Normalization

Broadly, normalization (also spelled normalisation) is any process that makes something more normal, which typically means conforming to some regularity or rule, or returning from some state of abnormality. It has specific meanings in various fields:

Mathematics

As a Technique for Poofs

In mathematics, normalization is often an intermediate step toward showing that a proof which applies to normal things -- also applies to many other things which are not normal. Examples of this meaning include:

• Greibach normal form in Formal language theory
• Conjunctive and Disjunctive Normal form in Boolean logic
• An abstract rewriting system is said normalizing if all objects have at least one normal form.
  • This notion has direct application to lambda calculus.

As a Generic Transformation

• Normalization of a scheme
• Mapping entries of a data set from their natural range to values between 0 and 1.
• Normalizing constant, perhaps most often in probability theory
• Normalization of statistics, the process of removing statistical error from measured data.
• Normalization of a function (in general calculus) is the process of removing a discontinuity (or singularity). Sometimes referred to in highly-mathematical realm of theoretical physics as Renormalization
• The process of obtaining a normalized vector

Science

• Social Normalization, the process through which ideas and actions are made to appear culturally "normal."
• Normalization model, used in visual neuroscience
• Normalisable wave function in quantum mechanics
• Numéraire, which pertains when only relative prices matter
• Normalization Process Theory, which explains the processes by which innovations become routinely incorporated in their social contexts.
• In Geographical Information Systems, division of one set of values by another set to correct for some deficiency or more accurately portray data.

Technology

• Database normalization, used in database theory. (See also denormalization)
• Normalization (audio)
• Normalization (image processing)
• Text normalization

Political science

• Normalization of international relations between states, expressed in diplomatic relations, trade relations, culture, tourism and various collaborations.

Other

• Normalisation (people with disabilities)
• Normalization (Czechoslovakia), the restoration of the conditions prevalent before the reform in Czechoslovakia, 1969
• Normalization (metallurgy)

See also

Mathematics:

• Fully normalized subgroup
• Noether normalization lemma
• Normalized moments