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  2. Singular value decomposition - Wikipedia

    en.wikipedia.org/wiki/Singular_value_decomposition

    In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any ⁠ m × n {\displaystyle m\times n} ⁠ matrix.

  3. Wahba's problem - Wikipedia

    en.wikipedia.org/wiki/Wahba's_problem

    A number of solutions to the problem have appeared in literature, notably Davenport's q-method, [2] QUEST and methods based on the singular value decomposition (SVD). Several methods for solving Wahba's problem are discussed by Markley and Mortari.

  4. Estimation of signal parameters via rotational invariance ...

    en.wikipedia.org/wiki/Estimation_of_signal...

    The singular value decomposition (SVD) of is given as = † where and are unitary matrices and is a diagonal matrix of size , that holds the singular values from the largest (top left) in descending order.

  5. Generalized singular value decomposition - Wikipedia

    en.wikipedia.org/wiki/Generalized_singular_value...

    In linear algebra, the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD).The two versions differ because one version decomposes two matrices (somewhat like the higher-order or tensor SVD) and the other version uses a set of constraints imposed on the left and right singular vectors of a single-matrix SVD.

  6. Singular spectrum analysis - Wikipedia

    en.wikipedia.org/wiki/Singular_spectrum_analysis

    The origins of SSA and, more generally, of subspace-based methods for signal processing, go back to the eighteenth century (Prony's method).A key development was the formulation of the spectral decomposition of the covariance operator of stochastic processes by Kari Karhunen and Michel Loève in the late 1940s (Loève, 1945; Karhunen, 1947).

  7. k-SVD - Wikipedia

    en.wikipedia.org/wiki/K-SVD

    In applied mathematics, k-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. k-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data.

  8. Sparse dictionary learning - Wikipedia

    en.wikipedia.org/wiki/Sparse_dictionary_learning

    K-SVD is an algorithm that performs SVD at its core to update the atoms of the dictionary one by one and basically is a generalization of K-means. It enforces that each element of the input data is encoded by a linear combination of not more than elements in a way identical to the MOD approach:

  9. Latent semantic analysis - Wikipedia

    en.wikipedia.org/wiki/Latent_semantic_analysis

    Latent semantic indexing (LSI) is an indexing and retrieval method that uses a mathematical technique called singular value decomposition (SVD) to identify patterns in the relationships between the terms and concepts contained in an unstructured collection of text. LSI is based on the principle that words that are used in the same contexts tend ...