High Dimensional Mode Hunting Using Pettiest Components Analysis
Principal components analysis has been used to reduce the dimensionality of datasets for a long time. In this paper, we will demonstrate that in mode detection the components of smallest variance, the pettiest components, are more important. We prove that for a multivariate normal or Laplace distrib...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 45(2023), 4 vom: 02. Apr., Seite 4637-4649 |
|---|---|
| 1. Verfasser: | |
| Weitere Verfasser: | , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2023
|
| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article |
| Zusammenfassung: | Principal components analysis has been used to reduce the dimensionality of datasets for a long time. In this paper, we will demonstrate that in mode detection the components of smallest variance, the pettiest components, are more important. We prove that for a multivariate normal or Laplace distribution, we obtain boxes of optimal volume by implementing "pettiest component analysis," in the sense that their volume is minimal over all possible boxes with the same number of dimensions and fixed probability. This reduction in volume produces an information gain that is measured using active information. We illustrate our results with a simulation and a search for modal patterns of digitized images of hand-written numbers using the famous MNIST database; in both cases pettiest components work better than their competitors. In fact, we show that modes obtained with pettiest components generate better written digits for MNIST than principal components |
|---|---|
| Beschreibung: | Date Completed 10.04.2023 Date Revised 23.09.2024 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2022.3195462 |