Symmetry in Data Mining and Analysis: A Unifying View based on Hierarchy

Abstract

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. "Structure" has long been understood as symmetry which can take many forms with respect to any transformation, including point, translational, rotational, and many others. Beginning with the role of number theory in expressing data, we show how we can naturally proceed to hierarchical structures. We show how this both encapsulates traditional paradigms in data analysis, and also opens up new perspectives towards issues that are on the order of the day, including data mining of massive, high dimensional, heterogeneous data sets. Linkages with other fields are also discussed including computational logic and symbolic dynamics. The structures in data surveyed here are based on hierarchy, represented as p-adic numbers or an ultrametric topology.

35 pages, 3 figures, 84 references

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• A p-Adic Model of DNA Sequence and Genetic Code
• p-Adic Modelling of the Genome and the Genetic Code
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• Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
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• A brief introduction to p-adic numbers
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Cited by in corpus (7)

• Methods of Hierarchical Clustering
• Ultrametric Model of Mind, I: Review
• Fast, Linear Time Hierarchical Clustering using the Baire Metric
• Sparse p-Adic Data Coding for Computationally Efficient and Effective Big Data Analytics
• Ultrametric and Generalized Ultrametric in Computational Logic and in Data Analysis
• Ultrametric Component Analysis with Application to Analysis of Text and of Emotion
• Fast redshift clustering with the Baire (ultra) metric