Cart (Loading....) | Create Account
Close category search window

Monotonicity of Linear Separability Under Translation

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

2 Author(s)
Bruckstein, Alfred M. ; Department of Electrical Engineering, Stanford University, Stanford, CA 94305. ; Cover, Thomas M.

A set of n pattern vectors are given in d-space and classified arbitrarily into two sets. The sets of patterns are said to be linearly separable if there exists a hyperplane that separates them. We ask whether translation of one of these sets in an arbitrary direction helps separability. Sometimes yes and sometimes no, but yes on the average. The average is taken over all classifications of the patterns into two sets. In fact, we prove that the probability of separability increases as the translation increases. Thus, we conclude that if points are drawn equiprobably from densities fo(x) and f1(x) = fo(x + tw) then the probability of linear separability is minimum at t = 0 and increases with t for t > 0.

Published in:

Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-7 ,  Issue: 3 )

Date of Publication:

May 1985

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.