We consider the tensor-based spectral-spatial feature extraction problem for hyperspectral image classification. First, a tensor framework based on circular convolution is proposed. Based on this framework, we extend the traditional principal component analysis (PCA) to its tensorial version tensor PCA (TPCA), which is applied to the spectral-spatial features of hyperspectral image data. The experiments show that the classification accuracy obtained using TPCA features is significantly higher than the accuracies obtained by its rivals.

To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the “t-matrix” model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This “t-matrix” model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and publicly available images. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts.

Facial expression recognition (FER) in the wild is challenging due to various unconstrained conditions, i.e., occlusions and head pose variations. Previous methods tend to improve the performance of facial expression recognition through resorting to holistic methods or coarse local-based methods, while ignoring the local fine-grained feature structure knowledge and the correlation between features. In this paper, we propose a Fine-Grained Association Graph Representation (FG-AGR) framework which can capture the local fine-grained facial expression representation. Firstly, an Adaptive Salient Region Induction (ASRI) is designed for adaptively highlighting the local saliency regions of facial expressions combined with spatial location information. Based on this, a Local Fine-grained Feature Extraction (LFFE) based on Visual Transformers is introduced to further extract fine but discriminative fine-grained features of saliency regions. Thirdly, an Adaptive Graph Association Reasoning (AGAR) based on Graph Convolutional Network is constructed to learn associated fine-grained feature combinations. Extensive experiments demonstrate that our FG-AGR achieves superior performance compared to the state-of-the-art methods with 90.81% on RAF-DB, 64.91% on AffectNet-7, 60.69% on AffectNet-8 and 91.09% on FERPlus.

Obtaining robust feature representations from multi-position wearable sensory data is challenging in human activity recognition (HAR) since data from different positions can have unordered implicit correlations. Graph neural networks (GNNs) represent data as structured graphs by mining complex relationships and interdependency via message passing between the nodes of graphs. This paper proposes a novel framework (MhaGNN) that combines GNNs and the multi-head attention mechanism, aiming to learn more informative representations for multi-position HAR tasks. The MhaGNN framework takes the sensor channels from multiple wearing positions as nodes to construct graph-structured data from the spatial dimension. Besides, the multi-head attention mechanism is introduced to complete the message passing and aggregation of the graphs for spatial-temporal feature extraction. The MhaGNN learns correlations among sensor channels that can be used as compensatory features together with the captured features from each single sensor channel to enhance HAR. Experimental evaluations on three publicly available HAR datasets and a ground-truth dataset demonstrate that our proposed MhaGNN achieves state-of-the-art recognition performance with the captured rich features, including PAMAP2, OPPORTUNITY, MHAEATH and MPWHAR.

High-order data are modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution product. Matrices with elements in the ring of t-scalars are referred to as t-matrices. The t-matrices can be scaled, added and multiplied in the usual way. There are t-matrix generalizations of positive matrices, orthogonal matrices and Hermitian symmetric matrices. With the t-matrix model, it is possible to generalize many well-known matrix algorithms. In particular, the t-matrices are used to generalize the singular value decomposition (SVD), high-order SVD (HOSVD), principal component analysis (PCA), two-dimensional PCA (2DPCA) and Grassmannian component analysis (GCA). The generalized t-matrix algorithms, namely TSVD, THOSVD, TPCA, T2DPCA and TGCA, are applied to low-rank approximation, reconstruction and supervised classification of images. Experiments show that the t-matrix algorithms compare favorably with standard matrix algorithms.

In this paper, we propose a more robust kernelized algorithm incorporating Gibbs spatial constraints for fuzzy segmentation of magnetic resonance imaging (MRI) data. The proposed method is implemented by incorporating a fuzzy Gibbs spatial compensation term in the objective function of kernelized fuzzy C-means algorithm. The spatial compensation term, modeled by Gibbs Random Field (GRF), is actually a normalized kernel-induced measure for the correlation of pixel neighborhoods, and very similar to Gaussian radial basis function (GRBF) kernel, which is usually used to measure the distances between the image data and the prototypes of clusters. The GRBF based kernel and the GRF based spatial constraints can bias the segmentation towards a better piecewise homogeneous classification. In this sense, the Gibbs compensation term can be considered as a coarser measurement for the correlation of neighboring pixels while GRBF kernel acts as a fine measurement for intensity information. The experiments on synthetic images, digital phantoms and real clinical MRI data show the proposed method is more robust and usually a better alternative than other algorithms.