Ju Sun

TL;DR: It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: When the data is clean, LRR exactly recovers the true subspace structures; when the data are contaminated by outliers, it is proved that under certain conditions LRR can exactly recover the row space of the original data.

TL;DR: This paper proposes to model the spatio-temporal context information in a hierarchical way, where three levels of context are exploited in ascending order of abstraction, and proposes to employ the Multiple Kernel Learning (MKL) technique to prune the kernels towards speedup in algorithm evaluation.

TL;DR: It is proved that when the measurement vectors are generic, with high probability, a natural least-squares formulation for GPR has the following benign geometric structure: (1) There are no spurious local minimizers, and all global minimizers are equal to the target signal, up to a global phase, and (2) the objective function has a negative directional curvature around each saddle point.

TL;DR: The objective landscape is highly structured: with high probability, there are no "spurious" local minimizers; and around all saddle points the objective has a negative directional curvature, which makes the problem amenable to efficient optimization algorithms.

TL;DR: In this paper, it was shown that when the measurement vectors are generic (i.i.d. complex Gaussian) and numerous enough, with high probability, a natural least-squares formulation for GPR has the following benign geometric structure: (1) there are no spurious local minimizers, and all global minimizers are equal to the target signal up to a global phase, and (2) the objective function has a negative directional curvature around each saddle point.