Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to subspace clustering, often takes on a sparse representation or a low-rank representation to learn a block diagonal self-representation matrix for subspace generation. However, existing methods require solving a large scale convex optimization problem with a large set of data, with computational complexity reaches O(N^3) for N data points. Therefore, the efficiency and scalability of traditional spectral clustering methods can not be guaranteed for large scale datasets. In this paper, we propose a subspace clustering model based on the Kronecker product. Due to the property that the Kronecker product of a block diagonal matrix with any other matrix is still a block diagonal matrix, we can efficiently learn the representation matrix which is formed by the Kronecker product of k smaller matrices. By doing so, our model significantly reduces the computational complexity to O(kN^{3/k}). Furthermore, our model is general in nature, and can be adapted to different regularization based subspace clustering methods. Experimental results on two public datasets show that our model significantly improves the efficiency compared with several state-of-the-art methods. Moreover, we have conducted experiments on synthetic data to verify the scalability of our model for large scale datasets.

In optical flow estimation task, coarse-to-fine warping strategy is widely used to deal with the large displacement problem and provides efficiency and speed. However, limited by the small search range between the first images and warped second images, current coarse-to-fine optical flow networks fail to capture small and fast-moving objects which has disappeared at coarse resolution levels. To address this problem, we introduce a lightweight but effective Global Matching Component (GMC) to grab global matching features. We propose a new Hybrid Matching Optical Flow Network (HMFlow) by integrating GMC into existing coarse-to-fine networks seamlessly. Besides keeping in high accuracy and small model size, our proposed HMFlow can apply global matching features to guide the network to discover the small and fast-moving objects mismatched by local matching features. We also build a new dataset, named SFChairs, for evaluation. The experimental results show that our proposed network achieves considerable performance, especially at regions with small and fast-moving objects.