Associative Memory: A System-Theoretical Approach by Teuvo Kohonen

By Teuvo Kohonen

About the Scope of this article This e-book comprises sorts of fabric ~ first, the various divergent and infrequently diffuse meanings given to the techniques of organization, associative reminiscence, and associative recaZZ are expounded. A evaluation of this sort was once felt invaluable simply because there it seems that doesn't exist any unmarried monograph which may function a connection with those issues. however the presentation of the most physique of this article is influenced via fairly different purposes: in recent times, lots of attention-grabbing mathematical and system-theoretical fabric has been released which makes it attainable to achieve a view of associative reminiscence that is assorted from the normal summary and computationally orientated techniques. it sounds as if the elemental operation of associative reminiscence, the garage of knowledge including the kin or hyperlinks among the information goods, and the selective remember of saved details relative to a bit of key or cue details offered, isn't limited to sure computer-technological implementations yet is also mirrored in additional common mathematically describable methods in yes actual or different structures, specifically of their adaptive kingdom adjustments. It extra turns out that a few normally recognized sorts of associative reminiscence, particularly, yes computing device technological artifacts, or summary platforms of suggestions or information, are in reality particular representations of a category of procedures characterised as associative memory.

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Which is almost exclusively used. in this book: for the vectors x = (~1"'" ~n) and y = (nl' .. 6) Another example of distances is the Hamming distance which has been defined for binary vectors; a binary vector has elements which are either 0 or 1. The Hamming distance indicates in how many positions (elements) the two vectors are different. Apparently the rules Cl to C3 are valid for Hamming distances. too. Norm. The magnitude of a vector can be defined in different ways. The name norm is used for it.

One needs a mathematical framework for the description of their quantitative interrelations. This is often provided by the vector formalism. The operations in vector spaces. on the other hand. can conveniently be manipulated by matrix algebra. These topics form the main contents of this section. As a mathematical representation. this section is more referential than formally complete; it is intended solely to serve as a collection of notations and results used elsewhere in the book. for their better readability.

For instance, Row and CoZumn Vectors. Since one-row and one-column matrices are linear arrays of numbers, they can be understood as vectors, called row and coZumn 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 xT.

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