Daniel@0: function [C,P]=knn(d, Cp, K)
Daniel@0: 
Daniel@0: %KNN K-Nearest Neighbor classifier using an arbitrary distance matrix
Daniel@0: %
Daniel@0: %  [C,P]=knn(d, Cp, [K])
Daniel@0: %
Daniel@0: %  Input and output arguments ([]'s are optional): 
Daniel@0: %   d     (matrix) of size NxP: This is a precalculated dissimilarity (distance matrix).
Daniel@0: %           P is the number of prototype vectors and N is the number of data vectors
Daniel@0: %           That is, d(i,j) is the distance between data item i and prototype j.
Daniel@0: %   Cp    (vector) of size Px1 that contains integer class labels. Cp(j) is the class of 
Daniel@0: %            jth prototype.
Daniel@0: %   [K]   (scalar) the maximum K in K-NN classifier, default is 1
Daniel@0: %   C     (matrix) of size NxK: integers indicating the class 
Daniel@0: %           decision for data items according to the K-NN rule for each K.
Daniel@0: %           C(i,K) is the classification for data item i using the K-NN rule
Daniel@0: %   P     (matrix) of size NxkxK: the relative amount of prototypes of 
Daniel@0: %           each class among the K closest prototypes for each classifiee. 
Daniel@0: %           That is, P(i,j,K) is the relative amount of prototypes of class j 
Daniel@0: %           among K nearest prototypes for data item i.
Daniel@0: %
Daniel@0: % If there is a tie between representatives of two or more classes
Daniel@0: % among the K closest neighbors to the classifiee, the class i selected randomly 
Daniel@0: % among these candidates.
Daniel@0: %
Daniel@0: % IMPORTANT  If K>1 this function uses 'sort' which is considerably slower than 
Daniel@0: %            'max' which is used for K=1. If K>1 the knn always calculates 
Daniel@0: %            results for all K-NN models from 1-NN up to K-NN.   
Daniel@0: %
Daniel@0: % EXAMPLE 1 
Daniel@0: %
Daniel@0: % sP;                           % a SOM Toolbox data struct containing labeled prototype vectors
Daniel@0: % [Cp,label]=som_label2num(sP); % get integer class labels for prototype vectors                 
Daniel@0: % sD;                           % a SOM Toolbox data struct containing vectors to be classified
Daniel@0: % d=som_eucdist2(sD,sP);        % calculate euclidean distance matrix
Daniel@0: % class=knn(d,Cp,10);           % classify using 1,2,...,10-rules
Daniel@0: % class(:,5);                   % includes results for 5NN 
Daniel@0: % label(class(:,5))             % original class labels for 5NN
Daniel@0: %
Daniel@0: % EXAMPLE 2 (leave-one-out-crossvalidate KNN for selection of proper K)
Daniel@0: %
Daniel@0: % P;                          % a data matrix of prototype vectors (rows)
Daniel@0: % Cp;                         % column vector of integer class labels for vectors in P 
Daniel@0: % d=som_eucdist2(P,P);        % calculate euclidean distance matrix PxP
Daniel@0: % d(eye(size(d))==1)=NaN;     % set self-dissimilarity to NaN:
Daniel@0: %                             % this drops the prototype itself away from its neighborhood 
Daniel@0: %                             % leave-one-out-crossvalidation (LOOCV)
Daniel@0: % class=knn(d,Cp,size(P,1));  % classify using all possible K
Daniel@0: %                             % calculate and plot LOOC-validated errors for all K
Daniel@0: % failratep = ...
Daniel@0: %  100*sum((class~=repmat(Cp,1,size(P,1))))./size(P,1); plot(1:size(P,1),failratep) 
Daniel@0: 
Daniel@0: % See also SOM_LABEL2NUM, SOM_EUCDIST2, PDIST. 
Daniel@0: %
Daniel@0: % Contributed to SOM Toolbox 2.0, October 29th, 2000 by Johan Himberg
Daniel@0: % Copyright (c) by Johan Himberg
Daniel@0: % http://www.cis.hut.fi/projects/somtoolbox/
Daniel@0: 
Daniel@0: % Version 2.0beta Johan 291000
Daniel@0: 
Daniel@0: %% Init %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: 
Daniel@0: % Check K 
Daniel@0: if nargin<3 | isempty(K),
Daniel@0:   K=1;
Daniel@0: end
Daniel@0: 
Daniel@0: if ~vis_valuetype(K,{'1x1'})
Daniel@0:   error('Value for K must be a scalar');
Daniel@0: end
Daniel@0: 
Daniel@0: % Check that dist is a matrix
Daniel@0: if ~vis_valuetype(d,{'nxm'}),
Daniel@0:   error('Distance matrix not valid.')
Daniel@0: end
Daniel@0: 
Daniel@0: [N_data N_proto]=size(d);
Daniel@0: 
Daniel@0: % Check class label vector: must be numerical and of integers
Daniel@0: if ~vis_valuetype(Cp,{[N_proto 1]});
Daniel@0:   error(['Class vector is invalid: has to be a N-of-data_rows x 1' ...
Daniel@0: 	 ' vector of integers']);
Daniel@0: elseif sum(fix(Cp)-Cp)~=0
Daniel@0:   error('Class labels in vector ''Cp'' must be integers.');
Daniel@0: end
Daniel@0: 
Daniel@0: if size(d,2) ~= length(Cp),
Daniel@0:   error('Distance matrix and prototype class vector dimensions do not match.');
Daniel@0: end
Daniel@0: 
Daniel@0: % Check if the classes are given as labels (no class input arg.)
Daniel@0: % if they are take them from prototype struct
Daniel@0: 
Daniel@0: % Find all class labels
Daniel@0: ClassIndex=unique(Cp);
Daniel@0: N_class=length(ClassIndex); % number of different classes  
Daniel@0: 
Daniel@0: 
Daniel@0: %%%% Classification %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: 
Daniel@0: if K==1,   % sort distances only if K>1
Daniel@0:   
Daniel@0:   % 1NN
Daniel@0:   % Select the closest prototype
Daniel@0:   [tmp,proto_index]=min(d,[],2); 
Daniel@0:   C=Cp(proto_index);
Daniel@0: 
Daniel@0: else 
Daniel@0:   
Daniel@0:   % Sort the prototypes for each classifiee according to distance
Daniel@0:   [tmp, proto_index]=sort(d');
Daniel@0:   
Daniel@0:   %% Select up to K closest prototypes
Daniel@0:   proto_index=proto_index(1:K,:);
Daniel@0:   knn_class=Cp(proto_index);
Daniel@0:   for i=1:N_class,
Daniel@0:     classcounter(:,:,i)=cumsum(knn_class==ClassIndex(i));
Daniel@0:   end
Daniel@0:   
Daniel@0:   %% Vote between classes of K neighbors 
Daniel@0:   [winner,vote_index]=max(classcounter,[],3);
Daniel@0:   
Daniel@0:   %%% Handle ties
Daniel@0:   
Daniel@0:   % Set index to classes that got as much votes as winner
Daniel@0:   
Daniel@0:   equal_to_winner=(repmat(winner,[1 1 N_class])==classcounter);
Daniel@0:  
Daniel@0:   % set index to ties
Daniel@0:   [tie_indexi,tie_indexj]=find(sum(equal_to_winner,3)>1); % drop the winner from counter 
Daniel@0:   
Daniel@0:   % Go through tie cases and reset vote_index randomly to one
Daniel@0:   % of them 
Daniel@0:   
Daniel@0:   for i=1:length(tie_indexi),
Daniel@0:     tie_class_index=find(squeeze(equal_to_winner(tie_indexi(i),tie_indexj(i),:)));
Daniel@0:     fortuna=randperm(length(tie_class_index));
Daniel@0:     vote_index(tie_indexi(i),tie_indexj(i))=tie_class_index(fortuna(1));
Daniel@0:   end
Daniel@0:   
Daniel@0:   C=ClassIndex(vote_index)';
Daniel@0: end
Daniel@0: 
Daniel@0: %% Build output %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: 
Daniel@0: % Relative amount of classes in K neighbors for each classifiee
Daniel@0: 
Daniel@0: if K==1,
Daniel@0:   P=zeros(N_data,N_class);
Daniel@0:   if nargout>1,
Daniel@0:     for i=1:N_data,
Daniel@0:       P(i,ClassIndex==C(i))=1;
Daniel@0:     end
Daniel@0:   end
Daniel@0: else
Daniel@0:   P=shiftdim(classcounter,1)./repmat(shiftdim(1:K,-1), [N_data N_class 1]);
Daniel@0: end
Daniel@0: