eta reduction - meaning and definition. What is eta reduction
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What (who) is eta reduction - definition

FORMAL SYSTEM IN MATHEMATICAL LOGIC
Lamda calculus; Lambda-calculus; Lambda abstraction; Lambda-definable function; Lambda-definable functions; Lambda calculas; Beta reduction; Alpha conversion; Lambda-recursive function; Lambda programming; Eta reduction; Lambda Calculus; Untyped lambda calculus; Λ-calculus; Alpha equivalence; Eta expansion; Abstraction operator; Alpha reduction; Beta substitution; Beta conversion; Α conversion; Λ calculus; Β-reduction; B-reduction; L-calculus; L calculus; A conversion; Beta-reduction; Λa-calculus; Lanbda-calculus; Lambda kalkül; Alpha renaming; Lambda calculi; Λ-abstraction; AlphaRenaming; Α-conversion; Capture-avoiding substitution; Lambda term; Lamda expression; Alpha-renaming; Alpha-conversion; Eta conversion; Eta-conversion; Η-conversion; Η conversion; Lambda language; Type-free lambda calculus; Typefree lambda calculus; Type free lambda calculus; Eta-reduction; Functional abstraction; Λx; Λy; Λz; Anonymous function abstraction; Lambda-calculi; Lambda-term bound variables; Lambda terms; Alpha equivalent

eta reduction         
Eta Hentz         
HUNGARIAN-BORN FASHION DESIGNER
Madame Eta
Eta Valer Hentz (1895–1986) was a Hungarian-American fashion designer active in the US from the 1920s to the 1940s. Mainly known as Madame Eta, she was particularly known for flattering ready-to-wear clothing inspired by Ancient Greece and the Middle Ages.
Dimensionality reduction         
  • A visual depiction of the resulting LDA projection for a set of 2D points.
  • A visual depiction of the resulting PCA projection for a set of 2D points.
PROCESS OF REDUCING THE NUMBER OF RANDOM VARIABLES UNDER CONSIDERATION
Dimension reduction; Dimensionality Reduction; Dimensionality reduction algorithm; Linear dimensionality reduction
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. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).

Wikipedia

Lambda calculus

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics.

Lambda calculus consists of constructing lambda terms and performing reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules:

  • x {\displaystyle x} – variable, a character or string representing a parameter or mathematical/logical value.
  • ( λ x . M ) {\textstyle (\lambda x.M)} – abstraction, function definition ( M {\textstyle M} is a lambda term). The variable x {\textstyle x} becomes bound in the expression.
  • ( M   N ) {\displaystyle (M\ N)} – application, applying a function M {\textstyle M} to an argument N {\textstyle N} . Both M {\textstyle M} and N {\textstyle N} are lambda terms.

The reduction operations include:

  • ( λ x . M [ x ] ) ( λ y . M [ y ] ) {\textstyle (\lambda x.M[x])\rightarrow (\lambda y.M[y])} – α-conversion, renaming the bound variables in the expression. Used to avoid name collisions.
  • ( ( λ x . M )   E ) ( M [ x := E ] ) {\textstyle ((\lambda x.M)\ E)\rightarrow (M[x:=E])} – β-reduction, replacing the bound variables with the argument expression in the body of the abstraction.

If De Bruijn indexing is used, then α-conversion is no longer required as there will be no name collisions. If repeated application of the reduction steps eventually terminates, then by the Church–Rosser theorem it will produce a β-normal form.

Variable names are not needed if using a universal lambda function, such as Iota and Jot, which can create any function behavior by calling it on itself in various combinations.