Revision as of 10:49, 10 March 2008 by Han47 (Talk)

ECE662 Main Page

Class Lecture Notes

Nearest Neighbors Clarification Rule(Alternative Approaches) --Han47 10:34, 10 March 2008 (EDT)

Alternative Approach

find invariant coordination $ \varphi : \Re ^k \rightarrow \Re ^n $ --Han47 10:41, 10 March 2008 (EDT) such that $ \varphi (x) = \varphi (\bar x) $ for all $ x, \bar x $ which are related by a rotation & translation

Do not trivialize!

e.g.) $ \varphi (x) =0 $ gives us invariant coordinate but lose separation

Want $ \varphi (x) = \varphi (\bar x) $ $ \Leftrightarrow x, \bar x $ are related by a rotation and translation

Example $ p=(p_1,p_2,\cdots, p_N) \in \Re ^{3 \times N} $ $ \varphi $ maps representation position of taps on body onto $ (d_{12},d_{13},d_{14},\cdots , d_{N-1, N} ) $ where $ d_{ij} $= Euclidean distance between $ p_i $ and $ p_j $

Can reconstruct up to a rotation and translation

Warning: Euclidean distance in invariant coordination space has nothing to do with Euclidean distance or proanstes distance in initial feature space

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett