Supervised classification in high-dimensional space: geometrical,statistical, and asymptotical properties of multivariate data

摘要

The recent development of more sophisticated remote-sensingnsystems enables the measurement of radiation in many more spectralnintervals than was previously possible. An example of this technology isnthe AVIRIS system, which collects image data in 220 bands. The increasedndimensionality of such hyperspectral data greatly enhances the data'sninformation content, but provides a challenge to the current techniquesnfor analyzing such data. Human experience in 3D space tends to misleadnour intuition of geometrical and statistical properties innhigh-dimensional space, properties which must guide our choices in thendata analysis process. Using Euclidean and Cartesian geometry,nhigh-dimensional space properties are investigated in this paper, andntheir implication for high-dimensional data and its analysis is studiednin order to illuminate the differences between conventional spaces andnhyperdimensional space