Self-similarity matrix

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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[2]). 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 sequences of feature vectors V=(v_{1},v_{2},\ldots ,v_{n}), where each vector 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})\quad j,k\in (1,\ldots ,n)

where 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}\cdot v_{k}. Then similar segments of feature vectors will show up as path of high similarity along diagonals of the matrix.[3]

Example

Similarity plot, a variant of recurrence plot, obtained for different views of human actions are shown to produce similar patterns.[1]

See also

References

  1. ↑ 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. doi:10.1007/978-3-540-88688-4_22. 
  2. ↑ M. A. Casey; A. Westner (July -00 2000). "Separation of mixed audio sources by independent subspace analysis". Proc. Int. Comput. Music Conf. Retrieved 2013-11-19. 
  3. ↑ Müller, Meinard; Michael Clausen (2007). "Transposition-invariant self-similarity matrices". Proceedings of the 8th International Conference on Music Information Retrieval (ISMIR 2007): 47–50. Retrieved 2013-11-19. 
  • J. Foote (1999). "Visualizing Music and Audio using Self-Similarity". In: Proceedings of ACM Multimedia '99, Orlando, Florida. doi:10.1145/319463.319472. 
  • M. A. Casey (2002). "Sound Classification and Similarity Tools". In B.S. Manjunath, P. Salembier and T. Sikora. Introduction to MPEG-7: Multimedia Content Description Language (J. Wiley): 309–323. ISBN 978-0471486787. 

External links

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