#### DMCA

## Fukunaga-Koontz Transform for Small Sample Size Problems (2005)

### Citations

3779 |
Introduction to Statistical Pattern Recognition
- Fukunaga
- 1990
(Show Context)
Citation Context ...2 Q . V Finding S using Feature Scatter a) Scatter Matrices Assuming that the mixture mean of the data is subtracted from all the signal samples in the database, we could compute the scatter matrices =-=[7]-=- from the zero mean data as follows. The ‘between class’ scatter matrix signals is ζ b = ∑ i=1,2 Piµ iµ T i , where µ i is the mean of the class Ci. The ‘within class’ scatter matrix is defined as ζw ... |

758 |
Matrix Analysis and Applied Linear Algebra
- Meyer
- 2000
(Show Context)
Citation Context ...ir direct sum spans R N . But the spaces spanned by ˆVz1 and ˆVz2 are the principal subspaces of Rz1 and Rz2 respectively and hence the proof. b) Classification Schemes using ˆVzi From linear algebra =-=[6]-=-, the best reconstruction of x ∈ Ci in the subspace spanned by ˆVzi is given by ˆxzi = ˆVzi ˆV T zi ST x. (9) By the orthogonal complementary property of the principal eigenspaces, viz., ˆVzi = ˆV ⊥ z... |

81 |
and W.Koontz, “Applications of the karhunen-loeve expansion to feature selection and ordering.”
- Fukunaga
- 1970
(Show Context)
Citation Context ... matrices Ri = PiE(xxT |x ∈ Ci). Let Q = VQΛQVT Q denote the eigenvalue decomposition of Q where Q = R1+R2 is the sum of the class autocorrelation matrices. The Fukunaga-Koontz transform (FKT) matrix =-=[1]-=- is defined as 1 S = VQΛ −1/2 Q (1) which transforms a signal x to xz = S T x. From equation (1), it can be easily observed that S T QS = I. (2) Certain applications of the FKT can be seen in [2], [3]... |

5 |
Image classification by an optical implementation of the Fukunaga-Koontz transformation
- Leger, Lee
- 1982
(Show Context)
Citation Context ...efined as 1 S = VQΛ −1/2 Q (1) which transforms a signal x to xz = S T x. From equation (1), it can be easily observed that S T QS = I. (2) Certain applications of the FKT can be seen in [2], [3] and =-=[4]-=- and [5] discusses some of the statistical properties of the FKT. III Classification using FK Transform a) Orthogonality of FK Principal Subspaces The class autocorrelation matrices for the FK transfo... |

3 |
Image classification at low light levels
- Wernick, Morris
- 1986
(Show Context)
Citation Context ...trix [1] is defined as 1 S = VQΛ −1/2 Q (1) which transforms a signal x to xz = S T x. From equation (1), it can be easily observed that S T QS = I. (2) Certain applications of the FKT can be seen in =-=[2]-=-, [3] and [4] and [5] discusses some of the statistical properties of the FKT. III Classification using FK Transform a) Orthogonality of FK Principal Subspaces The class autocorrelation matrices for t... |

3 | A statistical analysis of fukunaga-koontz transform
- Huo
(Show Context)
Citation Context ...s 1 S = VQΛ −1/2 Q (1) which transforms a signal x to xz = S T x. From equation (1), it can be easily observed that S T QS = I. (2) Certain applications of the FKT can be seen in [2], [3] and [4] and =-=[5]-=- discusses some of the statistical properties of the FKT. III Classification using FK Transform a) Orthogonality of FK Principal Subspaces The class autocorrelation matrices for the FK transformed sig... |

1 |
Signal-to-clutter measure for measuring automatic target recognition performance using complimentary eigenvalue distribution analysis
- Mahanalobis, Sims, et al.
(Show Context)
Citation Context ...[1] is defined as 1 S = VQΛ −1/2 Q (1) which transforms a signal x to xz = S T x. From equation (1), it can be easily observed that S T QS = I. (2) Certain applications of the FKT can be seen in [2], =-=[3]-=- and [4] and [5] discusses some of the statistical properties of the FKT. III Classification using FK Transform a) Orthogonality of FK Principal Subspaces The class autocorrelation matrices for the FK... |