Clustering in High-dimensional Data Spaces
By high-dimensional we mean dimensionality of the same order as the number of objects or observations to cluster, and the latter in the range of thousands upwards. Bellman’s “curse of dimensionality” applies to many widely-used data analysis methods in high-dimensional spaces. One way to address this problem is by array permuting methods, involving row/column reordering. Such methods are closely related to dimensionality reduction methods such as principal components analysis. An imposed order on an array is beneficial not only for visualization but also for use of a vast range of image processing methods. For example, clustering becomes in this context image feature detection.
KeywordsDimensionality Reduction Method Ultrametric Space Travel Salesperson Problem Sparse Array Progressive Transmission
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- CHEREUL, E., CREZE, M. and BIENAYME, O. (1997) “3D wavelet transform analysis of Hipparcos data”, in Maccarone, M.C., Murtagh, F., Kurtz, M. and Bijaoui, A. (eds.). Advanced Techniques and Methods for Astronomical Information Handling, Observatoire de la Côte d’Azur, Nice, France, 41–48.Google Scholar
- BYERS, S. and RAFTERY, A.E. (1996) “Nearest neighbor clutter removal for estimating features in spatial point processes”, Technical Report 305, Department of Statistics, University of Washington.Google Scholar
- BERRY, M.W., HENDRICKSON, B. and RAGHAVAN, P. (1996) Sparse matrix reordering schemes for browsing hypertext, in Lectures in Applied Mathematics (LAM) Vol. 32: The Mathematics of Numerical Analysis, Renegar, J., Shub, M. and Smale, S. (eds.). American Mathematical Society, pp. 99–123.Google Scholar