PROTSELFD

Forward Prototype Selection for Dissimilarity Matrices

    [W,E,KOPT] = PROTSELFD(D,CRIT,K)
     W = D*PROTSELFD([],CRIT,K)

Input
D	Dataset, dissimilarity matrix, not necessarily square.
K	Integer, desired number of prototypes. Default: select all, just  rank the columns of D
CRIT	'super' supervised selection using 1NN error on prototypes.  'nn' same as 'super'  'loo' - supervised selection using leave-one-out 1NN error estimation.  'maxdist' - unsupervised selection minimizing the maximum  distance to the nearest prototype.  'meandist' - unsupervised selection minimizing the average  distance to the nearest prototype.

Output
W	Selection mapping ('feature selection'). +W: Prototype indices.
E	Error stimate as a function of number of selected prototypes  (for supervised selection only reliable for prototype sizes >= class size)
KOPT	Estimate for best size in avoiding peaking  (supervised selection only)

Description

This procedure for optimizing the representation set of a dissimilarity  matrix is based on a greedy, forward selection of prototypes. This  implies that for larger values of K always the selected features always  start with the ones found for smaller K.

In case of a supervised selection, D should be a labeled dataset with  prototype labels stored as feature labels. The 1NN error to the nearest  prototype based on the given dissimilarities is used as a criterion.  In case of a leave-one-out error estimation it is assumed that the first  objects in D (rows) correspond with the objects used for the  representation set (columns).

For K=1 just a single prototype has to be returned, but computing the  1NN error is not possible as all objects are assigned to the same class.  In that case the centre object of the largest class will be returned.

Note that the search continues untill K prototypes are found. This might  be larger than desired due to peaking (overtraining). Therefor an  estimate for the optimal number of prototype is returned in KOPT.

The prototype selection may be applied by C = B*W(:,1:KSEL), in which B is a dissimilarity matrix based on the same representation set as A (e.g.  A itself) and C is a resulting dissimilarity matrix in which the KSEL (e.g. KOPT) best prototypes are selected.

In case of unsupervised selection the maximum or the mean distances to  the nearest prototype are minimized. These criteria are the same as used  in the k-centers and k-mediods cluster procedures.

A random selection just selects at random a set of columns of D.

Reference(s)

E. Pekalska, R.P.W. Duin, and P. Paclik, Prototype selection for dissimilarity-based classification, Pattern Recognition, vol. 39, no. 2, 2006, 189-208.

See also

datasets, mappings, knndc, disex_protselfd,