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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). A similarity plot can be the starting point for 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 sequence of feature vectors V = ( v 1 , v 2 , … , v n ) {\displaystyle V=(v_{1},v_{2},\ldots ,v_{n})} , where each vector v i {\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

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

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

See also

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. arXiv:2501.13933. Bibcode:2007PhR...438..237M. doi:10.1016/j.physrep.2006.11.001.
  • J. Foote (1999). "Visualizing music and audio using self-similarity". Proceedings of the seventh ACM international conference on Multimedia (Part 1). pp. 77–80. CiteSeerX 10.1.1.223.194. doi:10.1145/319463.319472. ISBN 978-1581131512. S2CID 3329298.{{cite book}}: CS1 maint: date and year (link)
  • M. A. Casey (2002). "Sound Classification and Similarity Tools". In B.S. Manjunath; P. Salembier; T. Sikora (eds.). Introduction to MPEG-7: Multimedia Content Description Language. J. Wiley. pp. 309–323. ISBN 978-0471486787.

References

  1. M. A. Casey; A. Westner (July 2000). "Separation of mixed audio sources by independent subspace analysis" (PDF). Proc. Int. Comput. Music Conf. Retrieved 2013-11-19. http://www.merl.com/publications/docs/TR2001-31.pdf ↩

  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. http://ismir2007.ismir.net/proceedings/ISMIR2007_p047_mullermuller.pdf ↩

  3. I.N. Junejo; E. Dexter; I. Laptev; Patrick Pérez (2008). "Cross-View Action Recognition from Temporal Self-similarities". Computer Vision – ECCV 2008. Lecture Notes in Computer Science. Vol. 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. 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. /wiki/CiteSeerX_(identifier) ↩