Self-similarity matrix

Definition

To construct a self-similarity matrix, one first transforms a data series into an ordered sequence 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. Similarity plots are used for action recognition that is invariant to point of view {{cite book and for audio segmentation using spectral clustering of the self-similarity matrix.

Example

References

References

1. (July 2000). "Separation of mixed audio sources by independent subspace analysis". Proc. Int. Comput. Music Conf.
2. Müller, Meinard. (2007). "Transposition-invariant self-similarity matrices". Proceedings of the 8th International Conference on Music Information Retrieval (ISMIR 2007).
3. Dubnov, Shlomo. (2004). "Audio segmentation by singular value clustering". Proceedings of Computer Music Conference (ICMC 2004).
4. Cross-View Action Recognition from Temporal Self-Similarities (2008), I. Junejo, E. Dexter, I. Laptev, and Patrick Pérez)