LP-classifier on dissimilarity (proximity) data
[W1,W2,W3] = DLPC(D,BIAS,TYPE,PARAM)
| 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|
DEFAULTS BIAS = 1 TYPE = 'STANDARD' PARAM = 
| 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.|
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.
|This file has been automatically generated. If badly readable, use the help-command in Matlab.|