Learning Curved Multinomial Subfamilies for Natural Language Processing and Information Retrieval
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
The SMART Retrieval System—Experiments in Automatic Document Processing
The SMART Retrieval System—Experiments in Automatic Document Processing
The Locally Weighted Bag of Words Framework for Document Representation
The Journal of Machine Learning Research
Bioinformatics
Persistence Diagrams of Cortical Surface Data
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Exploring uses of persistent homology for statistical analysis of landmark-based shape data
Journal of Multivariate Analysis
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Persistent homology is a mathematical tool from topological data analysis. It performs multi-scale analysis on a set of points and identifies clusters, holes, and voids therein. These latter topological structures complement standard feature representations, making persistent homology an attractive feature extractor for artificial intelligence. Research on persistent homology for AI is in its infancy, and is currently hindered by two issues: the lack of an accessible introduction to AI researchers, and the paucity of applications. In response, the first part of this paper presents a tutorial on persistent homology specifically aimed at a broader audience without sacrificing mathematical rigor. The second part contains one of the first applications of persistent homology to natural language processing. Specifically, our Similarity Filtration with Time Skeleton (SIFTS) algorithm identifies holes that can be interpreted as semantic "tie-backs" in a text document, providing a new document structure representation. We illustrate our algorithm on documents ranging from nursery rhymes to novels, and on a corpus with child and adolescent writings.