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REDUCTION OF DIMENSIONALITY FOR HEURISTIC PURPOSES
Author(s) -
Baum Bernard R.
Publication year - 1977
Publication title -
taxon
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.819
H-Index - 81
eISSN - 1996-8175
pISSN - 0040-0262
DOI - 10.2307/1220550
Subject(s) - eigenvalues and eigenvectors , matrix (chemical analysis) , dimensionality reduction , transformation (genetics) , mathematics , curse of dimensionality , reduction (mathematics) , distortion (music) , interpretation (philosophy) , transformation matrix , heuristic , combinatorics , computer science , statistics , mathematical optimization , physics , artificial intelligence , geometry , chemistry , amplifier , computer network , biochemistry , kinematics , bandwidth (computing) , chromatography , quantum mechanics , classical mechanics , gene , programming language
Summary Interpretation of numerical results in analysis of relationships between OTU's or between variables is profitably achieved when the Q or R matrix can be reduced in dimensionality. An approach is proposed, viz. transformation of the elements of the matrix such that the first few eigenvalues much increase relative to others while minimizing distortion of the matrix, for the cases when eigenvalues computed from such a matrix gradually decrease. A numerical example is given using the transformation Y ij = X ij n