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Typically data is discretized into partitions of K equal lengths/width (equal intervals) or K% of the total data (equal frequencies). [1] Mechanisms for discretizing continuous data include Fayyad & Irani's MDL method, [2] which uses mutual information to recursively define the best bins, CAIM, CACC, Ameva, and many others [3]
Functions which are not smooth can be made smooth using a mollifier prior to discretization. As an example, discretization of the function that is constantly yields the sequence [..,,,,..] which, interpreted as the coefficients of a linear combination of Dirac delta functions, forms a Dirac comb.
Data binning, also called data discrete binning or data bucketing, is a data pre-processing technique used to reduce the effects of minor observation errors. The original data values which fall into a given small interval, a bin , are replaced by a value representative of that interval, often a central value ( mean or median ).
In computational physics, the term advection scheme refers to a class of numerical discretization methods for solving hyperbolic partial differential equations. In the so-called upwind schemes typically, the so-called upstream variables are used to calculate the derivatives in a flow field. That is, derivatives are estimated using a set of data ...
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a data set. [1] Choosing informative, discriminating, and independent features is crucial to produce effective algorithms for pattern recognition, classification, and regression tasks.
In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
When the partial differential equation is discretized, for example by finite elements or finite differences, the discretization of the Poincaré–Steklov operator is the Schur complement obtained by eliminating all degrees of freedom inside the domain.
Multigrid methods can be applied in combination with any of the common discretization techniques. For example, the finite element method may be recast as a multigrid method. [3] In these cases, multigrid methods are among the fastest solution techniques known today.