Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/mModeCovariance.R

Estimates the m-mode covariance matrix from an array of array-valued observations.

1 | ```
mModeCovariance(x, m, center = TRUE)
``` |

`x` |
Array of order higher than two with the last dimension corresponding to the sampling units. |

`m` |
The mode with respect to which the covariance matrix is to be computed. |

`center` |
Logical, indicating whether the observations should be centered prior to computing the covariance matrix. Default is |

The m-mode covariance matrix provides a higher order analogy for the ordinary covariance matrix of a random vector and is computed for a random tensor *X* of size *p_1 x p_2 x ... x p_r* as *Cov_m(X) = E(X(m) X(m)^T)/(p_1 ... p_(m-1) p_(m+1) ... p_r)*, where *X(m)* is the centered *m*-flattening of *X*. The algorithm computes the estimate of this based on the sample `x`

.

The `m`

-mode covariance matrix of `x`

having the size *p_m x p_m*.

Joni Virta

Virta, J., Li, B., Nordhausen, K. and Oja, H., (2017), Independent component analysis for tensor-valued data, Journal of Multivariate Analysis, doi: 10.1016/j.jmva.2017.09.008

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