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]). A similarity plot can be the starting point for dot plots or recurrence plots.

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]

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

• 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.
• 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.

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