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

The recent development of more sophisticated remote-sensing systems enables the measurement of radiation in many more spectral intervals than previously possible. An example of this technology is the AVIRIS system, which collects image data in 220 bands. The increased dimensionality of such hyperspectral data greatly enhances the data information content, but provides a challenge to the current techniques for analyzing such data Human experience in three-dimensional (3-D) space tends to mislead our intuition of geometrical and statistical properties in high-dimensional space, properties which must guide our choices in the data analysis process. Using Euclidean and Cartesian geometry, in this paper, high-dimensional space properties are investigated and their implication for high-dimensional data and its analysis is studied to illuminate the differences between conventional spaces and hyperdimensional space.