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In [[data analysis]], the '''self-similarity matrix''' is a graphical representation of [[similarity measure|similar]] sequences in a data series.
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Similarity can be explained by different measures, like spatial distance ([[distance matrix]]), [[correlation]], or comparison of local [[histogram]]s or [[spectral properties]] (e.g. IXEGRAM<ref>{{cite journal|author1= M. A. Casey |author2=A. Westner|title=Separation of mixed audio sources by independent subspace analysis|journal=Proc. Int. Comput. Music Conf|date=July -00 2000|url=http://www.merl.com/papers/docs/TR2001-31.pdf|accessdate=2013-11-19}}</ref>). This technique is also applied for the search of a given pattern in a long data series as in [[gene matching]].{{Citation needed|date=November 2013}} A similarity plot can be the starting point for [[Dot plot (bioinformatics)|dot plots]] or [[recurrence plots]].
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==Definition==
 
To construct a self-similarity matrix, one first transforms a data series into an ordered sequences of [[feature vector]]s <math> V = (v_1, v_2, \ldots, v_n) </math>, where each vector <math> v_i </math> describes the relevant features of a data series in a given local interval.  Then the self-similarity matrix is formed by computing the similarity of pairs of feature vectors
 
:<math> S(j,k) = s(v_j, v_k) \quad j,k \in (1,\ldots,n)</math>
 
where <math>s(v_j, v_k)</math> is a function measuring the similarity of the two vectors, for instance, the [[inner product]] <math>s(v_j, v_k) = v_j \cdot v_k</math>. Then similar segments of feature vectors will show up as path of high similarity along diagonals of the matrix.<ref name=Muller2007>{{cite journal|last=Müller|first=Meinard|coauthors=Michael Clausen|title=Transposition-invariant self-similarity matrices|journal=Proceedings of the 8th International Conference on Music Information Retrieval (ISMIR 2007)|year=2007|pages=47–50|url=http://ismir2007.ismir.net/proceedings/ISMIR2007_p047_mullermuller.pdf|accessdate=2013-11-19}}</ref>
 
==Example==
 
[[Image:Junejoetal ssm eccv08.jpg|thumb|center|800px|Similarity plot, a variant of recurrence plot, obtained for different views of human actions are shown to produce similar patterns.<ref>{{cite journal
    | author=I.N. Junejo, E. Dexter, I. Laptev, Patrick Pérez
    | title=Cross-View Action Recognition from Temporal Self-Similarities
    | journal=In Proc. European Conference on Computer Vision (ECCV), Marseille, France.
    | year=2008
    | doi=10.1007/978-3-540-88688-4_22
}}</ref>]]
 
== See also==
* [[Recurrence plot]]
* [[Distance matrix]]
* [[Similarity matrix]]
* [[Substitution matrix]]
 
==References==
{{reflist}}
 
* {{cite journal
    | author=N. Marwan, M. C. Romano, M. Thiel, J. Kurths
    | title=Recurrence Plots for the Analysis of Complex Systems
    | journal=Physics Reports
    | volume=438
    | issue=5-6
    | year=2007
    | doi=10.1016/j.physrep.2006.11.001
    | pages=237
    | bibcode=2007PhR...438..237M
}}
 
* {{cite journal
    | author=J. Foote
    | title=Visualizing Music and Audio using Self-Similarity
    | journal=In: Proceedings of ACM Multimedia '99, Orlando, Florida.
    | year=1999
    | doi=10.1145/319463.319472
}}
 
* {{cite journal
    | author=M. A. Casey
    | title=Sound Classification and Similarity Tools
    | publisher=J. Wiley
    | year=2002
    | pages=309–323
    | editors=B.S. Manjunath, P. Salembier and T. Sikora
    | work=Introduction to MPEG-7: Multimedia Content Description Language
    | isbn=978-0471486787
}}
 
== External links==
* http://www.recurrence-plot.tk/related_methods.php
 
[[Category:Statistical charts and diagrams]]
[[Category:Visualization (graphic)]]

Latest revision as of 20:39, 19 September 2014

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