View source for Self-similarity matrix

In [[Data analysis|data analysis]], the '''self-similarity matrix''' is a graphical representation of [[Similarity measure|similar]] sequences in a data series.
Similarity can be explained by different measures, like spatial distance ([[Distance matrix|distance matrix]]), [[Correlation|correlation]], or comparison of local [[Histogram|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 2000|url=http://www.merl.com/publications/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.

==Definition==

To construct a self-similarity matrix, one first transforms a data series into an ordered sequence of feature vectors <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|author2=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>
Similarity plots are used for action recognition that is invariant to point of view <ref>{{cite book
    |author1=I.N. Junejo |author2=E. Dexter |author3=I. Laptev |author4=Patrick Pérez |title=Computer Vision – ECCV 2008 |chapter=Cross-View Action Recognition from Temporal Self-similarities |volume=5303 |pages=293–306 | year=2008
    | doi=10.1007/978-3-540-88688-4_22
|series=Lecture Notes in Computer Science |isbn=978-3-540-88685-3 |citeseerx=10.1.1.405.1518 }}</ref>
and for audio segmentation using [[Spectral clustering|spectral clustering]] of the self-similarity matrix.<ref>{{cite journal|last=Dubnov|first=Shlomo|author2=Ted Apel |title=Audio segmentation by singular value clustering|journal=Proceedings of Computer Music Conference (ICMC 2004)|year=2004|citeseerx=10.1.1.324.4298}}</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>Cross-View Action Recognition from Temporal Self-Similarities (2008), I. Junejo, E. Dexter, I. Laptev, and Patrick Pérez)</ref>]]

== See also==
* [[Recurrence plot]]
* [[Distance matrix]]
* Similarity matrix
* [[Substitution matrix]]
* [[Dot plot (bioinformatics)]]

==References==
{{reflist}}

==Further reading==

* {{cite journal
    |author1=N. Marwan |author2=M. C. Romano |author3=M. Thiel |author4=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 book
    | author=J. Foote
    | title=Proceedings of the seventh ACM international conference on Multimedia (Part 1)
 | chapter=Visualizing music and audio using self-similarity
 | date=1999
 | pages=77–80
    | year=1999
    | doi=10.1145/319463.319472
| isbn=978-1581131512
    | citeseerx=10.1.1.223.194
    | s2cid=3329298
 }}
* {{cite book
    | author=M. A. Casey
    | title=Sound Classification and Similarity Tools
    | publisher=J. Wiley
    | year=2002
    | pages=309–323
    |editor1=B.S. Manjunath |editor2=P. Salembier |editor3=T. Sikora
    | journal=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]]

{{Sourceattribution|Self-similarity matrix}}