We propose a general Laplacian regularized low-rank representation framework for data representation where a hypergraph Laplacian regularizer can be readily introduced into, i.e., a Non-negative Sparse Hyper-Laplacian regularized LRR model (NSHLRR).
We regard geodesic distance as a kind of kernel, which maps data from linearly inseparable space to linear separable distance space. In doing this, a new semisupervised manifold learning algorithm, namely regularized geodesic feature learning algorithm, is proposed.
This paper studies algorithms for solving the problem of recovering a low-rank matrix with a fraction of its entries arbitrarily corrupted. This paper develops and compares two complementary approaches for solving this problem by a convex programming. The first is an accelerated proximal gradient algorithm directly applied to the primal; while the second is a gradient algorithm applied to the dual problem.
We develop the Laplacian PCA (LPCA) algorithm which is the extension of PCA to a more general form by locally optimizing the weighted scatter. In addition to the simplicity of PCA, the benefits brought by LPCA are twofold: the strong robustness against noise and the weak metric-dependence on sample spaces.