Pseudo-Euclidean Linear Embedding
W = PE_EM(D,ALF,P)
W = D*PE_EM(,ALF,P)
| D|| NxN symmetric dissimilarity matrix (dataset)|
| ALF|| Parameter determining the dimensionality and the mapping (optional, default: Inf)|
| (0,1)|| Fraction of the total (absolute value) preserved variance Inf - No dimensionality reduction, keeping all dimensions (it's VERY noisy) 'p' - Projection into a Euclidean space based on positive eigenvalues only 'PARp' - Projection into a Euclidean space based on the PAR fraction of positive eigenvalues; e.g. ALF = '0.9p' 'n' - Projection into a Euclidean space based on negative eigenvalues only 'PARn' - Projection into a (negative) Euclidean space based on the PAR fraction of negative eigenvalues; e.g. ALF = '0.7n' 'P1pP2n'- Projection into a Euclidean space based on the P1 positive eigenvalues and P2 negative eigenvalues; e.g. ALF = '0.7p0.1n', ALF = '7p2n'|
| 1|| .. N - Number of dimensions in total|
| [P1|| P2] - P1 dimensions or preserved fraction of variance in the positive subspace and P2 dimensions or preserved fraction of variance in the negative subspace; e.g. ALF = [5 10], ALF = [0.9 0.1] |
| P|| Integer between 0 and N specifying which object is mapped at the origin;|
| 0|| stands for the mean; (optional, default: 0) |
| W|| Linear embedding into a pseudo-Euclidean space|
Linear mapping W onto an M-dimensional Pseudo-Euclidean _PE) subspace from a symmetric, square dissimilarity matrix D such that the dissimilarities are preserved. M is determined by ALF. E.g., the subspace is found such that at least a fraction ALF of the total variance is preserved for ALF in (0,1). The resulting X is found by D*W. The signature of the obtained PE space (numbers of positive and negative directions) can be found by GETDATA(W,'sig'). The spectrum of the obtained space can be found by GETDAT(W,'eval').
1. L. Goldfarb, A unified approach to pattern recognition, Pattern Recognition, vol.17, 575-582, 1984.
2. E. Pekalska, P. Paclik, and R.P.W. Duin, A Generalized Kernel Approach to Dissimilarity-based Classification, Journal of Machine Learning Research, vol.2, no.2, 175-211, 2002.
3. E. Pekalska and R.P.W. Duin, Beyond traditional kernels: classification % in two dissimilarity-based representation spaces, IEEE Trans. on Systems, Man Cybernetics, vol. 38, no. 6, 2008, 729-744.
mappings, datasets, pcam, getsig, setsig,
|This file has been automatically generated. If badly readable, use the help-command in Matlab.|