Tree PCA for Extracting Dominant Substructures from Labeled Rooted Trees

Abstract

We propose novel principal component analysis (PCA) for rooted labeled trees to discover dominant substructures from a collection of trees. The principal components of trees are defined in analogy to the ordinal principal component analysis on numerical vectors. Our methods substantially extend earlier work, in which the input data are restricted to binary trees or rooted unlabeled trees with unique vertex indexing, and the principal components are also restricted to the form of paths. In contrast, our extension allows the input data to accept general rooted labeled trees, and the principal components to have more expressive forms of subtrees instead of paths. For this extension, we can employ the technique of flexible tree matching; various mappings used in tree edit distance algorithms. We design an efficient algorithm using top-down mappings based on our framework, and show the applicability of our algorithm by applying it to extract dominant patterns from a set of glycan structures.