Hilbert Space Becomes Ultrametric in the High Dimensional Limit: Application to Very High Frequency Data Analysis
| dc.creator | Murtagh, Fionn | |
| dc.date | 2007-02-07 | |
| dc.date.accessioned | 2026-07-07T07:45:38Z | |
| dc.date.available | 2026-07-07T07:45:38Z | |
| dc.description | An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural 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. | |
| dc.description | 22 pp., 9 figs., 4 tables | |
| dc.identifier | https://arxiv.org/abs/physics/0702064 | |
| dc.identifier | http://arxiv.org/abs/physics/0702064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123597 | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.title | Hilbert Space Becomes Ultrametric in the High Dimensional Limit: Application to Very High Frequency Data Analysis | |
| dc.type | text |