By Topic

Parameter identification using intrinsic dimensionality

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)

Let W be an N -dimensional vector space and V be a K - dimensional topological hypersurface in W . The intrinsic dimensionality problem can be stated as follows. Given M randomly selected points \nu_i, \nu_i \in V , estimate K , which is the dimensionality of V and is called the intrinsic dimensionality of the points \nu_i . This problem has been attacked by several authors. If signals are represented by vectors in an abstract signal space W , rather than as time or frequency functions, the locus of signals that are generated by a hypothetical signal generator possessing K free parameters is a K -dimensional hypersurface V in the signal space. The purpose of this paper is to identify some of the free parameters of the signals. Let H be a one-parameter group that acts on W, HW = W . To say that a parameter associated with a group H is a free parameter of V means that V is closed under H , i.e., HV = V . To decide whether HV = V , the estimated dimensionalities of HV and V are compared. The method is illustrated by presenting several examples from the field of signal analysis. Finally, a slight modification is suggested so that parameters can he identified even when the vectors of interest do not represent time or frequency functions.

Published in:

Information Theory, IEEE Transactions on  (Volume:18 ,  Issue: 1 )