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Anthony So

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2 papers

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NeurIPS Conference 2012 Conference Paper

Learning with Partially Absorbing Random Walks

Xiao-ming Wu
Zhenguo Li
Anthony So
John Wright
Shih-Fu Chang

We propose a novel stochastic process that is with probability $\alpha_i$ being absorbed at current state $i$, and with probability $1-\alpha_i$ follows a random edge out of it. We analyze its properties and show its potential for exploring graph structures. We prove that under proper absorption rates, a random walk starting from a set $\mathcal{S}$ of low conductance will be mostly absorbed in $\mathcal{S}$. Moreover, the absorption probabilities vary slowly inside $\mathcal{S}$, while dropping sharply outside $\mathcal{S}$, thus implementing the desirable cluster assumption for graph-based learning. Remarkably, the partially absorbing process unifies many popular models arising in a variety of contexts, provides new insights into them, and makes it possible for transferring findings from one paradigm to another. Simulation results demonstrate its promising applications in graph-based learning.

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NeurIPS Conference 2009 Conference Paper

Fast Graph Laplacian Regularized Kernel Learning via Semidefinite–Quadratic–Linear Programming

Xiao-ming Wu
Anthony So
Zhenguo Li
Shuo-yen Li

Kernel learning is a powerful framework for nonlinear data modeling. Using the kernel trick, a number of problems have been formulated as semidefinite programs (SDPs). These include Maximum Variance Unfolding (MVU) (Weinberger et al. , 2004) in nonlinear dimensionality reduction, and Pairwise Constraint Propagation (PCP) (Li et al. , 2008) in constrained clustering. Although in theory SDPs can be efficiently solved, the high computational complexity incurred in numerically processing the huge linear matrix inequality constraints has rendered the SDP approach unscalable. In this paper, we show that a large class of kernel learning problems can be reformulated as semidefinite-quadratic-linear programs (SQLPs), which only contain a simple positive semidefinite constraint, a second-order cone constraint and a number of linear constraints. These constraints are much easier to process numerically, and the gain in speedup over previous approaches is at least of the order $m^{2. 5}$, where m is the matrix dimension. Experimental results are also presented to show the superb computational efficiency of our approach.

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