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  2. Principal component analysis - Wikipedia

    en.wikipedia.org/wiki/Principal_component_analysis

    Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.

  3. Principal component regression - Wikipedia

    en.wikipedia.org/wiki/Principal_component_regression

    PCR can aptly deal with such situations by excluding some of the low-variance principal components in the regression step. In addition, by usually regressing on only a subset of all the principal components, PCR can result in dimension reduction through substantially lowering the effective number of parameters characterizing the underlying model.

  4. L1-norm principal component analysis - Wikipedia

    en.wikipedia.org/wiki/L1-norm_principal...

    In ()-(), L1-norm ‖ ‖ returns the sum of the absolute entries of its argument and L2-norm ‖ ‖ returns the sum of the squared entries of its argument.If one substitutes ‖ ‖ in by the Frobenius/L2-norm ‖ ‖, then the problem becomes standard PCA and it is solved by the matrix that contains the dominant singular vectors of (i.e., the singular vectors that correspond to the highest ...

  5. Scree plot - Wikipedia

    en.wikipedia.org/wiki/Scree_plot

    In multivariate statistics, a scree plot is a line plot of the eigenvalues of factors or principal components in an analysis. [1] The scree plot is used to determine the number of factors to retain in an exploratory factor analysis (FA) or principal components to keep in a principal component analysis (PCA).

  6. Dynamic mode decomposition - Wikipedia

    en.wikipedia.org/wiki/Dynamic_mode_decomposition

    In data science, dynamic mode decomposition (DMD) is a dimensionality reduction algorithm developed by Peter J. Schmid and Joern Sesterhenn in 2008. [1] [2] Given a time series of data, DMD computes a set of modes, each of which is associated with a fixed oscillation frequency and decay/growth rate.

  7. Data and information visualization - Wikipedia

    en.wikipedia.org/wiki/Data_and_information...

    The most fundamental data analysis approaches are visualization (histograms, scatter plots, surface plots, tree maps, parallel coordinate plots, etc.), statistics (hypothesis test, regression, PCA, etc.), data mining (association mining, etc.), and machine learning methods (clustering, classification, decision trees, etc.). Among these ...

  8. Eigenface - Wikipedia

    en.wikipedia.org/wiki/Eigenface

    Performing PCA directly on the covariance matrix of the images is often computationally infeasible. If small images are used, say 100 × 100 pixels, each image is a point in a 10,000-dimensional space and the covariance matrix S is a matrix of 10,000 × 10,000 = 10 8 elements.

  9. Robust principal component analysis - Wikipedia

    en.wikipedia.org/wiki/Robust_principal_component...

    The 2014 guaranteed algorithm for the robust PCA problem (with the input matrix being = +) is an alternating minimization type algorithm. [12] The computational complexity is (⁡) where the input is the superposition of a low-rank (of rank ) and a sparse matrix of dimension and is the desired accuracy of the recovered solution, i.e., ‖ ^ ‖ where is the true low-rank component and ^ is the ...