Self-similarity matrix explained
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]). 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
S(j,k)=s(vj,vk) j,k\in(1,\ldots,n)
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] See also
Further reading
- N. Marwan . M. C. Romano . M. Thiel . J. Kurths . Recurrence Plots for the Analysis of Complex Systems . Physics Reports . 438 . 5–6 . 2007 . 10.1016/j.physrep.2006.11.001 . 237 . 2007PhR...438..237M.
- Book: J. Foote . Proceedings of the seventh ACM international conference on Multimedia (Part 1) . Visualizing music and audio using self-similarity . 1999 . 77–80 . 1999 . 10.1145/319463.319472. 978-1581131512 . 10.1.1.223.194 . 3329298 .
- Book: M. A. Casey . Sound Classification and Similarity Tools . J. Wiley . 2002 . 309–323 . B.S. Manjunath . P. Salembier . T. Sikora . Introduction to MPEG-7: Multimedia Content Description Language . 978-0471486787.
External links
- http://www.recurrence-plot.tk/related_methods.php
Notes and References
- M. A. Casey . A. Westner. Separation of mixed audio sources by independent subspace analysis. Proc. Int. Comput. Music Conf. July 2000. 2013-11-19.
- Müller. Meinard. Michael Clausen . Transposition-invariant self-similarity matrices. Proceedings of the 8th International Conference on Music Information Retrieval (ISMIR 2007). 2007. 47–50. 2013-11-19.
- Book: I.N. Junejo . E. Dexter . I. Laptev . Patrick Pérez . Computer Vision – ECCV 2008 . Cross-View Action Recognition from Temporal Self-similarities . 5303 . 293–306 . 2008 . 10.1007/978-3-540-88688-4_22. Lecture Notes in Computer Science . 978-3-540-88685-3 . 10.1.1.405.1518 .
- Dubnov. Shlomo. Ted Apel . Audio segmentation by singular value clustering. Proceedings of Computer Music Conference (ICMC 2004). 2004. 10.1.1.324.4298.
