Learning incoherent sparse and low-rank patterns from multiple tasks

We consider the problem of learning incoherent sparse and lowrank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a lowrank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained o...

• Type: Conference
• Year: 2010
• Where: KDD
• Authors: Jianhui Chen, Ji Liu, Jieping Ye
• Keywords: Data Mining, Gradient, KDD 2010, Multi-task Learning Formulation, Projected Gradient Algorithms