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. 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.[2]

Example

Similarity plot, a variant of recurrence plot, obtained for different views of human actions are shown to produce similar patterns.[3]

See also

References

  1. ↑ 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. Check date values in: |date= (help)
  2. ↑ 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.
  3. ↑ 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.

External links