Daniel@0: function csS = som_stats(D,varargin)
Daniel@0: 
Daniel@0: %SOM_STATS Calculate descriptive statistics for the data.
Daniel@0: %  
Daniel@0: % csS = som_stats(D,[sort]); 
Daniel@0: % 
Daniel@0: %  csS = som_stats(D); 
Daniel@0: %  csS = som_stats(D,'nosort'); 
Daniel@0: %  som_table_print(som_stats_table(csS))
Daniel@0: %
Daniel@0: %  Input and output arguments ([]'s are optional): 
Daniel@0: %   D           (matrix) a matrix, size dlen x dim
Daniel@0: %               (struct) data or map struct
Daniel@0: %   [sort]      (string) 'sort' (default) or 'nosort'
Daniel@0: %                        If 'nosort' is specified, the data is not 
Daniel@0: %                        sorted, and therefore the values of
Daniel@0: %                        nunique, uvalues, ucount, fvalues, fcount, and tiles fields 
Daniel@0: %                        are not calculated. This may be useful if
Daniel@0: %                        there is a very large amount of data, and
Daniel@0: %                        one wants to reduce calculation time.
Daniel@0: %
Daniel@0: %   csS         (cell array) size dim x 1, of statistics structs with 
Daniel@0: %                        the following fields
Daniel@0: %      .type             (string) 'som_stat'
Daniel@0: %      .name             (string) name of the variable
Daniel@0: %      .normalization    (struct array) variable normalization (see SOM_NORMALIZE)
Daniel@0: %      .ntotal           (scalar) total number of values
Daniel@0: %      .nvalid           (scalar) number of valid values (not Inf or NaN)
Daniel@0: %      .min              (scalar) minimum value 
Daniel@0: %      .max              (scalar) maximum value 
Daniel@0: %      .mean             (scalar) mean value (not Inf or NaN)
Daniel@0: %      .std              (scalar) standard deviation (not Inf or NaN)
Daniel@0: %      .nunique          (scalar) number of unique values
Daniel@0: %      .mfvalue          (vector) most frequent value
Daniel@0: %      .mfcount          (vector) number of occurances of most frequent value
Daniel@0: %      .values           (vector) at most MAXDISCRETE (see below) sample values 
Daniel@0: %      .counts           (vector) number of occurances for each sampled value
Daniel@0: %      .tiles            (vector) NT-tile values, for example
Daniel@0: %                                    NT=4   for quartiles: 25%, 50% and 75%
Daniel@0: %                                    NT=100 for percentiles: 1%, 2%, ... and 99%
Daniel@0: %      .hist             (struct) histogram struct with the following fields
Daniel@0: %           .type        (string) 'som_hist'
Daniel@0: %           .bins        (vector) histogram bin centers 
Daniel@0: %           .counts      (vector) count of values in each bin
Daniel@0: %           .binlabels   (cellstr) labels for the bins (denormalized bin
Daniel@0: %                                  center values)
Daniel@0: %           .binlabels2  (cellstr) labels for the bins (denormalized bin
Daniel@0: %                                  edge values, e.g. '[1.4,2.5['
Daniel@0: %
Daniel@0: %   Constants: 
Daniel@0: %      MAXDISCRETE = 10
Daniel@0: %      NT          = 10
Daniel@0: %
Daniel@0: % See also  SOM_STATS_PLOT, SOM_STATS_TABLE, SOM_TABLE_PRINT, SOM_STATS_REPORT.
Daniel@0: 
Daniel@0: % Contributed to SOM Toolbox 2.0, December 31st, 2001 by Juha Vesanto
Daniel@0: % Copyright (c) by Juha Vesanto
Daniel@0: % http://www.cis.hut.fi/projects/somtoolbox/
Daniel@0: 
Daniel@0: % Version 2.0beta juuso 311201
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
Daniel@0: %% arguments
Daniel@0: 
Daniel@0: % default values
Daniel@0: nosort      = 0; 
Daniel@0: nbins       = 10; 
Daniel@0: maxdiscrete = 20; 
Daniel@0: ntiles      = 10; 
Daniel@0: 
Daniel@0: % first argument
Daniel@0: if isstruct(D), 
Daniel@0:     switch D.type, 
Daniel@0:     case 'som_map',  cn = D.comp_names; sN = D.comp_norm; D = D.codebook; 
Daniel@0:     case 'som_data', cn = D.comp_names; sN = D.comp_norm; D = D.data; 
Daniel@0:     otherwise, error('Invalid first argument')
Daniel@0:     end    
Daniel@0: else
Daniel@0:     cn = cell(size(D,2),1); 
Daniel@0:     cn(:) = {'Variable'};
Daniel@0:     for i=1:length(cn), cn{i} = sprintf('%s%d',cn{i},i); end    
Daniel@0:     sN = cell(size(D,2),1); 
Daniel@0: end
Daniel@0: [dlen dim] = size(D);
Daniel@0: 
Daniel@0: % other arguments
Daniel@0: 
Daniel@0: if length(varargin)>0, 
Daniel@0:   if strcmp(varargin{1},'nosort'), nosort = 1; end
Daniel@0: end
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
Daniel@0: %% action
Daniel@0: 
Daniel@0: sStat = struct('type','som_stat','name','','normalization',[],...
Daniel@0:                'min',NaN,'max',NaN,'mean',NaN,'std',NaN,...
Daniel@0:                'nunique',NaN,'values',[],'counts',[],'mfvalue',NaN,'mfcount',NaN,'tiles',[],...
Daniel@0:                'ntotal',dlen,'nvalid',NaN,'hist',[]);
Daniel@0: csS = cell(0);
Daniel@0:            
Daniel@0: for i=1:dim, 
Daniel@0:     sS = sStat;
Daniel@0:     sS.name = cn{i};
Daniel@0:     sS.normalization = sN{i}; 
Daniel@0:     x = D(:,i); 
Daniel@0:     x(find(~isfinite(x))) = [];
Daniel@0:     % basic descriptive statistics
Daniel@0:     sS.nvalid = length(x);
Daniel@0:     if length(x), 
Daniel@0:         sS.min  = min(x);
Daniel@0:         sS.max  = max(x);
Daniel@0:         sS.mean = mean(x);  
Daniel@0:         sS.std = std(x);
Daniel@0:         bins = [];
Daniel@0:         if ~nosort, 
Daniel@0:             xsorted    = sort(x);
Daniel@0:             % number of unique values
Daniel@0:             repeated   = (xsorted(1:end-1)==xsorted(2:end));
Daniel@0:             j          = [1; find(~repeated)+1];         
Daniel@0:             xunique    = xsorted(j); 
Daniel@0:             sS.nunique = length(xunique);           
Daniel@0:             ucount     = diff([j; length(xsorted)+1]);
Daniel@0:             % most frequent value
Daniel@0:             [fcount,j] = max(ucount);
Daniel@0:             sS.mfvalue = xunique(j);
Daniel@0:             sS.mfcount = fcount;
Daniel@0:             % -tiles (k*100/ntiles % of values, k=1..)
Daniel@0:             pickind    = round(linspace(1,sS.nvalid,ntiles+1)); 
Daniel@0:             pickind    = pickind(2:end-1);
Daniel@0:             sS.tiles   = xsorted(pickind);
Daniel@0:             if sS.nunique <= sS.nvalid/2, 
Daniel@0:                 % unique values
Daniel@0:                 sS.values = xunique; 
Daniel@0: 	            sS.counts = ucount; 
Daniel@0:                 bins = sS.values; 
Daniel@0:             else
Daniel@0:                 % just maxdiscrete values, evenly  picked
Daniel@0:                 pickind    = round(linspace(1,sS.nunique,maxdiscrete));
Daniel@0:                 sS.values  = xunique(pickind);
Daniel@0:                 sS.counts  = ucount(pickind);
Daniel@0:  	    
Daniel@0:                 %% OPTION 2: maxdiscrete most frequent values
Daniel@0:                 %[v,j]     = sort(ucount); 
Daniel@0:                 %pickind   = j(1:maxdiscrete);             
Daniel@0:                 %sS.values = xunique(pickind);
Daniel@0:                 %sS.counts = ucount(pickind);
Daniel@0: 
Daniel@0:                 % OPTION 3: representative values - calculated using k-means
Daniel@0:                 %[y,bm,qe] = kmeans(x,maxdiscrete);
Daniel@0:                %sS.values = y; 
Daniel@0:                 %sS.counts = full(sum(sparse(bm,1:length(bm),1,maxdiscrete,length(bm)),2));
Daniel@0:             end 
Daniel@0:         end 
Daniel@0:         if isempty(bins), 
Daniel@0:             bins = linspace(sS.min,sS.max,nbins+1); 
Daniel@0:             bins = (bins(1:end-1)+bins(2:end))/2; 
Daniel@0:         end
Daniel@0:         sS.hist = som_hist(x,bins,sS.normalization);    
Daniel@0:     else
Daniel@0:         sS.hist = som_hist(x,0);
Daniel@0:     end
Daniel@0:     csS{end+1} = sS; 
Daniel@0: end
Daniel@0: 
Daniel@0: return;
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
Daniel@0: %% subfunctions
Daniel@0: 
Daniel@0: function sH = som_hist(x,bins,sN)
Daniel@0: 
Daniel@0:     binlabels  = []; 
Daniel@0:     binlabels2 = []; 
Daniel@0:     if nargin<2 | isempty(bins) | isnan(bins), 
Daniel@0:         bins = linspace(min(x),max(x),10);    
Daniel@0:     end
Daniel@0:     if isstruct(bins), 
Daniel@0:         bins = sH.bins; 
Daniel@0:         binlabels  = sH.binlabels;
Daniel@0:         binlabels2 = sH.binlabels2;
Daniel@0:     end 
Daniel@0:     if nargin<3, sN = []; end
Daniel@0: 
Daniel@0:     sH = struct('type','som_hist','bins',bins,'counts',[],...
Daniel@0:                 'binlabels',binlabels,'binlabels2',binlabels2);                         
Daniel@0:             
Daniel@0:     if length(bins)==1,
Daniel@0:         sH.counts = [length(x)];
Daniel@0:         edges = bins;
Daniel@0:     elseif length(x),
Daniel@0:         edges = (bins(1:end-1)+bins(2:end))/2;
Daniel@0:         counts = histc(x,[-Inf; edges(:); Inf]);
Daniel@0:         sH.counts = counts(1:end-1);       
Daniel@0:     end 
Daniel@0: 
Daniel@0:     if isempty(sH.binlabels),
Daniel@0:         b = som_denormalize(bins(:),sN); 
Daniel@0:         sH.binlabels = numtostring(b,4);
Daniel@0:     end 
Daniel@0: 
Daniel@0:     if isempty(sH.binlabels2),
Daniel@0:         if length(edges)==1, 
Daniel@0:             sH.binlabels2 = numtostring(som_denormalize(edges,sN),2);
Daniel@0:             if length(bins)>1, 
Daniel@0:               sH.binlabels2 = sH.binlabels2([1 1]);
Daniel@0:               sH.binlabels2{1} = [']' sH.binlabels2{1} '['];
Daniel@0:               sH.binlabels2{2} = ['[' sH.binlabels2{2} '['];
Daniel@0:             end 
Daniel@0:         else
Daniel@0:             if size(edges,1)==1, edges = edges'; end
Daniel@0:             bstr = numtostring(som_denormalize(edges,sN),4);
Daniel@0:             sH.binlabels2 = bstr([1:end end]);
Daniel@0:             sH.binlabels2{1} = [bstr{1} '['];
Daniel@0:             for i=2:length(sH.binlabels2)-1,
Daniel@0:                 sH.binlabels2{i} = ['[' bstr{i-1} ',' bstr{i} '[']; 
Daniel@0:             end 
Daniel@0:             sH.binlabels2{end} = ['[' bstr{end}];
Daniel@0:         end         
Daniel@0:     end 
Daniel@0:     
Daniel@0:     if 0, 
Daniel@0:         if length(bins)==1, sH.binlabels2 = {'constant'}; 
Daniel@0:         else    
Daniel@0:             ntiles = 10; 
Daniel@0:             plim = [1:ntiles-1] / ntiles; 
Daniel@0:             cp = cumsum(sH.counts)/sum(sH.counts);
Daniel@0:             [dummy,i] = histc(cp,[-Inf plim Inf]);            
Daniel@0:             l2 = cell(length(bins),1);            
Daniel@0:             for j=1:length(bins), l2{j} = sprintf('Q%d',i(j)); end
Daniel@0:             if i(1) > 1, l2{1} = ['...' l2{1}]; end            
Daniel@0:             k = 0; 
Daniel@0:             for j=2:length(bins), 
Daniel@0:                 if i(j)==i(j-1), 
Daniel@0:                     if k==0, l2{j-1} = [l2{j-1} '.1']; k = 1; end
Daniel@0:                     k = k + 1; 
Daniel@0:                     l2{j} = [l2{j} '.' num2str(k)]; 
Daniel@0:                 else k = 0; end
Daniel@0:             end 
Daniel@0:             if i(end) < ntiles, l2{end} = [l2{end} '...']; end
Daniel@0:             sH.binlabels2 = l2; 
Daniel@0:         end 
Daniel@0:     end    
Daniel@0: 
Daniel@0:     return;
Daniel@0: 
Daniel@0: function vstr = numtostring(v,d)
Daniel@0: 
Daniel@0:     r = max(v)-min(v); 
Daniel@0:     if r==0, r=1; end
Daniel@0:     nearzero = (abs(v)/r < 10.^-d);
Daniel@0:     i1 = find(v > 0 & nearzero); 
Daniel@0:     i2 = find(v < 0 & nearzero);     
Daniel@0:     vstr = strrep(cellstr(num2str(v,d)),' ','');
Daniel@0:     vstr(i1) = {'0.0'};
Daniel@0:     vstr(i2) = {'-0.0'};
Daniel@0:     return;
Daniel@0: