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comparison toolboxes/MIRtoolbox1.3.2/somtoolbox/som_quality.m @ 0:e9a9cd732c1e tip

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1 function [mqe,tge] = som_quality(sMap, D)
2
3 %SOM_QUALITY Calculate the mean quantization and topographic error.
4 %
5 % [qe,te] = som_quality(sMap, D)
6 %
7 % qe = som_quality(sMap,D);
8 % [qe,te] = som_quality(sMap,sD);
9 %
10 % Input and output arguments:
11 % sMap (struct) a map struct
12 % D the data
13 % (struct) a data struct
14 % (matrix) a data matrix, size dlen x dim
15 %
16 % qe (scalar) mean quantization error
17 % te (scalar) topographic error
18 %
19 % The issue of SOM quality is a complicated one. Typically two
20 % evaluation criterias are used: resolution and topology preservation.
21 % If the dimension of the data set is higher than the dimension of the
22 % map grid, these usually become contradictory goals.
23 %
24 % The first value returned by this function measures resolution and the
25 % second the topology preservation.
26 % qe : Average distance between each data vector and its BMU.
27 % te : Topographic error, the proportion of all data vectors
28 % for which first and second BMUs are not adjacent units.
29 %
30 % NOTE: when calculating BMUs of data vectors, the mask of the given
31 % map is used.
32 %
33 % For more help, try 'type som_quality' or check out the online documentation.
34 % See also SOM_BMUS.
35
36 %%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
37 %
38 % som_quality
39 %
40 % PURPOSE
41 %
42 % Calculates two quality measures for the given map.
43 %
44 % SYNTAX
45 %
46 % qe = som_quality(sM,sD);
47 % qe = som_quality(sM,D);
48 % [qe,te] = som_quality(...);
49 %
50 % DESCRIPTION
51 %
52 % This function measures the quality of the given map. The measures are
53 % data-dependent: they measure the map in terms of the given
54 % data. Typically, the quality of the map is measured in terms of the
55 % training data. The returned quality measures are average quantization
56 % error and topographic error.
57 %
58 % The issue of SOM quality is a complicated one. Typically two evaluation
59 % criterias are used: resolution and topology preservation. There are
60 % many ways to measure them. The ones implemented here were chosen for
61 % their simplicity.
62 %
63 % qe : Average distance between each data vector and its BMU.
64 % Measures map resolution.
65 % te : Topographic error, the proportion of all data vectors
66 % for which first and second BMUs are not adjacent units.
67 % Measures topology preservation.
68 %
69 % NOTE: when calculating BMUs of data vectors, the mask of the given
70 % map is used. The mask affects the quantization errors, too.
71 % If you want the quantization errors without the weighting given
72 % by the mask, you can use the following code:
73 % bmus = som_bmus(sMap,D); % this uses the mask in finding the BMUs
74 % for i=1:length(bmus),
75 % dx = sMap.codebook(bmus(i),:)-D(i,:); % m - x
76 % dx(isnan(dx)) = 0; % remove NaNs
77 % qerr(i) = sqrt(sum(dx.^2)); % euclidian distance
78 % end
79 % qe = mean(qerr); % average quantization error
80 %
81 % Please note that you should _not_ trust the measures blindly. Generally,
82 % both measures give the best results when the map has overfitted the
83 % data. This may happen when the number of map units is as large or larger
84 % than the number of training samples. Beware when you have such a case.
85 %
86 % REFERENCES
87 %
88 % Kohonen, T., "Self-Organizing Map", 2nd ed., Springer-Verlag,
89 % Berlin, 1995, pp. 113.
90 % Kiviluoto, K., "Topology Preservation in Self-Organizing Maps",
91 % in the proceeding of International Conference on Neural
92 % Networks (ICNN), 1996, pp. 294-299.
93 %
94 % INPUT ARGUMENTS
95 %
96 % sMap (struct) Map struct.
97 % D The data to be used.
98 % (matrix) A data matrix, size dlen x dim.
99 % (struct) A data struct.
100 %
101 % OUTPUT ARGUMENTS
102 %
103 % qe (scalar) mean quantization error
104 % te (scalar) topographic error
105 %
106 % EXAMPLES
107 %
108 % qe = som_quality(sMap,D);
109 % [qe,te] = som_quality(sMap,sD);
110 %
111 % SEE ALSO
112 %
113 % som_bmus Find BMUs for the given set of data vectors.
114
115 % Copyright (c) 1997-2000 by the SOM toolbox programming team.
116 % http://www.cis.hut.fi/projects/somtoolbox/
117
118 % Version 1.0beta juuso 220997
119 % Version 2.0beta juuso 151199
120
121 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
122 %% check arguments
123
124 % input arguments
125 if nargin < 2, error('Not enough input arguments.'); end
126
127 % data
128 if isstruct(D), D = D.data; end
129 [dlen dim] = size(D);
130
131 % calculate topographic error, too?
132 if nargout==1, b=1; else b=[1:2]; end
133 [bmus qerrs]= som_bmus(sMap,D,b);
134 inds = find(~isnan(bmus(:,1)));
135 bmus = bmus(inds,:);
136 qerrs = qerrs(inds,:);
137 l = length(inds);
138 if ~l, error('Empty data set.'); end
139
140 % mean quantization error
141 mqe = mean(qerrs(:,1));
142
143 if length(b)==2, % topographic error
144 Ne = full(som_unit_neighs(sMap.topol));
145 tge = 0;
146 for i=1:l, tge = tge+(Ne(bmus(i,1),bmus(i,2)) ~= 1); end
147 tge = tge / l;
148 else
149 tge = NaN;
150 end
151
152 return;
153
154 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
155
156