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dlpc

DLPC

### LP-classifier on dissimilarity (proximity) data

[W1,W2,W3] = DLPC(D,BIAS,TYPE,PARAM)

 Input D Dissimilarity (proximity) dataset BIAS YES or NO (optional; default: 1 (YES)) TYPE Type of a classifier 'SIMPLE' the most simple formulation; no sparse solution; PARAM = []; 'STANDARD' minimization of the training misclassification errors;  no sparse solution; PARAM = []; 'C-SPARSE' sparse solution; a formulation similar to the LP_1 SVM; PARAM is a tradeoff parameter, similar as in the traditional SVM; (optional; DEFAULT: 1). 'MU-SPARSE' sparse solution; a formulation similar to the LP_1 SVM,  based on the paper of Graepel, Herbrich, Smola etc  'Classification on proximity data with LP-machines'. PARAM is a tradeoff parameter, usually PARAM = 0.05 or 0.1.  It is an upper bound on the misclassfied training objects.  So, for well separable problems, PARAM = 0.01 or PARAM = 0.02.  (optional; DEFAULT: the LOO 1-NN error * 1.3). PARAM Parameter connected to the TYPE, as above

 Output W1 LP-Classifier in the complete dissimilarity space W2 LP-Classifier in a reduced dissimilarity space W3 Object selection prmapping; the indices of support objects are in +W3.
DEFAULTS BIAS = 1 TYPE = 'STANDARD' PARAM = []

### Description

Classification problem on a N x M dissimilarity dataset D with LP-machines.  D should be described by both label and feature lists. If D is a square,  symmetric matrix, then the feature list should be the same as the label list.

Assume a 2-class problem. Let DLPC select J support objects. Then
W1 is an M x 2 classifier in the original dissimilarity space, W2 is an J x 2 classifier in the dissimilarity space defined by the J support objects  and W3 is an M x R feature selection such that W1 = W3 * W2.  Note that the indices of the support objects can be retrieved by +W3.

A linear classifier is built on D

f(D(x,*)) = diag(Y) * D(x,*) * W + W0,

where Y are labels (+/- 1) and W are the weights. If BIAS is 1, then W0 is also  sought, otherwise it equals 0, hence the hyperplane is forced to go through the origin.

For C-class problems, C classifiers are trained, one against all others.  In such a case, only W1 is returned and W3 in now NOT a feature selection,  but directly the indices of the support objects.

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