pe_em
PE_EM
Embedding to a PseudoEuclidean (PE) space
W = PE_EM(D,ALF,P)
W = D*PE_EM([],ALF,P)
X = C*W
Input  D  NxN symmetric dissimilarity matrix (dataset)  ALF  Determines dimensionality of the mapping (optional, default: Inf)  (0,1)  Fraction of the total (absolute value) preserved variance Inf  No reduction (default) 'p'  Mapping to Euclidean space using positive eigenvalues only 'PARp'  Projection to Euclidean space based on the PAR fraction of positive eigenvalues; e.g. ALF = '0.9p' (the positive space) 'n'  Mapping to Euclidean space using negative eigenvalues only 'PARn'  Projection to Euclidean space based on the PAR fraction of negative eigenvalues; e.g. ALF = '0.7n' (the negative space) 'P1pP2n' Mapping to Euclidean space using 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)  C  Dataset, dissimilarity matrix to be mapped to PE space. 
Output  W  Mapping to PE space  X  PseudoEuclidean dataset, see PE_DATASET 
Description Mapping W onto an Mdimensional PseudoEuclidean _PE) subspace from a symmetric, square dissimilarity matrix D such that the dissimilarities are preserved. W is linear in D.^2. 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 C*W in which C is a dissimilarity matrix referring to the same objects as D (same number columns). In case D equal C, the resulting X = D*W is a PEDATASET such that PE_DISTM(X) approximates the the original D.^2. In case W = PE_EM(D) this is exact.
X is an object of class PE_DATASET which is a child of PRDATASET.It stores the positive and negative subspaces of the PE_space. See PE_DATASET for more information. Reference(s)1. L. Goldfarb, A unified approach to pattern recognition, Pattern Recognition, vol.17, 575582, 1984. 2. E. Pekalska and R.P.W. Duin, The Dissimilarity Representation for Pattern Recognition, Foundations and Applications, World Scientific, Singapore, 2005, 1607. 3. E. Pekalska, P. Paclik and R.P.W. Duin, A Generalized Kernel Approach to Dissimilaritybased Classification, Journal of Machine Learning Research, vol.2, no.2, 175211, 2002. 4. E. Pekalska and R.P.W. Duin, Beyond traditional kernels: classification % in two dissimilaritybased representation spaces, IEEE Trans. on Systems, Man Cybernetics, vol. 38, no. 6, 2008, 729744. See also
mappings, datasets, pe_dataset, pe2complex, pcam, getsig, setsig, This file has been automatically generated. If badly readable, use the helpcommand in Matlab. 
