TITLE:
High Dimensional Dataset Compression Using Principal Components
AUTHORS:
Michael B. Richman, Andrew E. Mercer, Lance M. Leslie, Charles A. Doswell III, Chad M. Shafer
KEYWORDS:
Data Compression; Eigenanalysis; Computational Complexity; Severe Weather; Rotated Principal Components
JOURNAL NAME:
Open Journal of Statistics,
Vol.3 No.5,
October
9,
2013
ABSTRACT: Until recently, computational power was insufficient to diagonalize
atmospheric datasets of order 108 - 109 elements. Eigenanalysis of tens of thousands of variables now can achieve
massive data compression for spatial fields with strong correlation properties. Application
of eigenanalysis to 26,394 variable dimensions, for three severe weather
datasets (tornado, hail and wind) retains 9 - 11 principal
components explaining 42% - 52% of the variability. Rotated principal
components (RPCs) detect localized coherent data variance structures for each
outbreak type and are related to standardized anomalies of the meteorological
fields. Our analyses of the RPC loadings and scores show that these graphical
displays can efficiently reduce and interpret large datasets. Data is
analyzed 24 hours prior to severe weather as a forecasting aid. RPC loadings of
sea-level pressure fields show different morphology loadings for each outbreak
type. Analysis of low level moisture and temperature RPCs suggests moisture
fields for hail and wind which are more related than for tornado outbreaks.
Consequently, these patterns can identify precursors of severe weather and
discriminate between tornadic and non-tornadic outbreaks.