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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,128 @@ | ||
| function b = pca(a, varargin) | ||
| % [b] = pca(X, k) : Principal component analysis of iData object(s) | ||
| % | ||
| % @iData/pca function to perform a Principal component analysis of object(s) | ||
| % | ||
| % b = pca(a,k) computes the principal component analysis of an object in a k-D | ||
| % space representation. This corresponds to a classification of the objects | ||
| % rows, searching for similarities/correlations. The resulting principal | ||
| % component coefficients object contains the same number of rows as 'a', and | ||
| % k columns for coordinates. | ||
| % Rows (rank 1) of X correspond to observations and further ranks correspond | ||
| % to variables. | ||
| % b = pca(a) assumes k=2 (2D space classifier). | ||
| % b = pca([a1 a2 ...], k) performs the PCA along all objects specified in the | ||
| % array, and return the principal component coefficients. The resulting object | ||
| % contains as many rows as the number of objects specified, and k columns. | ||
| % b = pca(a, key, value, ...) | ||
| % specifies the PCA configuration as key=value pairs: | ||
| % 'NumComponents',k | ||
| % Number of components requested, specified as the comma-separated pair | ||
| % consisting of 'NumComponents' and a scalar integer k satisfying | ||
| % 0 < k <= p, where p is the number of original variables in X. When | ||
| % specified, pca returns the first k PCA coefficients. | ||
| % 'Centered', True(default) or False | ||
| % Center the variables by subtracting the mean values | ||
| % 'VariableWeights', false or 'variance' | ||
| % 'variance' to normalize variables to their variance (default) | ||
| % | ||
| % input: X: object or array (iData) | ||
| % k: number of components wanted (integer, default is 2) | ||
| % output: b: principal component object (iData) | ||
| % ex: b=pca(a); plot(b); text(b{1},b{2}, get(a,'Title')); | ||
| % | ||
| % See: http://en.wikipedia.org/wiki/Principal_component_analysis | ||
| % | ||
| % Version: $Revision: 1035 $ | ||
| % See also iData, iData/kmeans, iData/cwt, iData/corrcoef | ||
|
|
||
| % handle input iData arrays | ||
| if numel(a) > 1 | ||
| % first align all objects (union) | ||
| a = union(a); | ||
| labls = get(a, 'Title'); | ||
| % then add all array signals as 1D vectors, one per row | ||
| for index=1:numel(a) | ||
| s = subsref(a(index),struct('type','.','subs','Signal')); | ||
| a(index) = set(a(index), 'Signal', s(:)'); | ||
| end | ||
| s = []; | ||
| a = cat(2, a); | ||
|
|
||
| % then call pca | ||
| b = pca(a, varargin{:}); | ||
| return | ||
| end | ||
|
|
||
| % default config | ||
| k = 2; | ||
| algorithm = 'svd'; | ||
| centered = 1; | ||
| scale = 'variance'; | ||
|
|
||
| % parse input key/values | ||
| for index=1:numel(varargin) | ||
| key = varargin{index}; | ||
| if ischar(key) && index < numel(varargin) | ||
| value = varargin{index+1}; | ||
| index = index + 1; | ||
| else | ||
| value = []; | ||
| end | ||
| if index==1 && isscalar(key) | ||
| k = key; | ||
| else | ||
| switch lower(key) | ||
| case 'numcomponents' | ||
| k = value; | ||
| case 'centered' | ||
| centered = value; | ||
| case 'variableweights' | ||
| scale = value; | ||
| end | ||
| end | ||
| end | ||
|
|
||
| % get data set signal | ||
| S = subsref(a,struct('type','.','subs','Signal')); | ||
|
|
||
| [n m] = size(S); | ||
|
|
||
| if centered, | ||
| S=S - repmat(mean(S),[n 1]); | ||
| end | ||
| if strcmp(scale, 'variance') | ||
| S=S./ repmat(std(S),[n 1]); | ||
| end | ||
|
|
||
| % compute PCA | ||
| [V D] = eig(cov(S)); | ||
| D = diag(D); | ||
| [D, index] = sort(D,'descend'); | ||
| % permute coefficients from highest to lowest weight | ||
| V = V(:,index); | ||
| % restrict to dimensionality 'k' | ||
| if k > size(V,2), k=size(V,2); end | ||
| if k > 0 | ||
| V = V(:, 1:k); | ||
| end | ||
| coeff = V; | ||
| latent = D; | ||
| score = S*coeff; | ||
|
|
||
| % assemble output object | ||
| b = copyobj(a); | ||
| b.Data.Observations = 1:size(V,1); | ||
| b = setalias(b, 'Observations', 'Data.Observations'); | ||
| b = setalias(b, 'Coefficients', coeff, 'Principal component coefficients'); | ||
| b = setalias(b, 'Scores', score, 'Principal component scores'); | ||
| b = setalias(b, 'Variances', latent, 'Principal component variances'); | ||
| b = set(b, 'Signal', 'Observations', 'Error', 0); | ||
| for index=1:k | ||
| b.Data.([ 'PCA' num2str(index)]) = V(:,index); | ||
| b = setalias(b, [ 'PCA' num2str(index)], ['Data.PCA' num2str(index)] ); | ||
| b = setaxis( b, index, [ 'PCA' num2str(index)]); | ||
| end | ||
|
|
||
| b = iData_private_history(b, mfilename, a, varargin{:}); | ||
|
|
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,26 @@ | ||
| function result=test_iData_pca | ||
|
|
||
| A = [269.8 38.9 50.5 | ||
| 272.4 39.5 50.0 | ||
| 270.0 38.9 50.5 | ||
| 272.0 39.3 50.2 | ||
| 269.8 38.9 50.5 | ||
| 269.8 38.9 50.5 | ||
| 268.2 38.6 50.2 | ||
| 268.2 38.6 50.8 | ||
| 267.0 38.2 51.1 | ||
| 267.8 38.4 51.0 | ||
| 273.6 39.6 50.0 | ||
| 271.2 39.1 50.4 | ||
| 269.8 38.9 50.5 | ||
| 270.0 38.9 50.5 | ||
| 270.0 38.9 50.5 | ||
| ]; | ||
|
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| a=iData(A); | ||
| b = pca(a); | ||
| if all(abs(sum(b.Coefficients) - [ -0.6142 1.6051 ]) < 1e-4 ) | ||
| result = 1; | ||
| else | ||
| result = 0; end | ||
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