In this letter, we propose a novel supervised dimensionality reduction (DR) method termed linear discriminant analysis based on kernel-based possibilistic c-means (LDA-KPCM) for hyperspectral images (HSIs). The basic idea of this method is to use KPCM algorithm to generate different weights for different samples so that the newly-proposed method can learn the optimal transformation directions according to the relative importance of samples. The weights generated by KPCM are relatively higher for important samples but relatively lower for outliers. The experimental results on two HSI benchmark data sets demonstrate that LDA-KPCM can achieve better performance than the other state-of-the-art DR methods.

As a classical supervised dimensionality reduction (DR) method, linear discriminant analysis (LDA) has been developed for many variants. However, it is not applicable to the case that labeled samples are scarce and unlabeled samples are in large quantity, which always happens in the real world. In this letter, we propose a novel technique format termed semisupervised LDA based on pairwise constraint propagation (SLDA-PCP) for hyperspectral images (HSIs). The basic idea of this method is to use a specially designed PCP technique to propagate label information from the labeled samples to the unlabeled samples. In addition, an extended LDA format to learn the optimal projection vectors according to the newly obtained label information is also created. Comprehensive experiments on two HSIs show that our SLDA-PCP performs better than some state-of-the-art semisupervised DR methods.

Although support vector machine (SVM) has become a powerful tool for pattern classification and regression, a major disadvantage is it fails to exploit the underlying correlation between any pair of data points as much as possible. Inspired by the modified pairwise constraints trick, in this paper, we propose a novel classifier termed as support vector machine with hypergraph-based pairwise constraints to improve the performance of the classical SVM by introducing a new regularization term with hypergraph-based pairwise constraints (HPC). The new classifier is expected to not only learn the structural information of each point itself, but also acquire the prior distribution knowledge about each constrained pair by combining the discrimination metric and hypergraph learning together. Three major contributions of this paper can be summarized as follows: (1) acquiring the high-order relationships between different samples by hypergraph learning; (2) presenting a more reasonable discriminative regularization term by combining the discrimination metric and hypergraph learning; (3) improving the performance of the existing SVM classifier by introducing HPC regularization term. And the comprehensive experimental results on twenty-five datasets demonstrate the validity and advantage of our approach.

In this paper, the limitations of Lemma 4.4 and Theorem 4.6 in "Partially symmetric nonnegative rectangular tensors and copositive rectangular tensors" (J. Ind. Manag. Optim., 15(2) (2019), 775-789) are highlighted. New bounds of the minimum $ H^+ $-singular value are proposed to verify the (strict) copositiveness of rectangular tensors.

Based on collaborative representation, we present a novel semisupervised dimensionality reduction (DR) method termed collaborative label propagation-based semisupervised linear discriminant analysis (CLP-SLDA) for hyperspectral images (HSIs). The new method needs three steps to obtain the optimal projection vector. Firstly, CLP-SLDA utilizes the collaborative label propagation (CLP) technique to obtain the weak labels of the unlabeled samples and the confidence scores of the weak labels. Secondly, a novel weight matrix is constructed based on the known labels, newly acquired weak labels and confidence scores of the weak labels. Thirdly, the newly obtained weight matrix is utilized to learn the optimal transformation vectors to achieve DR for HSIs. Compared to some other state-of-the-art semisupervised DR methods, our proposed CLP-SLDA can acquire the highest classification accuracy in 9 of 13 classes for KSC and 4 of 9 classes for PU and achieve the best performance in AA, OA, and k.

The importance of the signless Laplacian H-spectral radius is highlighted by its known links to connectivity and the maximum cut and independence number. In this paper, we establish signless Laplacian H-spectral radius bounds by simultaneously incorporating both pairwise and higher-order outdegree information. In contrast to the important estimates based solely on the maximum outdegree, our approach yields substantially improved bounds by leveraging richer structural parameters. We further introduce outdegree regularity and semiregularity, under which the tightness of the proposed bounds is fully characterized. Based on similarity transformations, we construct improved bounds using average two-outdegree data. These bounds reveal distinct behaviors between the adjacency and signless Laplacian H-spectral radius of directed hypergraphs. Numerical examples are provided to illustrate the effectiveness of these bounds.