- Definition
- Example
- See also
- References
- Further reading
In data analysis, the self-similarity matrix is a graphical representation of similar sequences in a data series.
Similarity can be explained by different measures, like spatial distance (distance matrix), correlation, or comparison of local histograms or spectral properties (e.g. IXEGRAM[1]). 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 plots or recurrence plots.
Definition
To construct a self-similarity matrix, one first transforms a data series into an ordered sequence of feature vectors 
, where each vector 
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
where 
is a function measuring the similarity of the two vectors, for instance, the inner product 
. Then similar segments of feature vectors will show up as path of high similarity along diagonals of the matrix.[2]
Similarity plots are used for action recognition that is invariant to point of view [3]
and for audio segmentation using spectral clustering of the self-similarity matrix.[4]
Example
See also
- Recurrence plot
- Distance matrix
- Similarity matrix
- Substitution matrix
- Dot plot (bioinformatics)
References
2. ^{{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}}
3. ^{{cite book |author1=I.N. Junejo |author2=E. Dexter |author3=I. Laptev |author4=Patrick Pérez | title=Cross-View Action Recognition from Temporal Self-Similarities | journal=In Proc. European Conference on Computer Vision (ECCV), Marseille, France. |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 }}
4. ^{{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}}
5. ^Cross-View Action Recognition from Temporal Self-Similarities (2008), I. Junejo, E. Dexter, I. Laptev, and Patrick Pérez)
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=Visualizing Music and Audio using Self-Similarity
| journal=In: Proceedings of ACM Multimedia '99, Orlando, Florida.
| pages=77–80
| year=1999
| doi=10.1145/319463.319472
| isbn=978-1581131512
| citeseerx=10.1.1.223.194
- {{cite book
| 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
| journal=Introduction to MPEG-7: Multimedia Content Description Language
| isbn=978-0471486787
}}
- http://www.recurrence-plot.tk/related_methods.php
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