A vector space model for automatic indexing
Communications of the ACM
Stability of Persistence Diagrams
Discrete & Computational Geometry
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
Listing all maximal cliques in large sparse real-world graphs
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
Computational topology in text mining
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
PHOG: photometric and geometric functions for textured shape retrieval
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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In this paper we present ideas from computational topology, applicable in analysis of point cloud data. In particular, the point cloud can represent a feature space of a collection of objects such as images or text documents. Computing persistent homology reveals the global structure of similarities between the data. Furthermore, we argue that it is essential to incorporate higher-degree relationships between objects. Finally, we show that new computational topology algorithms expose much better practical performance compared to standard techniques.