Hyperspectral Dimensionality Reduction by Tensor Sparse and Low-Rank Graph-Based Discriminant Analysis

Estimation of the rice aboveground biomass based on the first derivative spectrum and Boruta algorithm

Aboveground biomass (AGB) is regarded as a critical variable in monitoring crop growth and yield. The use of hyperspectral remote sensing has emerged as a viable method for the rapid and precise monitoring of AGB. Due to the extensive dimensionality and volume of hyperspectral data, it is crucial to effectively reduce data dimensionality and select sensitive spectral features to enhance the accuracy of rice AGB estimation models. At present, derivative transform and feature selection algorithms have become important means to solve this problem. However, few studies have systematically evaluated the impact of derivative spectrum combined with feature selection algorithm on rice AGB estimation. To this end, at the Xiaogang Village (Chuzhou City, China) Experimental Base in 2020, this study used an ASD FieldSpec handheld 2 ground spectrometer (Analytical Spectroscopy Devices, Boulder, Colorado, USA) to obtain canopy spectral data at the critical growth stage (tillering, jointing, booting, heading, and maturity stages) of rice, and evaluated the performance of the recursive feature elimination (RFE) and Boruta feature selection algorithm through partial least squares regression (PLSR), principal component regression (PCR), support vector machine (SVM) and ridge regression (RR). Moreover, we analyzed the importance of the optimal derivative spectrum. The findings indicate that (1) as the growth stage progresses, the correlation between rice canopy spectrum and AGB shows a trend from high to low, among which the first derivative spectrum (FD) has the strongest correlation with AGB. (2) The number of feature bands selected by the Boruta algorithm is 19~35, which has a good dimensionality reduction effect. (3) The combination of FD-Boruta-PCR (FB-PCR) demonstrated the best performance in estimating rice AGB, with an increase in R² of approximately 10% ~ 20% and a decrease in RMSE of approximately 0.08% ~ 14%. (4) The best estimation stage is the booting stage, with R2 values between 0.60 and 0.74 and RMSE values between 1288.23 and 1554.82 kg/hm2. This study confirms the accuracy of hyperspectral remote sensing in estimating vegetation biomass and further explores the theoretical foundation and future direction for monitoring rice growth dynamics.

Central Attention Network for Hyperspectral Imagery Classification

In this article, the intrinsic properties of hyperspectral imagery (HSI) are analyzed, and two principles for spectral-spatial feature extraction of HSI are built, including the foundation of pixel-level HSI classification and the definition of spatial information. Based on the two principles, scaled dot-product central attention (SDPCA) tailored for HSI is designed to extract spectral-spatial information from a central pixel (i.e., a query pixel to be classified) and pixels that are similar to the central pixel on an HSI patch. Then, employed with the HSI-tailored SDPCA module, a central attention network (CAN) is proposed by combining HSI-tailored dense connections of the features of the hidden layers and the spectral information of the query pixel. MiniCAN as a simplified version of CAN is also investigated. Superior classification performance of CAN and miniCAN on three datasets of different scenarios demonstrates their effectiveness and benefits compared with state-of-the-art methods.

Unsupervised dimensionality reduction of medical hyperspectral imagery in tensor space

BACKGROUND AND OBJECTIVES

Compared with traditional RGB images, medical hyperspectral imagery (HSI) has numerous continuous narrow spectral bands, which can provide rich information for cancer diagnosis. However, the abundant spectral bands also contain a large amount of redundancy information and increase computational complexity. Thus, dimensionality reduction (DR) is essential in HSI analysis. All vector-based DR methods ignore the cubic nature of HSI resulting from vectorization. To overcome the disadvantage of vector-based DR methods, tensor-based techniques have been developed by employing multi-linear algebra.

METHODS

To fully exploit the structure features of medical HSI and enhance computational efficiency, a novel method called unsupervised dimensionality reduction via tensor-based low-rank collaborative graph embedding (TLCGE) is proposed. TLCGE introduces entropy rate superpixel (ERS) segmentation algorithm to generate superpixels. Then, a low-rank collaborative graph weight matrix is constructed on each superpixel, greatly improving the efficiency and robustness of the proposed method. After that, TLCGE reduces dimensions in tensor space to well preserve intrinsic structure of HSI.

RESULTS

The proposed TLCGE is tested on cholangiocarcinoma microscopic hyperspectral data sets. To further demonstrate the effectiveness of the proposed algorithm, other machine learning DR methods are used for comparison. Experimental results on cholangiocarcinoma microscopic hyperspectral data sets validate the effectiveness of the proposed TLCGE.

CONCLUSIONS

The proposed TLCGE is a tensor-based DR method, which can maintain the intrinsic 3-D data structure of medical HSI. By imposing the low-rank and sparse constraints on the objective function, the proposed TLCGE can fully explore the local and global structures within each superpixel. The computational efficiency of the proposed TLCGE is better than other tensor-based DR methods, which can be used as a preprocessing step in real medical HSI classification or segmentation.

Hyperspectral Image Classification via Discriminant Gabor Ensemble Filter

For a broad range of applications, hyperspectral image (HSI) classification is a hot topic in remote sensing, and convolutional neural network (CNN)-based methods are drawing increasing attention. However, to train millions of parameters in CNN requires a large number of labeled training samples, which are difficult to collect. A conventional Gabor filter can effectively extract spatial information with different scales and orientations without training, but it may be missing some important discriminative information. In this article, we propose the Gabor ensemble filter (GEF), a new convolutional filter to extract deep features for HSI with fewer trainable parameters. GEF filters each input channel by some fixed Gabor filters and learnable filters simultaneously, then reduces the dimensions by some learnable 1×1 filters to generate the output channels. The fixed Gabor filters can extract common features with different scales and orientations, while the learnable filters can learn some complementary features that Gabor filters cannot extract. Based on GEF, we design a network architecture for HSI classification, which extracts deep features and can learn from limited training samples. In order to simultaneously learn more discriminative features and an end-to-end system, we propose to introduce the local discriminant structure for cross-entropy loss by combining the triplet hard loss. Results of experiments on three HSI datasets show that the proposed method has significantly higher classification accuracy than other state-of-the-art methods. Moreover, the proposed method is speedy for both training and testing.

Latent Low-Rank Projection Learning with Graph Regularization for Feature Extraction of Hyperspectral Images

Due to the great benefit of rich spectral information, hyperspectral images (HSIs) have been successfully applied in many fields. However, some problems of concern also limit their further applications, such as high dimension and expensive labeling. To address these issues, an unsupervised latent low-rank projection learning with graph regularization (LatLRPL) method is presented for feature extraction and classification of HSIs in this paper, in which discriminative features can be extracted from the view of latent space by decomposing the latent low-rank matrix into two different matrices, also benefiting from the preservation of intrinsic subspace structures by the graph regularization. Different from the graph embedding-based methods that need two phases to obtain the low-dimensional projections, one step is enough for LatLRPL by constructing the integrated projection learning model, reducing the complexity and simultaneously improving the robustness. To improve the performance, a simple but effective strategy is exploited by conducting the local weighted average on the pixels in a sliding window for HSIs. Experiments on the Indian Pines and Pavia University datasets demonstrate the superiority of the proposed LatLRPL method.

Discriminant Tensor-Based Manifold Embedding for Medical Hyperspectral Imagery

Medical hyperspectral imagery has recentlyattracted considerable attention. However, for identification tasks, the high dimensionality of hyperspectral images usually leads to poor performance. Thus, dimensionality reduction (DR) is crucial in hyperspectral image analysis. Motivated by exploiting the underlying structure information of medical hyperspectral images and enhancing the discriminant ability of features, a discriminant tensor-based manifold embedding (DTME) is proposed for discriminant analysis of medical hyperspectral images. Based on the idea of manifold learning, a new discriminant similarity metric is designed, which takes into account the tensor representation, sparsity, low-rank and distribution characteristics. Then, an inter-class tensor graph and an intra-class tensor graph are constructed using the new similarity metric to reveal intrinsic manifold of hyperspectral data. Dimensionality reduction is achieved by embedding this supervised tensor graphs into the low-dimensional tensor subspace. Experimental results on membranous nephropathy and white bloodcells identification tasks demonstrate the potential clinical value of the proposed DTME.

Dimensionality reduction for tensor data based on projection distance minimization and hilbert-schmidt independence criterion maximization1

Tensor data are becoming more and more common in machine learning. Compared with vector data, the curse of dimensionality of tensor data is more serious. The motivation of this paper is to combine Hilbert-Schmidt Independence Criterion (HSIC) and tensor algebra to create a new dimensionality reduction algorithm for tensor data. There are three contributions in this paper. (1) An HSIC-based algorithm is proposed in which the dimension-reduced tensor is determined by maximizing HSIC between the dimension-reduced and high-dimensional tensors. (2) A tensor algebra-based algorithm is proposed, in which the high-dimensional tensor are projected onto a subspace and the projection coordinate is set to be the dimension-reduced tensor. The subspace is determined by minimizing the distance between the high-dimensional tensor data and their projection in the subspace. (3) By combining the above two algorithms, a new dimensionality reduction algorithm, called PDMHSIC, is proposed, in which the dimensionality reduction must satisfy two criteria at the same time: HSIC maximization and subspace projection distance minimization. The proposed algorithm is a new attempt to combine HSIC with other algorithms to create new algorithms and has achieved better experimental results on 8 commonly-used datasets than the other 7 well-known algorithms.

Unsupervised and Supervised Feature Extraction Methods for Hyperspectral Images Based on Mixtures of Factor Analyzers

This paper proposes three feature extraction (FE) methods based on density estimation for hyperspectral images (HSIs). The methods are a mixture of factor analyzers (MFA), deep MFA (DMFA), and supervised MFA (SMFA). The MFA extends the Gaussian mixture model to allow a low-dimensionality representation of the Gaussians. DMFA is a deep version of MFA and consists of a two-layer MFA, i.e, samples from the posterior distribution at the first layer are input to an MFA model at the second layer. SMFA consists of single-layer MFA and exploits labeled information to extract features of HSI effectively. Based on these three FE methods, the paper also proposes a framework that automatically extracts the most important features for classification from an HSI. The overall accuracy of a classifier is used to automatically choose the optimal number of features and hence performs dimensionality reduction (DR) before HSI classification. The performance of MFA, DMFA, and SMFA FE methods are evaluated and compared to five different types of unsupervised and supervised FE methods by using four real HSIs datasets.

Tensor Discriminant Analysis via Compact Feature Representation for Hyperspectral Images 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.

Tensor Based Multiscale Low Rank Decomposition for Hyperspectral Images Dimensionality Reduction

Dimensionality reduction is an essential and important issue in hyperspectral image processing. With the advantages of preserving the spatial neighborhood information and the global structure information, tensor analysis and low rank representation have been widely considered in this field and yielded satisfactory performance. In available tensor- and low rank-based methods, how to construct appropriate tensor samples and determine the optimal rank of hyperspectral images along each mode are still challenging issues. To address these drawbacks, an unsupervised tensor-based multiscale low rank decomposition (T-MLRD) method for hyperspectral images dimensionality reduction is proposed in this paper. By regarding the raw cube hyperspectral image as the only tensor sample, T-MLRD needs no labeled samples and avoids the processing of constructing tensor samples. In addition, a novel multiscale low rank estimating method is proposed to obtain the optimal rank along each mode of hyperspectral image which avoids the complicated rank computing. Finally, the multiscale low rank feature representation is fused to achieve dimensionality reduction. Experimental results on real hyperspectral datasets demonstrate the superiority of the proposed method over several state-of-the-art approaches.

Comparison of flavour fingerprint, electronic nose and multivariate analysis for discrimination of extra virgin olive oils

Flavour is a special way to discriminate extra virgin olive oils (EVOOs) from other aroma plant oils. In this study, different ratios (5, 10, 15, 20, 30, 50, 70 and 100%) of peanut oil (PO), corn oil (CO) and sunflower seed oil (SO) were discriminated from raw EVOO using flavour fingerprint, electronic nose and multivariate analysis. Fifteen different samples of EVOO were selected to establish the flavour fingerprint based on eight common peaks in solid-phase microextraction-gas chromatography-mass spectrometry corresponding to 4-methyl-2-pentanol, (E)-2-hexenal, 1-tridecene, hexyl acetate, (Z)-3-hexenyl acetate, (E)-2-heptenal, nonanal and α-farnesene. Partial least square discrimination analysis (PLS-DA) was used to differentiate EVOOs and mixed oils containing more than 20% of PO, CO and SO. Furthermore, better discrimination efficiency was observed in PLS-DA than PCA (70% of CO and SO), which was equivalent to the correlation coefficient method of the fingerprint (20% of PO, CO and SO). The electronic nose was able to differentiate oil samples from samples containing 5% mixture. The discrimination method was selected based on the actual requirements of quality control.

DCT-Based Preprocessing Approach for ICA in Hyperspectral Data Analysis

The huge quantity of information and the high spectral resolution of hyperspectral imagery present a challenge when performing traditional processing techniques such as classification. Dimensionality and noise reduction improves both efficiency and accuracy, while retaining essential information. Among the many dimensionality reduction methods, Independent Component Analysis (ICA) is one of the most popular techniques. However, ICA is computationally costly, and given the absence of specific criteria for component selection, constrains its application in high-dimension data analysis. To overcome this limitation, we propose a novel approach that applies Discrete Cosine Transform (DCT) as preprocessing for ICA. Our method exploits the unique capacity of DCT to pack signal energy in few low-frequency coefficients, thus reducing noise and computation time. Subsequently, ICA is applied on this reduced data to make the output components as independent as possible for subsequent hyperspectral classification. To evaluate this novel approach, the reduced data using (1) ICA without preprocessing; (2) ICA with the commonly used preprocessing techniques which is Principal Component Analysis (PCA); and (3) ICA with DCT preprocessing are tested with Support Vector Machine (SVM) and K-Nearest Neighbor (K-NN) classifiers on two real hyperspectral datasets. Experimental results in both instances indicate that data after our proposed DCT preprocessing method combined with ICA yields superior hyperspectral classification accuracy.