Active learning based on minimization of the expected path-length of random walks on the learned manifold structure

Abstract Active learning algorithms aim at selecting important samples to label for subsequent machine learning tasks. Many active learning algorithms make use of the reproducing kernel Hilbert space (RKHS) induced by a Gaussian radial basis function (RBF) kernel and leverage the geometrical structure of the data for query-sample selection. Parameters for the kernel function and the k -nearest-neighborhood graph must be properly set beforehand. As a tool exploring the structure of data, active learning algorithms with automatic tuning of those parameters are desirable. In this paper, local linear embedding (LLE) with convex constraints on neighbor weights is used to learn the geometrical structure of the data in the RKHS induced by a Gaussian RBF kernel. Automatic tuning of the kernel parameter is based on the assumption that the geometrical structure of the data in the RKHS is sparse and local. With the Markov matrix established based on the learned LLE weight matrix, the total expected path-length of the random walks from all samples to selected samples is proposed to be a criterion for query-sample selection. A greedy algorithm having a guaranteed solution bound is developed to select query samples and a two-phase scheme is also proposed for scaling the proposed active learning algorithm. Experimental results on data sets including hundreds to tens of thousands of samples have shown the feasibility of the proposed approach.