classdef PCA < handle %PCA Principal Component Analysis class % % The class is used to compute a special basis for a set of vectors. % The basis will consist of eigenvectors of the covariance matrix % computed from the input set of vectors. The class PCA can also % transform vectors to/from the new coordinate space defined by the % basis. Usually, in this new coordinate system, each vector from the % original set (and any linear combination of such vectors) can be % quite accurately approximated by taking its first few components, % corresponding to the eigenvectors of the largest eigenvalues of the % covariance matrix. Geometrically it means that you compute a % projection of the vector to a subspace formed by a few eigenvectors % corresponding to the dominant eigenvalues of the covariance matrix. % And usually such a projection is very close to the original vector. % So, you can represent the original vector from a high-dimensional % space with a much shorter vector consisting of the projected vector's % coordinates in the subspace. Such a transformation is also known as % Karhunen-Loeve Transform, or KLT. See % http://en.wikipedia.org/wiki/Principal_component_analysis % % The following shows a quick example of how to reduce dimensionality % of samples from 10 to 3. % % Xtrain = randn(100,10); % Xtest = randn(100,10); % pca = cv.PCA(Xtrain, 'MaxComponents', 3); % Y = pca.project(Xtest); % Xapprox = pca.backProject(Y); % % See also cv.PCA.PCA % properties (SetAccess = protected) % Object ID id % Eigenvectors eigenvectors % Eigenvalues eigenvalues % Sample mean mean end methods function this = PCA(varargin) %PCA PCA constructors % % pca = cv.PCA() % pca = cv.PCA(X, 'OptionName', optionValue, ...) % pca = cv.PCA(S) % % ## Input % * __X__ Vectors to be analyzed % * __S__ A scalar struct to be imported % % ## Options % * __DataAs__ Data layout option. One of 'row' or 'col'. % default 'row'. % * __MaxComponents__ Maximum number of components that PCA % should retain. By default, all the components are % retained. % * __Mean__ Optional mean value. By default, the mean is % computed from the data. % % The constructor creates an empty pca object without an % argument. Use pca.compute to analyze data samples. The second % form accepts data samples with the same argument to % pca.compute. The third form create a new pca object from a % scalar struct with 'eigenvectors', 'eigenvalues', and 'mean' % fields. % % See also cv.PCA cv.PCA.compute % this.id = PCA_(0,'new'); if nargin==1 && isscalar(varargin{1}) && isstruct(varargin{1}) s = varargin{1}; props = intersect(fieldnames(s),properties(this)); props = setdiff(props,'id'); for i = 1:numel(props) this.(props{i}) = s.(props{i}); end else this.compute(varargin{:}); end end function delete(this) %DELETE PCA destructor % % See also cv.PCA % PCA_(this.id, 'delete'); end function S = struct(this) %STRUCT Converts to a struct array % % S = this.struct % S = struct(this) % % % ## Output % * __S__ struct array % % See also cv.PCA % S = struct('eigenvectors',{this.eigenvectors},... 'eigenvalues', {this.eigenvalues},... 'mean', {this.mean}); end function obj = saveobj(this) %SAVEOBJ Serialization before save % % See also cv.PCA % obj = this.struct; end function compute(this, X, varargin) %COMPUTE Performs Principal Component Analysis of the supplied dataset % % pca.compute(X) % % ## Input % * __X__ Vectors to be analyzed % % ## Options % * __DataAs__ Data layout option. One of 'row' or 'col'. % default 'row'. % * __MaxComponents__ Maximum number of components that PCA % should retain. By default, all the components are % retained. % * __Mean__ Optional mean value. By default, the mean is % computed from the data. % % The method performs PCA of the supplied dataset. It is safe % to reuse the same PCA structure for multiple datasets. That % is, if the structure has been previously used with another % dataset, the existing internal data is reclaimed and the new % eigenvalues, eigenvectors, and mean are allocated and % computed. % % The computed eigenvalues are sorted from the largest to the % smallest and the corresponding eigenvectors are stored as % pca.eigenvectors rows. % % See also cv.PCA cv.PCA.project cv.PCA.backProject % PCA_(this.id, 'compute', X, varargin{:}); this.eigenvectors = []; this.eigenvalues = []; this.mean = []; end function Y = project(this, X) %PROJECT Projects vector(s) to the principal component subspace % % Y = pca.project(X) % % ## Input % * __X__ Vectors to be projected % % ## Output % * __Y__ PC coefficients % % The methods project one or more vectors to the principal % component subspace, where each vector projection is % represented by coefficients in the principal component basis. % The first form of the method returns the matrix that the % second form writes to the result. So the first form can be % used as a part of expression while the second form can be % more efficient in a processing loop. % % See also cv.PCA cv.PCA.backProject % Y = PCA_(this.id, 'project', X); end function X = backProject(this, Y) %BACKPROJECT Reconstructs vectors from their PC projections % % X = pca.backProject(Y) % % ## Input % * __Y__ PC coefficients % % ## Output % * __X__ Reconstructed vectors % % The methods are inverse operations to pca.project. They % take PC coordinates of projected vectors and reconstruct the % original vectors. Unless all the principal components have % been retained, the reconstructed vectors are different from % the originals. But typically, the difference is small if the % number of components is large enough (but still much smaller % than the original vector dimensionality). As a result, PCA is % used. % % See also cv.PCA cv.PCA.project % X = PCA_(this.id, 'backProject', Y); end function value = get.eigenvectors(this) %GET.EIGENVECTORS if isempty(this.eigenvectors) this.eigenvectors = PCA_(this.id, 'eigenvectors'); end value = this.eigenvectors; end function value = get.eigenvalues(this) %GET.EIGENVALUES if isempty(this.eigenvalues) this.eigenvalues = PCA_(this.id, 'eigenvalues'); end value = this.eigenvalues; end function value = get.mean(this) %GET.MEAN if isempty(this.mean) this.mean = PCA_(this.id, 'mean'); end value = this.mean; end end methods (Static) function this = loadobj(obj) %LOADOBJ Deserialization after load % % See also cv.PCA % this = cv.PCA(obj); end end end