By Teuvo Kohonen

ISBN-10: 3540183140

ISBN-13: 9783540183143

ISBN-10: 3662007843

ISBN-13: 9783662007846

Whereas the current version is bibliographically the 3rd one in every of Vol. eight of the Springer sequence in info Sciences (IS 8), the publication truly stems from Vol. 17 of the sequence conversation and Cybernetics (CC 17), entitled Associative reminiscence - A System-Theoretical technique, which seemed in 1977. That publication used to be the 1st monograph on allotted associative thoughts, or "content-addressable stories" as they're often known as, in particular in neural-networks study. This writer, even if, wish to reserve the time period "content-addressable reminiscence" for yes extra conventional constructs, the reminiscence destinations of that are chosen via parallel seek. Such units are mentioned in Vol. 1 of the Springer sequence in details Sciences, Content-Addressable stories. This 3rd version of IS eight is quite just like the second. new discussions were further: one to the tip of Chap. five, and the opposite (the L VQ 2 set of rules) to the tip of Chap. 7. furthermore, the convergence evidence in Sect. 5.7.2 has been revised.

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**Sample text**

1 Notice again the compatibility of indices. Linear Transformations. The main reason for the introduction of matrices is a possibility to denote and manipulate with linear transformation operations on vectors. The transformation of vector x into vector y is generally denoted by function y = T(x). 27) The general linear transformation of vector x = (t;1' t;2' ... , t;n) into vector y = (111' 112, ... 28) j=l with the aij parameters defining the transformation. 28) can be expressed symbolically as a matrix-vector product.

X) (associativity) = 0 and 1 . x = x. An example of Y would be R n. The sum of two vectors is then defined as a vector with elements (coordinates, components) which are obtained by summing up the respective elements of the addends. The scalar multiplication is an operation in which all elements of a vector are multiplied by this scalar. ) Inner Product. The concept of inner product refers to a two-argument, scalar- valued function which has been introduced to facilitate an analytic description of certain geometric operations.

Since one-row and one-column matrices are linear arrays of numbers, they can be understood as vectors, called row and column vectors, respectively. Such vectors can be denoted by lower-case letters. In a matrix-vector product, the row vector always stands on the left, and the column vector on the right. For reasons which become more apparent below, representation patterns are normally understood as column vectors. For better clarity, column vectors are normally denoted by simple lower case letters like x, whereas row vectors are written in the transpose notation as x T.

### Self-Organization and Associative Memory by Teuvo Kohonen

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