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A counter example in linear feature selection theory
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Brown, D. R. Omalley, M. J. |
| Copyright Year | 1975 |
| Description | The linear feature selection problem in multi-class pattern recognition is described as that of linearly transforming statistical information from n-dimensional (real Euclidean) space into k-dimensional space, while requiring that average interclass divergence in the transformed space decrease as little as possible. Divergence is the expected interclass divergence derived from Hajek two-class divergence; it is known that there always exists a k x n matrix B such that the transformation determined by B maximizes the divergence in k-dimensional space. It is known that, if Q is any k x k invertible matrix, and B is as defined above, then QB again maximizes the divergence in k-space. It is shown that the converse of this result is false: two matrices exist, B sub 1 and B sub 2, each of which maximizes transformed divergence, which are not related in the fashion B sub 2 = QB sub 1 for any k x k matrix Q. |
| File Size | 1551575 |
| Page Count | 10 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19750018669 |
| Archival Resource Key | ark:/13960/t24b7vd7s |
| Language | English |
| Publisher Date | 1975-03-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Linear Systems Problem Solving Euclidean Geometry Pattern Recognition Divergence Matrices Mathematics Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
