A vector space model for automatic indexing
Communications of the ACM
Modern Information Retrieval
Cover trees for nearest neighbor
ICML '06 Proceedings of the 23rd international conference on Machine learning
Technical Section: Fast construction of the Vietoris-Rips complex
Computers and Graphics
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Memory-Efficient Computation of Persistent Homology for 3D Images Using Discrete Morse Theory
SIBGRAPI '11 Proceedings of the 2011 24th SIBGRAPI Conference on Graphics, Patterns and Images
Towards topological analysis of high-dimensional feature spaces
Computer Vision and Image Understanding
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In this paper we present our ongoing research on applying computational topology to analysis of structure of similarities within a collection of text documents. Our work is on the fringe between text mining and computational topology, and we describe techniques from each of these disciplines. We transform text documents to the so-called vector space model, which is often used in text mining. This representation is suitable for topological computations. We compute homology, using discrete Morse theory, and persistent homology of the Flag complex built from the point-cloud representing the input data. Since the space is high-dimensional, many difficulties appear. We describe how we tackle these problems and point out what challenges are still to be solved.