NDLI: The intrinsic dimensionality of signal collections

Content Provider	IEEE Xplore Digital Library
Author	Bennett, R.
Copyright Year	1963
Description	In view of the trend toward the representation of signals as physical observables characterized by vectors in an abstract signal space, rather than as time or frequency functions, it is desirable that dimensionality be defined in a manner independent of the choice of basis on which the vectors are projected. The intrinsic dimensionality of a collection of signals is defined to be equal to the number of free parameters required in a hypothetical signal generator capable of producing a close approximation to each signal in the collection. Thus defined, the dimensionality becomes a relationship between the vectors representing the signals. This relationship need not be a linear one and does not depend on the basis onto which the vectors are projected in the signal-measuring process. A digital computer program for estimating this dimensionality from the signal coefficients on an arbitrary basis has been developed. The program makes use of some results obtained from a multi-dimensional scaling problem in experimental psychology and utilizes an inverse relationship between the variance in interpoint distances within a hypersphere and the dimensionality of the hypersphere. Using this method, the results are believed to be independent of the choice of orthogonal basis, and no prior knowledge of the analytical form of the signals is assumed. The validity of the program is tested and verified by using it to estimate the dimensionality of signals of known structure.
Sponsorship	IEEE Information Theory Society
Starting Page	517
Ending Page	525
Page Count	9
File Size	1438062
File Format	PDF
ISSN	00189448
Volume Number	15
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1969-09-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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