Self-similarity matrix

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. 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 ${\displaystyle V=(v_{1},v_{2},\ldots ,v_{n})}$, where each vector ${\displaystyle v_{i}}$ 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

${\displaystyle S(j,k)=s(v_{j},v_{k})\quad j,k\in (1,\ldots ,n)}$

where ${\displaystyle s(v_{j},v_{k})}$ is a function measuring the similarity of the two vectors, for instance, the inner product ${\displaystyle s(v_{j},v_{k})=v_{j}\cdot v_{k}}$. 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

Similarity plot, a variant of recurrence plot, obtained for different views of human actions are shown to produce similar patterns.[5]

See also

• Recurrence plot
• Distance matrix
• Similarity matrix
• Substitution matrix
• Dot plot (bioinformatics)

References

1. M. A. Casey; A. Westner (July -00 2000). "Separation of mixed audio sources by independent subspace analysis" (PDF). Proc. Int. Comput. Music Conf. Retrieved 2013-11-19. Check date values in: |date= (help)
2. Müller, Meinard; Michael Clausen (2007). "Transposition-invariant self-similarity matrices" (PDF). Proceedings of the 8th International Conference on Music Information Retrieval (ISMIR 2007): 47–50. Retrieved 2013-11-19.
3. I.N. Junejo; E. Dexter; I. Laptev; Patrick Pérez (2008). Cross-View Action Recognition from Temporal Self-Similarities. In Proc. European Conference on Computer Vision (ECCV), Marseille, France. Lecture Notes in Computer Science. 5303. pp. 293–306. CiteSeerX 10.1.1.405.1518. doi:10.1007/978-3-540-88688-4_22. ISBN 978-3-540-88685-3.
4. Dubnov, Shlomo; Ted Apel (2004). "Audio segmentation by singular value clustering". Proceedings of Computer Music Conference (ICMC 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

• N. Marwan; M. C. Romano; M. Thiel; J. Kurths (2007). "Recurrence Plots for the Analysis of Complex Systems". Physics Reports. 438 (5–6): 237. Bibcode:2007PhR...438..237M. doi:10.1016/j.physrep.2006.11.001.
• J. Foote (1999). Visualizing Music and Audio using Self-Similarity. In: Proceedings of ACM Multimedia '99, Orlando, Florida. pp. 77–80. CiteSeerX 10.1.1.223.194. doi:10.1145/319463.319472. ISBN 978-1581131512.
• M. A. Casey (2002). B.S. Manjunath; P. Salembier; T. Sikora (eds.). Sound Classification and Similarity Tools. Introduction to MPEG-7: Multimedia Content Description Language. J. Wiley. pp. 309–323. ISBN 978-0471486787.

External links

• http://www.recurrence-plot.tk/related_methods.php