Realtime Data Mining by Alexander Paprotny & Michael Thess

Author:Alexander Paprotny & Michael Thess
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(8.1)

The rank r is usually chosen to be considerably smaller than n p . The function f is referred to as the cost function of the factorization and, more often than not, is chosen to be a metric. It stipulates a notion of quality of a factorization. The sets C 1, C 2 determine the parameter space. In terms of our signal processing metaphor, the factor X characterizes the source, which is restricted to be a low-dimensional subspace, and the columns Y are the intrinsic low-dimensional parameter vectors determining the signals given by the corresponding columns of A.

To put it even simpler, we approximate the matrix A by the product of two smaller matrices X and Y. The cost function stipulates a notion of “closeness,” i.e., distance, of two matrices. Since the rank r is typically much smaller than n p and n s , the representation in terms of X and Y is much more compact than an explicit representation of the entries of A.

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