K-nearest neighbors algorithmIn statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. It is used for classification and regression. In both cases, the input consists of the k closest training examples in a data set. The output depends on whether k-NN is used for classification or regression: In k-NN classification, the output is a class membership.
Matching pursuitMatching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary . The basic idea is to approximately represent a signal from Hilbert space as a weighted sum of finitely many functions (called atoms) taken from . An approximation with atoms has the form where is the th column of the matrix and is the scalar weighting factor (amplitude) for the atom . Normally, not every atom in will be used in this sum.
Coordinate vectorIn linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular ordered basis. An easy example may be a position such as (5, 2, 1) in a 3-dimensional Cartesian coordinate system with the basis as the axes of this system. Coordinates are always specified relative to an ordered basis. Bases and their associated coordinate representations let one realize vector spaces and linear transformations concretely as column vectors, row vectors, and matrices; hence, they are useful in calculations.
DictionaryA dictionary is a listing of lexemes from the lexicon of one or more specific languages, often arranged alphabetically (or by consonantal root for Semitic languages or radical and stroke for logographic languages), which may include information on definitions, usage, etymologies, pronunciations, translation, etc. It is a lexicographical reference that shows inter-relationships among the data. A broad distinction is made between general and specialized dictionaries.
Independent component analysisIn 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. ICA is a special case of blind source separation. A common example application is the "cocktail party problem" of listening in on one person's speech in a noisy room.
Symmetric matrixIn linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
Square root of a matrixIn mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is equal to A. Some authors use the name square root or the notation A1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = BTB = A (for real-valued matrices, where BT is the transpose of B).
Cholesky decompositionIn linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ʃəˈlɛski ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.
Linear discriminant analysisLinear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.
Facial recognition systemA facial recognition system is a technology potentially capable of matching a human face from a or a video frame against a database of faces. Such a system is typically employed to authenticate users through ID verification services, and works by pinpointing and measuring facial features from a given image. Development began on similar systems in the 1960s, beginning as a form of computer application. Since their inception, facial recognition systems have seen wider uses in recent times on smartphones and in other forms of technology, such as robotics.
