Self-similarity matrix

To construct a self-similarity matrix, one first transforms a data series into an ordered sequence of feature vectors $V\; =\; (v\_1,\; v\_2,\; \backslash ldots,\; v\_n)$, 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

:$S(j,k)\; =\; s(v\_j,\; v\_k)\; \backslash quad\; j,k\; \backslash in\; (1,\backslash ldots,n)$

where $s(v\_j,\; v\_k)$ is a function measuring the similarity of the two vectors, for instance, the inner product $s(v\_j,\; v\_k)\; =\; v\_j\; \backslash cdot\; v\_k$. Then similar segments of feature vectors will show up as path of high similarity along diagonals of the matrix.{{cite journal|last=Müller|first=Meinard|author2=Michael Clausen |title=Transposition-invariant self-similarity matrices|journal=Proceedings of the 8th International Conference on Music Information Retrieval (ISMIR 2007)|year=2007|pages=47–50|url=http://ismir2007.ismir.net/proceedings/ISMIR2007_p047_mullermuller.pdf|accessdate=2013-11-19}}

Similarity plots are used for action recognition that is invariant to point of view {{cite book

|author1=I.N. Junejo |author2=E. Dexter |author3=I. Laptev |author4=Patrick Pérez |title=Computer Vision – ECCV 2008 |chapter=Cross-View Action Recognition from Temporal Self-similarities |volume=5303 |pages=293–306 | year=2008

| doi=10.1007/978-3-540-88688-4_22

|series=Lecture Notes in Computer Science |isbn=978-3-540-88685-3 |citeseerx=10.1.1.405.1518 }}

and for audio segmentation using spectral clustering of the self-similarity matrix.{{cite journal|last=Dubnov|first=Shlomo|author2=Ted Apel |title=Audio segmentation by singular value clustering|journal=Proceedings of Computer Music Conference (ICMC 2004)|year=2004|citeseerx=10.1.1.324.4298}}

Image:Junejoetal ssm eccv08.jpg

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

{{reflist}}

• {{cite journal

|author1=N. Marwan |author2=M. C. Romano |author3=M. Thiel |author4=J. Kurths | title=Recurrence Plots for the Analysis of Complex Systems

| journal=Physics Reports

| volume=438

| issue=5–6

| year=2007

| doi=10.1016/j.physrep.2006.11.001

| pages=237

| bibcode=2007PhR...438..237M

| arxiv=2501.13933

}}

• {{cite book

| author=J. Foote

| title=Proceedings of the seventh ACM international conference on Multimedia (Part 1)

| chapter=Visualizing music and audio using self-similarity

| pages=77–80

| year=1999

| doi=10.1145/319463.319472

| isbn=978-1581131512

| citeseerx=10.1.1.223.194

| s2cid=3329298

}}

• {{cite book

| author=M. A. Casey

| contribution=Sound Classification and Similarity Tools

| publisher=J. Wiley

| year=2002

| pages=309–323

|editor1=B.S. Manjunath |editor2=P. Salembier |editor3=T. Sikora

| title=Introduction to MPEG-7: Multimedia Content Description Language

| isbn=978-0471486787

}}

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

Category:Statistical charts and diagrams

Category:Visualization (graphics)