alexa Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition
Engineering

Engineering

Journal of Information Technology & Software Engineering

Author(s): Thomas M Cover

Abstract Share this page

This paper develops the separating capacities of families of nonlinear decision surfaces by a direct application of a theorem in classical combinatorial geometry. It is shown that a family of surfaces having d degrees of freedom has a natural separating capacity of 2d pattern vectors, thus extending and unifying results of Winder and others on the pattern-separating capacity of hyperplanes. Applying these ideas to the vertices of a binary n-cube yields bounds on the number of spherically, quadratically, and, in general, nonlinearly separable Boolean functions of n variables. It is shown that the set of all surfaces which separate a dichotomy of an infinite, random, separable set of pattern vectors can be characterized, on the average, by a subset of only 2d extreme pattern vectors. In addition, the problem of generalizing the classifications on a labeled set of pattern points to the classification of a new point is defined, and it is found that the probability of ambiguous generalization is large unless the number of training patterns exceeds the capacity of the set of separating surfaces.

This article was published in IEEE and referenced in Journal of Information Technology & Software Engineering

Relevant Expert PPTs

Relevant Speaker PPTs

Peer Reviewed Journals
 
Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals
International Conferences 2017-18
 
Meet Inspiring Speakers and Experts at our 3000+ Global Annual Meetings

Contact Us

Agri & Aquaculture Journals

Dr. Krish

agriaquaculture@omicsonline.com

1-702-714-7001Extn: 9040

Biochemistry Journals

Datta A

biochemjournals@omicsonline.com

1-702-714-7001Extn: 9037

Business & Management Journals

Ronald

business@omicsonline.com

1-702-714-7001Extn: 9042

Chemistry Journals

Gabriel Shaw

chemistryjournals@omicsonline.com

1-702-714-7001Extn: 9040

Clinical Journals

Datta A

clinicaljournals@omicsonline.com

1-702-714-7001Extn: 9037

Engineering Journals

James Franklin

engineeringjournals@omicsonline.com

1-702-714-7001Extn: 9042

Food & Nutrition Journals

Katie Wilson

nutritionjournals@omicsonline.com

1-702-714-7001Extn: 9042

General Science

Andrea Jason

generalscience@omicsonline.com

1-702-714-7001Extn: 9043

Genetics & Molecular Biology Journals

Anna Melissa

geneticsmolbio@omicsonline.com

1-702-714-7001Extn: 9006

Immunology & Microbiology Journals

David Gorantl

immunomicrobiol@omicsonline.com

1-702-714-7001Extn: 9014

Materials Science Journals

Rachle Green

materialsci@omicsonline.com

1-702-714-7001Extn: 9039

Nursing & Health Care Journals

Stephanie Skinner

nursinghealthcare@omicsonline.com

1-702-714-7001Extn: 9039

Medical Journals

Nimmi Anna

medicaljournals@omicsonline.com

1-702-714-7001Extn: 9038

Neuroscience & Psychology Journals

Nathan T

neuropsychology@omicsonline.com

1-702-714-7001Extn: 9041

Pharmaceutical Sciences Journals

Ann Jose

pharmajournals@omicsonline.com

1-702-714-7001Extn: 9007

Social & Political Science Journals

Steve Harry

social_politicalsci@omicsonline.com

1-702-714-7001Extn: 9042

 
© 2008- 2017 OMICS International - Open Access Publisher. Best viewed in Mozilla Firefox | Google Chrome | Above IE 7.0 version
adwords