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Euclidean distance between list of Vectors with different size of lists

Posted on 2011-03-01
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Last Modified: 2012-05-11
Hello,
I have 2 lists
List1 = [ V1,V2,V3,...,Vn] and List2 = [V1,V2,V3,....,Vk]   ==> Where K != n
And Where all the vectors in both lists have same length of course.

How can i compute the distance between these 2 lists of vectors?
1. Shall i take the centrois of each lists?


Thank you.
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Question by:dadadude
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Author Comment

by:dadadude
ID: 35015076
say i take the centroids or center of gravity how can i compute it?
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Expert Comment

by:ozo
ID: 35015082
That's one way.
Other ways include
Minimum distance from a vector in one list to a vector in the other list
Maximum distance from a vector in one list to a vector in the other list
Average distance from a vector in one list to a vector in the other list
Sum of distances from the centroid of both lists to the vectors in each list
...
What properties do you want this distance to have?
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Author Comment

by:dadadude
ID: 35015126
Actually i want to compute the dissimilarity between list1 and list2.
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Author Comment

by:dadadude
ID: 35015163
if i want to compute the center of gravity or centroid for a list of elements it's easy:
L = [e1,e2,...,en] it's easy just the mean.
But what is confusing me a little is this i can't figure it out:
If L = [v1,v2,....,vn] with each vi = [ x1,...xk] now how can i do it?? ouf it's a little complicated.
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Expert Comment

by:ozo
ID: 35015189
for the centroid, you can take the centroid of each component.
What properties do you want the dissimilarity to have?
What kinds of lists do you want to be dissimilar to other lists?
For example, one property of the centroid measure you propose is that changing the order of the elements of a list does not change its dissimilarity.
Another is that it satisfies the triangle inequality.
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Author Comment

by:dadadude
ID: 35015229
Well actually it should satisfy the Triangle inequality.
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Author Comment

by:dadadude
ID: 35015233
well i have a question for the centroid but i'll ask it later.
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Accepted Solution

by:
ozo earned 500 total points
ID: 35015256
Ok, but many kinds of dissimilarity measures satisfy the triangle inequality.
one advantage of centroid over some others is that it is fast and easy to compute
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Author Comment

by:dadadude
ID: 35015260
Sorry Correction, Correction
dadadude:
Well actually it should satisfy the Triangle inequality. NOT TRIANGLE INEQUALITY!!!
I want to have a Diagonal Matrix. all entries on the diagonal should be 0.
So i should compute the euclidean distance.


SORRY !!!!!!!!!!!!!
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Author Comment

by:dadadude
ID: 35015263
Ouf it's confusing now. Sorry for the mistake.
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Author Comment

by:dadadude
ID: 35015683
yeah well maybe i can work on the hausdorff distance i just find something on google. It's not bad and it's close to what u said. MAx[Min[d1,....dn]]

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Author Closing Comment

by:dadadude
ID: 35016666
no follow up sorry. I got the answer from a free forum.
Thank you anyway.
take care....
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