diff Problems/private/dictdist.m @ 10:207a6ae9a76f version1.0

(none)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/dictdist.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,61 @@
+function [dist,ratio] = dictdist(approxD,D,epsilon)
+%DICTDIST Distance between dictionaries.
+%  [DIST,RATIO] = DICTDIST(APPROXD,D) computes the distance between the
+%  approximate dictionary APPROXD and the true dictionary D, where APPROXD
+%  is NxK and D is NxM.
+%
+%  The distance between the dictionary APPROXD and a single atom A of D is
+%  defined as:
+%
+%      DIST(APPROXD,A) = min  { 1-abs(APPROXD(:,i)' * A) }
+%                         i
+%
+%  The distance between the dictionaries APPROXD and D is defined as:
+%
+%      DIST(APPROXD,D) = sum { dist(APPROXD, D(:,k)) } / M
+%                         k
+%
+%  Note that 0 <= DIST(APPROXD,D) <= 1, where 0 implies that all atoms in D
+%  appear in APPROXD, and 1 implies that the atoms of D are orthogonal to
+%  APPROXD.
+%
+%  The similarity ratio between APPROXD and D is defined as:
+%
+%      RATIO(APPROXD,D) = #(atoms in D that appear in APPROXD) / M
+%
+%  where two atoms are considered identical when DIST(A1,A2) < EPSILON with
+%  EPSILON=0.01 by default. Note that 0 <= RATIO(APPROXD,D) <= 1, where 0
+%  means APPROXD and D have no identical atoms, and 1 means that all atoms
+%  of D appear in APPROXD.
+%
+%  [DIST,RATIO] = DICTDIST(DICT1,DICT2,EPSILON) specifies a different value
+%  for EPSILON.
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  October 2007
+
+
+if (nargin < 3), epsilon = 0.01; end
+
+[n,m] = size(D);
+
+approxD = normcols(approxD*spdiag(sign(approxD(1,:))));
+D = normcols(D*spdiag(sign(D(1,:))));
+
+identical_atoms = 0;
+dist = 0;
+
+for i = 1:m
+  atom = D(:,i);
+  distances = 1-abs(atom'*approxD);
+  mindist = min(distances);
+  dist = dist + mindist;
+  identical_atoms = identical_atoms + (mindist < epsilon);
+end
+
+dist = dist / m;
+ratio = identical_atoms / m;