High-dimensional cluster boundary detection using directed Markov tree

Abstract

Hypersurface of an inscribed geometry decides the distribution of an embedded cluster, in which its boundary points approximately fit this surface. To detect these points, capturing the implicit features of a local space is used to distinguish whether the data is an inner or outer feature. However, this approximation on the boundary is coarse-grained and may be ineffective in a high-dimensional space due to unbalanced feature distribution. In this paper, we introduce a directed Markov tree in high-dimensional cluster boundary detection. The key idea is to project each one-dimensional subspace of a local high-dimensional feature space into a layer of a directed Markov tree, covering absorptive and reflective walls. We then derive a fine-grained detection coefficient against on the Markov process of knight’s tour over each layer of the tree. In this fine-grained view, the local feature space centered with a cluster boundary point has lower estimate on the tour cost than the internal data of the cluster. Based on this observation, we propose a knight algorithm to detect the boundary points of a high-dimensional feature space. Experiments on gene expression and video retrieval datasets demonstrate that the proposed algorithm can achieve a higher F-measure score than the other boundary detection baselines.