Distance metrics for high dimensional nearest neighborhood recovery: Compression and normalization
Information Sciences: an International Journal
A survey on unsupervised outlier detection in high-dimensional numerical data
Statistical Analysis and Data Mining
Model-based clustering of high-dimensional data: A review
Computational Statistics & Data Analysis
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An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial sparsity increases. This leads us to assert that very high dimensional data are of simple structure. We exemplify this finding through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling.