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Die eigentliche Produktion dauerte aber nur rund ein Jahr. Von der ersten vagen Idee bis zur Realisierung dieses neuen Sonderheftes vergingen letztlich rund 10 Jahre. Naturist Magazines Sonnenfreunde Sonderheft Nr. Macht mächtig was her: das neue Sonderheft Rund um das Feuerwehrhaus des Feuerwehr-Magazins. Reusable Principal Component AnalysisWe can calculate a Principal Component Analysis on a dataset using the PCA class in the scikit-learn library.Sonnenfreunde Sonderheft 117 ->->->-> DOWNLOAD From numpy import arrayfrom numpy import meanfrom numpy import covfrom numpy.linalg import eig# define a matrixA = array(1, 2, 3, 4, 5, 6)print(A)# calculate the mean of each columnM = mean(A.T, axis=1)print(M)# center columns by subtracting column meansC = A - Mprint(C)# calculate covariance matrix of centered matrixV = cov(C.T)print(V)# eigendecomposition of covariance matrixvalues, vectors = eig(V)print(vectors)print(values)# project dataP = vectors.T.dot(C.T)print(P.T). The eigenvectors and eigenvalues are taken as the principal components and singular values and used to project the original data. Manually Calculate Principal Component AnalysisThere is no pca function in NumPy, but we can easily calculate the Principal Component Analysis step-by-step using NumPy functions.The example below defines a small 3×2 matrix, centers the data in the matrix, calculates the covariance matrix of the centered data, and then the eigendecomposition of the covariance matrix. AWhere A is the original data that we wish to project, B^T is the transpose of the chosen principal components and P is the projection of A.This is called the covariance method for calculating the PCA, although there are alternative ways to to calculate it. Ideally, we would select k eigenvectors, called principal components, that have the k largest eigenvalues. If there are eigenvalues close to zero, they represent components or axes of B that may be discarded.A total of m or less components must be selected to comprise the chosen subspace. For more on this topic, see the post.The eigenvectors can be sorted by the eigenvalues in descending order to provide a ranking of the components or axes of the new subspace for A.If all eigenvalues have a similar value, then we know that the existing representation may already be reasonably compressed or dense and that the projection may offer little. Values, vectors = eig(V)The eigenvectors represent the directions or components for the reduced subspace of B, whereas the eigenvalues represent the magnitudes for the directions. Let’s walk through the steps of this operation. Principal Component AnalysisPrincipal Component Analysis, or PCA for short, is a method for reducing the dimensionality of data.It can be thought of as a projection method where data with m-columns (features) is projected into a subspace with m or fewer columns, whilst retaining the essence of the original data.The PCA method can be described and implemented using the tools of linear algebra.PCA is an operation applied to a dataset, represented by an n x m matrix A that results in a projection of A which we will call B.