# The m-Mode Covariance Matrix

### Description

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

### Usage

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

### Arguments

`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 |

### Details

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`

.

### Value

The `m`

-mode covariance matrix of `x`

having the size *p_m x p_m*.

### Author(s)

Joni Virta

### References

Virta, J., Li, B., Nordhausen, K. and Oja, H., (2016), Independent component analysis for tensor-valued data, *submitted*, **???**, ???–???. Preprint available on ArXiv http://arxiv.org/abs/1602.00879.

### See Also

`mModeAutoCovariance`

### Examples

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