Hi,
a dissimilarity is simply a measure of how difference a vector A is from a
vector B. A metric also has to satisfy four extra rules:
http://en.wikipedia.org/wiki/Metric_(mathematics)
Wikipedia makes it more complicated than it has to be, but basically:
1. *d*(*x*, *y*) ≥ 0 (*non-negativity
<http://en.wikipedia.org/wiki/Non-negative>*, or separation axiom)
2. *d*(*x*, *y*) = 0 if and only if *x* = *y* (*identity of
indiscernibles <http://en.wikipedia.org/wiki/Identity_of_indiscernibles>*,
or coincidence axiom)
3. *d*(*x*, *y*) = *d*(*y*, *x*) (*symmetry
<http://en.wikipedia.org/wiki/Symmetric_function>*)
4. *d*(*x*, *z*) ≤ *d*(*x*, *y*) + *d*(*y*, *z*) (*subadditivity
<http://en.wikipedia.org/wiki/Subadditivity>* / *triangle inequality
<http://en.wikipedia.org/wiki/Triangle_inequality>*).
The main one is point 4: For a lot of dissimilarities, this is not the
case.
For example - take a simple relationship like A likes B:
Alice can like Bob, but Bob can dislike Alice
It would however be meaningless to say:
Alice is 2 meters from Bob, but Bob is 1 meter from Alice.
A lot of clustering and scaling algorithms only work if the distance you
are working with is a metric. You can sometimes force the algorithm to
work with something which isn't a metric, but you will get results which
can be a bit absurd, especially if your dissimilarity is particularly badly
behaved.
On Tue, Mar 3, 2015 at 11:42 AM, Jean-Baptiste Pressac <
jean-baptiste.pres...@univ-brest.fr> wrote:
> But what could be a dissimilarity matrix in the case of events
> co-attended by people ? What is more, in the publication I try to
> reproduce, the author made a MDS from the Jaccard coefficients... What is
> more, my trial is inspired from a code which analyses a matrix of
> distances between european citie
> <http://baoilleach.blogspot.fr/2014/01/convert-distance-matrix-to-2d.html>
> s.
>
> By the way, I don't understand the meaning of the dissimilarity parameter
> of manifold.MDS. In which case a "dissimilarity" is euclidean ? Sorry, I am
> quite knew with some concepts.
>
> Jean-Baptiste Pressac
>
> Traitement et analyse de bases de données
> Production et diffusion de corpus numériques
>
> Centre de Recherche Bretonne et Celtique
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> 20 rue Duquesne
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>
> tel : +33 (0)2 98 01 68 95
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>
> Le 03/03/2015 11:09, Joel Nothman a écrit :
>
> I think DSW_jaccard_matrix is a matrix of similarity (which is what
> Jaccard usually means) not of dissimilarity. Try negating it before MDS.
>
> On 3 March 2015 at 20:07, Jean-Baptiste Pressac <
> jean-baptiste.pres...@univ-brest.fr> wrote:
>
>> Hello,
>> I tried to reproduce the analysis of events co-attended by woman via
>> manifold MDS (shared on IPython Notebook)
>> <http://nbviewer.ipython.org/github/JBPressac/MDS-of-DGG/blob/master/Davis%20Southern%20Women%20MDS%20of%20Jaccard%20coefficient.ipynb>,
>> but the MDS does not reflects the data. I certainly did something wrong,
>> but I could'nt figure out how to do a proper MDS. Any clue would be
>> appreciated.
>> Thanks,
>>
>> --
>> Jean-Baptiste Pressac
>>
>> Traitement et analyse de bases de données
>> Production et diffusion de corpus numériques
>>
>> Centre de Recherche Bretonne et Celtique
>> Unité mixte de service (UMS) 3554
>> 20 rue Duquesne
>> CS 93837
>> 29238 Brest cedex 3
>>
>> tel : +33 (0)2 98 01 68 95
>> fax : +33 (0)2 98 01 63 93
>>
>>
>>
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