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

@article{citeulike:2518603, abstract = {The recent development of more sophisticated remote-sensing systems enables the measurement of radiation in many more spectral intervals than was 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's information content, but provides a challenge to the current techniques for analyzing such data. Human experience in 3D 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, high-dimensional space properties are investigated in this paper, and their implication for high-dimensional data and its analysis is studied in order to illuminate the differences between conventional spaces and hyperdimensional space}, author = {Jimenez, L. O. and Landgrebe, D. A. }, booktitle = {Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on}, citeulike-article-id = {2518603}, doi = {http://dx.doi.org/10.1109/5326.661089}, journal = {Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on}, keywords = {dimension-reduction, dr-for-classification, generalization, geometry}, number = {1}, pages = {39--54}, posted-at = {2008-03-12 08:23:52}, priority = {2}, title = {Supervised classification in high-dimensional space: geometrical, statistical, and asymptotical properties of multivariate data}, url = {http://dx.doi.org/10.1109/5326.661089}, volume = {28}, year = {1998} }

TY - JOUR ID - citeulike:2518603 L3 - citeulike-article-id:2518603 TI - Supervised classification in high-dimensional space: geometrical, statistical, and asymptotical properties of multivariate data T2 - Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on JF - Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on VL - 28 IS - 1 SP - 39 EP - 54 N2 - The recent development of more sophisticated remote-sensing systems enables the measurement of radiation in many more spectral intervals than was 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's information content, but provides a challenge to the current techniques for analyzing such data. Human experience in 3D 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, high-dimensional space properties are investigated in this paper, and their implication for high-dimensional data and its analysis is studied in order to illuminate the differences between conventional spaces and hyperdimensional space KW - dimension-reduction KW - dr-for-classification KW - generalization KW - geometry AU - Jimenez, LO AU - Landgrebe, DA PY - 1998/// UR - http://dx.doi.org/10.1109/5326.661089 ER -