With the rapid advances in digital imaging and communication technologies, recently image set classification has attracted significant attention and has been widely used in many real-world scenarios. As an effective technology, the class-specific representation theory-based methods have demonstrated their superior performances. However, this type of methods either only uses one gallery set to measure the gallery-to-probe set distance or ignores the inner connection between different metrics, leading to the learned distance metric lacking robustness, and is sensitive to the size of image sets. In this article, we propose a novel joint metric learning-based class-specific representation framework (JMLC), which can jointly learn the related and unrelated metrics. By iteratively modeling probe set and related or unrelated gallery sets as affine hull, we reconstruct this hull sparsely or collaboratively over another image set. With the obtained representation coefficients, the combined metric between the query set and the gallery set can then be calculated. In addition, we also derive the kernel extension of JMLC and propose two new unrelated set constituting strategies. Specifically, kernelized JMLC (KJMLC) embeds the gallery sets and probe sets into the high-dimensional Hilbert space, and in the kernel space, the data become approximately linear separable. Extensive experiments on seven benchmark databases show the superiority of the proposed methods to the state-of-the-art image set classifiers.

Deep subspace clustering (DSC) has achieved considerable success in the classification task of hyperspectral images (HSIs) without background (defined as noisy samples) compared with traditional subspace clustering methods. Unfortunately, directly applying DSC to classify land-cover on HSI datasets with background may suffer from the degradation of classification performance. In this article, we propose an effective deep low-rank graph convolutional subspace clustering (DLR-GCSC) framework for improving the performance of land-cover classification on HSI datasets with background. Specifically, we design a joint spatial–spectral network to extract band- and patch-level features simultaneously by combining 1-D and 2-D autoencoders. Moreover, we construct a low-rank constrained fully connected layer as a self-expression layer in the network to make the joint features more discriminative. To reduce the influence of noisy samples and obtain an informative affinity matrix, we recast the joint features into a non-Euclidean domain by introducing graph convolution. Finally, spectral clustering is applied to the informative affinity matrix to obtain the classification results. Experiments on three benchmark HSI datasets show that our proposed method achieves competitive classification performance to the state-of-the-art methods on both HSI data with background and without background.