed TMSPE algorithm in terms of classification accuracy.

Advances in hyper spectral imaging sensors makes it possible to obtain high dimensional and high resolution data which poses challenges for computational cost and time. As the inter-band resolution is high in hyper spectral images, the spectral dimension could be reduced without significant loss of useful information. This requires careful application of dimensionality reduction techniques to reduce the dimension but preserve the original spectral characteristics. It is observed in the literature that filtering techniques can address some of the challenges concerning dimensionality reduction in hyper spectral imaging. In this paper a dimensionality reduction method adopting Discrete Wavelet Transform and Distance Classifier Correlation filter has been proposed for hyper spectral imaging. The experimental results show that the combination of ID-DWT with DCCF outperforms the other methods in dimensionality reduction and classification of given data set.

QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm generalized differential evolution (DE) algorithm to matrix form. QUATRE was originally designed for a continuous search space, but many practical applications are binary optimization problems. Therefore, we designed a novel binary version of QUATRE. The proposed binary algorithm is implemented using two different approaches. In the first approach, the new individuals produced by mutation and crossover operation are binarized. In the second approach, binarization is done after mutation, then cross operation with other individuals is performed. Transfer functions are critical to binarization, so four families of transfer functions are introduced for the proposed algorithm. Then, the analysis is performed and an improved transfer function is proposed. Furthermore, in order to balance exploration and exploitation, a new liner increment scale factor is proposed. Experiments on 23 benchmark functions show that the proposed two approaches are superior to state-of-the-art algorithms. Moreover, we applied it for dimensionality reduction of hyperspectral image (HSI) in order to test the ability of the proposed algorithm to solve practical problems. The experimental results on HSI imply that the proposed methods are better than Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA).

As one of the most popular dimensionality reduction techniques, locality preserving projections (LPP) has been widely used in computer vision and pattern recognition. However, in practical applications, data is always corrupted by noises. For the corrupted data, samples from the same class may not be distributed in the nearest area, thus LPP may lose its effectiveness. In this paper, it is assumed that data is grossly corrupted and the noise matrix is sparse. Based on these assumptions, we propose a novel dimensionality reduction method, named low-rank preserving projections (LRPP) for image classification. LRPP learns a low-rank weight matrix by projecting the data on a low-dimensional subspace. We use the L21 norm as a sparse constraint on the noise matrix and the nuclear norm as a low-rank constraint on the weight matrix. LRPP keeps the global structure of the data during the dimensionality reduction procedure and the learned low rank weight matrix can reduce the disturbance of noises in the data. LRPP can learn a robust subspace from the corrupted data. To verify the performance of LRPP in image dimensionality reduction and classification, we compare LRPP with the state-of-the-art dimensionality reduction methods. The experimental results show the effectiveness and the feasibility of the proposed method with encouraging results.

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.

Independent component analysis (ICA) is a technique that extracts independent source signals by searching for a linear or nonlinear transformation which minimizes the statistical dependence between components. ICA has been used in a variety of signal processing applications including dimensionality reduction in hyperspectral image (HSI) analysis. Due to the computation complexities and convergence rates, ICA is very time-consuming for high volume or dimension data set like hyperspectral images. Hardware implementation provides not only an optimal parallelism environment, but also a potential faster and real-time solution. This work synthesizes a parallel ICA (pICA) algorithm on field programmable gate array (FPGA). In the proposed implementation method, the pICA is partitioned into three temporally independent functional modules, and each of which is synthesized individually with several ICA-related reconfigurable components (RCs) that are developed for reuse and retargeting purpose. All modules are then integrated into a design and development environment for performing many subtasks such as FPGA synthesis, optimization, placement and routing. In a case study, we synthesize the pICA algorithm for hyperspectral image dimensionality reduction on the pilchard reconfigurahle computing platform embedded with Xilinx: VIRTEX V1000E. The FPGA executes at the maximum frequency of 20.161 MHz, and the pilchard board transfers data directly with CPU on the 64-bit memory bus at the maximum frequency of 133MHz. The performance comparisons between the proposed and another two ICA-related FPGA implementations show that the proposed FPGA implementation of pICA has potential in performing complicated algorithms on large volume data sets.

The nonlinear dimensionality reduction and its effects on vector classification and segmentation of hyperspectral images are investigated in this letter. In particular, the way dimensionality reduction influences and helps classification and segmentation is studied. The proposed framework takes into account the nonlinear nature of high-dimensional hyperspectral images and projects onto a lower dimensional space via a novel spatially coherent locally linear embedding technique. The spatial coherence is introduced by comparing pixels based on their local surrounding structure in the image domain and not just on their individual values as classically done. This spatial coherence in the image domain across the multiple bands defines the high-dimensional local neighborhoods used for the dimensionality reduction. This spatial coherence concept is also extended to the segmentation and classification stages that follow the dimensionality reduction, introducing a modified vector angle distance. We present the underlying concepts of the proposed framework and experimental results showing the significant classification improvements

ABSTRACTIn the area of hyperspectral image (HSI) classification, graph-based semi-supervised learning (SSL) has been proved to be highly effective. Constructing a proper graph is critical for graph-based SSL tasks. In HSI, spectral distance is widely used to calculate the weight of graph edge, though it can be influenced by noise and outliers. Meanwhile, links among all the data points are incorporated in the graph, including those from different subspaces. Thus the constructed graph might contain incorrect information. In this letter, a novel semi-supervised HSI classification method using local low-rank representation (SL2R) is proposed. Edge weight calculation will not be affected by noise or outliers thanks to the robustness of low-rank representation (LRR). Since each graph is constructed at local level, where pixels are basically embedded in the same subspace, links among uncorrelated pixels can be removed. Moreover, spatial context is naturally characterized by low-rank constraint on adjacent pixels. Experimental results on two data sets (Indian Pines and Botswana) confirm the effectiveness of the proposed method.

Target detection (TD) is a major task in hyperspectral image (HSI) processing which, due to the high spectral resolution, requires dealing with the curse of dimensionality. The integrated feature extraction and selection is a well-known solution for dimensionality reduction of HSIs. In this study, a new method is presented to improve the performance of TD algorithms based on principal component analysis (PCA) feature space. In this method, using the implantation of the target spectrum (TS) in the HSI and following the simulated targets in the PCA feature space, the best principal components (PCs) are selected. Then, using the mixing and unmixing coefficients of the PCs, a new TS and a new image in the PCA feature space are created. Afterwards, using the new spectrum of the target, the TD algorithm is run on the new HSI. The performance of the proposed method is compared to nine counterpart algorithms on Hymap and Hyperion HSI. All the comparisons are performed using adaptive coherence estimator (ACE) TD algorithm. Experimental results illustrate that the proposed method, compared to its counterparts, yields superior performance based on the false alarm rate (FAR) measure. It gives an average FAR value of about 16, which is approximately 9% better than that of its best counterparts.

Many applications, including the image search engine, image inpainting, hyperspectral image dimensionality reduction, pattern recognition, and time series prediction, can be facilitated by considering the given discrete data–set as a point-cloud P {\mathcal P} in some high dimensional Euclidean space R s {\mathbb R}^{s} . Then the problem is to extend a desirable objective function f f from a certain relatively smaller training subset C ⊂ P \mathcal {C}\subset {\mathcal P} to some continuous manifold X ⊂ R s {\mathbb X}\subset {\mathbb R}^{s} that contains P {\mathcal P} , at least approximately. More precisely, when the point cloud P {\mathcal P} of the given data–set is modeled in the abstract by some unknown compact manifold embedded in the ambient Euclidean space R s {\mathbb R}^{s} , the extension problem can be considered as the interpolation problem of seeking the objective function on the manifold X {\mathbb X} that agrees with f f on C \mathcal {C} under certain desirable specifications. For instance, by considering groups of cardinality s s of data values as points in a point-cloud in R s {\mathbb R}^{s} , such groups that are far apart in the original spatial data domain in R 1 {\mathbb R}^{1} or R 2 {\mathbb R}^{2} , but have similar geometric properties, can be arranged to be close neighbors on the manifold. The objective of this paper is to incorporate the consideration of data geometry and spatial approximation, with immediate implications to the various directions of application areas. Our main result is a point-cloud interpolation formula that provides a near-optimal degree of approximation to the target objective function on the unknown manifold.

Discriminative low-rank preserving projection for dimensionality reduction

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.