dlpc
DLPC
LPclassifier 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 = [];  'CSPARSE'  sparse solution; a formulation similar to the LP_1 SVM;  PARAM  is a tradeoff parameter, similar as in the traditional  SVM;  (optional; DEFAULT: 1).  'MUSPARSE'  sparse solution; a formulation similar to the LP_1 SVM, based on the paper of Graepel, Herbrich, Smola etc 'Classification on proximity data with LPmachines'.  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 1NN error * 1.3).  PARAM  Parameter connected to the TYPE, as above 
Output  W1  LPClassifier in the complete dissimilarity space  W2  LPClassifier 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 LPmachines. 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 2class 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 Cclass 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 helpcommand in Matlab. 
