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.[citation needed] 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 [math]\displaystyle{ V = (v_1, v_2, \ldots, v_n) }[/math], where each vector [math]\displaystyle{ 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]\displaystyle{ S(j,k) = s(v_j, v_k) \quad j,k \in (1,\ldots,n) }[/math]
where [math]\displaystyle{ s(v_j, v_k) }[/math] is a function measuring the similarity of the two vectors, for instance, the inner product [math]\displaystyle{ 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.[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
- ↑ M. A. Casey; A. Westner (July 2000). "Separation of mixed audio sources by independent subspace analysis". Proc. Int. Comput. Music Conf. http://www.merl.com/publications/docs/TR2001-31.pdf. Retrieved 2013-11-19.
- ↑ Müller, Meinard; Michael Clausen (2007). "Transposition-invariant self-similarity matrices". Proceedings of the 8th International Conference on Music Information Retrieval (ISMIR 2007): 47–50. http://ismir2007.ismir.net/proceedings/ISMIR2007_p047_mullermuller.pdf. Retrieved 2013-11-19.
- ↑ 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. 5303. pp. 293–306. doi:10.1007/978-3-540-88688-4_22. ISBN 978-3-540-88685-3.
- ↑ Dubnov, Shlomo; Ted Apel (2004). "Audio segmentation by singular value clustering". Proceedings of Computer Music Conference (ICMC 2004).
- ↑ 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. doi:10.1016/j.physrep.2006.11.001. Bibcode: 2007PhR...438..237M.
- J. Foote (1999). "Visualizing music and audio using self-similarity". Proceedings of the seventh ACM international conference on Multimedia (Part 1). pp. 77–80. doi:10.1145/319463.319472. ISBN 978-1581131512.
- M. A. Casey (2002). Sound Classification and Similarity Tools. J. Wiley. 309–323. ISBN 978-0471486787.
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