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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. 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 ...

  4. Kernel principal component analysis - Wikipedia

    en.wikipedia.org/wiki/Kernel_principal_component...

    In the field of multivariate statistics, kernel principal component analysis (kernel PCA) [1] is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space .

  5. 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 ...

  6. Whitening transformation - Wikipedia

    en.wikipedia.org/wiki/Whitening_transformation

    Commonly used choices are = / (Mahalanobis or ZCA whitening), = where is the Cholesky decomposition of (Cholesky whitening), [3] or the eigen-system of (PCA whitening). [ 4 ] Optimal whitening transforms can be singled out by investigating the cross-covariance and cross-correlation of X {\displaystyle X} and Y {\displaystyle Y} . [ 3 ]

  7. Generalized Hebbian algorithm - Wikipedia

    en.wikipedia.org/wiki/Generalized_Hebbian_algorithm

    The generalized Hebbian algorithm is an iterative algorithm to find the highest principal component vectors, in an algorithmic form that resembles unsupervised Hebbian learning in neural networks. Consider a one-layered neural network with n {\displaystyle n} input neurons and m {\displaystyle m} output neurons y 1 , … , y m {\displaystyle y ...

  8. Principal component regression - Wikipedia

    en.wikipedia.org/wiki/Principal_component_regression

    In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). PCR is a form of reduced rank regression. [1] More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model.

  9. Multilinear principal component analysis - Wikipedia

    en.wikipedia.org/wiki/Multilinear_principal...

    Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA) that is used to analyze M-way arrays, also informally referred to as "data tensors". M-way arrays may be modeled by linear tensor models, such as CANDECOMP/Parafac, or by multilinear tensor models, such as multilinear principal ...