pyActigraphy.analysis.SSA.X_elementary

SSA.X_elementary(r)

Elementary matrix

Parameters

r (int) – Index of the elementary matrix. Must lower or equal to the embedding dimension, L.

Returns

x_elem

Return type

ndarray of shape (L,K)

Notes

The SVD of the trajectory matrix X can be written as [1] :

where \(X_r = \sqrt{\lambda_r} u_r v_{r}^\intercal\).

The matrices \(X_r\) have rank 1. Such matrices are sometimes called elementary matrices.

References

1

Golyandina, N., & Zhigljavsky, A. (2013). Singular Spectrum Analysis for Time Series. Springer Berlin Heidelberg http://doi.org/10.1007/978-3-642-34913-3