Ultrametricity in Data Analysis

  • startdate:

    March 2011

Summary

Ultrametricity is responsible for hierarchical structure in data. Therefore, the task is to find and understand ultrametricity inherent to data, instead of imposing an ultrametricity, what most clustering methods do. Ultrametricity can also be exploited in order to reduce the number of features in high-dimensional data.

Publications


Bradley, P. E. (2019). On the Logistic Behaviour of the Topological Ultrametricity of Data. Journal of classification, 36 (2), 266–276.
Bradley, P. E.; Keller, S.; Weinmann, M. (2018). Unsupervised Feature Selection Based on Ultrametricity and Sparse Training Data: A Case Study for the Classification of High-Dimensional Hyperspectral Data. Remote sensing, 10 (10), Art.Nr.: 1564. doi:10.3390/rs10101564
Bradley, P. E. (2017). Finding Ultrametricity in Data using Topology. Journal of classification, 34 (1), 76–84. doi:10.1007/s00357-017-9228-8
Bradley, P. E. (2016). Ultrametricity indices for the Euclidean and Boolean hypercubes. P-adic numbers, ultrametric analysis, and applications, 8 (4), 298–311. doi:10.1134/S2070046616040038
Bradley, P. E.; Braun, A. C. (2015). Finding the Asymptotically Optimal Baire Distance for Multi-Channel Data. Applied mathematics, 06 (3), 484–495. doi:10.4236/am.2015.63046