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In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called " reducing a fraction ".
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.
Dimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics , a theory in D spacetime dimensions can be redefined in a lower number of dimensions d , by taking all the fields to be independent of the location in the extra D − d dimensions.
Domain-specific terms must be recategorized into the corresponding mathematical domain. If the domain is unclear, but reasonably believed to exist, it is better to put the page into the root category:mathematics, where it will have a better chance of spotting and classification. See also: Glossary of mathematics
Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%. For signals of indefinite size, such as streaming audio and video, the compression ratio is defined in terms of uncompressed and compressed data rates instead of data sizes:
Optimal reduction reduces all computations with the same label in one step, avoiding duplicated work, but the number of parallel β-reduction steps to reduce a given term to normal form is approximately linear in the size of the term. This is far too small to be a reasonable cost measure, as any Turing machine may be encoded in the lambda ...
Reduction system, reduction strategy, the application of rewriting systems to eliminate reducible expressions Reduced form , in statistics, an equation which relates the endogenous variable X to all the available exogenous variables, both those included in the regression of interest (W) and the instruments (Z)
In computer science and mathematics, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result. This article describes the properties in the most abstract setting of an abstract rewriting system .