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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. Linear complementarity problem - Wikipedia

    en.wikipedia.org/wiki/Linear_complementarity_problem

    If M is positive definite, any algorithm for solving (strictly) convex QPs can solve the LCP. Specially designed basis-exchange pivoting algorithms, such as Lemke's algorithm and a variant of the simplex algorithm of Dantzig have been used for decades. Besides having polynomial time complexity, interior-point methods are also effective in practice.

  4. Principal component regression - Wikipedia

    en.wikipedia.org/wiki/Principal_component_regression

    The PCR method may be broadly divided into three major steps: 1. Perform PCA on the observed data matrix for the explanatory variables to obtain the principal components, and then (usually) select a subset, based on some appropriate criteria, of the principal components so obtained for further use.

  5. Eigendecomposition of a matrix - Wikipedia

    en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

    Once the eigenvalues are computed, the eigenvectors could be calculated by solving the equation (), = using Gaussian elimination or any other method for solving matrix equations. However, in practical large-scale eigenvalue methods, the eigenvectors are usually computed in other ways, as a byproduct of the eigenvalue computation.

  6. Kernel methods for vector output - Wikipedia

    en.wikipedia.org/wiki/Kernel_methods_for_vector...

    This regularizer is a combination of limiting the complexity of each component of the estimator and forcing each component of the estimator to be close to the mean of all the components. Setting ω = 0 {\displaystyle \omega =0} treats all the components as independent and is the same as solving the scalar problems separately.

  7. Vector notation - Wikipedia

    en.wikipedia.org/wiki/Vector_notation

    Vectors can be specified using either ordered pair notation (a subset of ordered set notation using only two components), or matrix notation, as with rectangular coordinates. In these forms, the first component of the vector is r (instead of v 1), and the second component is θ (instead of v 2).

  8. Independent component analysis - Wikipedia

    en.wikipedia.org/wiki/Independent_component_analysis

    In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. [1]

  9. Vector (mathematics and physics) - Wikipedia

    en.wikipedia.org/wiki/Vector_(mathematics_and...

    In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.