- 主题： A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding
- 主题：Learning Euclidean-to-Riemannian Metric for Point-to-Set Classification
- Wangmeng Zuo, Deyu Meng, Lei Zhang, Xiangchu Feng, and David Zhang, A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding, ICCV 2013. [pdf]
- Zhiwu Huang, Ruiping Wang, Shiguang Shan, Xilin Chen, Learning Euclidean-to-Riemannian Metric for Point-to-Set Classification. CVPR 2014 (Oral). [pdf] [supplementary]
- A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding. [Slides]
- 文章摘要: In many sparse coding based image restoration and image classification problems, using non-convex $\ell_p$-norm minimization ($0 < p < 1$) can often obtain better results than the convex $\ell_1$-norm minimization. A number of algorithms, e.g., iteratively reweighted least squares (IRLS), iteratively thresholding method (ITM-$\ell_p$), and look-up table (LUT), have been proposed for non-convex $\ell_p$-norm sparse coding, while some analytic solutions have been suggested for some specific values of $p$. In this paper, by extending the popular soft-thresholding operator, we propose a generalized iterated shrinkage algorithm (GISA) for $\ell_p$-norm non-convex sparse coding. Unlike the analytic solutions, the proposed GISA algorithm is easy to implement, and can be adopted for solving non-convex sparse coding problems with arbitrary $p$ values. Compared with LUT, GISA is more general and does not need to compute and store the look-up tables. Compared with IRLS and ITM-$\ell_p$, GISA is theoretically more solid and can achieve better solutions. Experiments on image restoration and sparse coding based face recognition are conducted to validate the performance of GISA.
- Learning Euclidean-to-Riemannian Metric for Point-to-Set Classification.[Slides]
- 文章摘要: In this paper, we focus on the problem of point-to-set classification (one instance of this problem is still-to-video face recognition), where single points (e.g., single still face images) are matched against sets of correlated points (e.g., videos containing face frames). Since the points commonly lie in Euclidean space while the sets are typically modeled as elements on Riemannian manifold, they can be treated as Euclidean points and Riemannian points respectively. To learn a metric between the heterogeneous points, we propose a novel Euclidean-to-Riemannian metric learning framework. Specifically, by exploiting typical Riemannian metrics, the Riemannian manifold is first embedded into a high dimensional Hilbert space to reduce the gaps between the heterogeneous spaces and meanwhile respect the Riemannian geometry of the manifold. The final distance metric is then learned by pursuing multiple transformations from the Hilbert space and the original Euclidean space (or its corresponding Hilbert space) to a common subspace, where classical Euclidean distances of transformed heterogeneous points can be measured. Extensive experiments clearly demonstrate the superiority of our proposed approach over the state-of-the-art methods.
- A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding
- Learning Euclidean-to-Riemannian Metric for Point-to-Set Classification [Codes]