# zeroMeasure

##### Zero measure

Compute the average zero measures and total zero measure for a list of matrices.

- Keywords
- algebra

##### Usage

`zeroMeasure(Plist, P, prec = 10^(-5))`

##### Arguments

- Plist
List of estimated loadings matrices or a single estimated loadings matrix. All these matrices should be numeric matrices of size \(p\) by \(k\).

- P
True loadings matrix, a numeric matrix of size \(p\) by \(k\).

- prec
Precision used when determining if an element is non-zero, default is \(10^{-5}\). We say that all elements with an absolute value smaller than

`prec`

are ``equal to zero''.

##### Details

The *zero measure* is a way to compare how correctly a PCA method estimates the sparse loadings matrix `P`

. For each element of an estimated loadings matrix, it is equal to one if the estimated and true value are both zero or both non-zero, and zero otherwise. We then take the average zero measure over all elements of an estimated loadings matrix and over all estimated loadings matrices which we call the *total zero measure*.

##### Value

A list with components:

Numeric matrix of size \(p\) by \(k\) containing the average zero measure over all `length(Plist)`

simulations for each element of `P`

.

Numeric vector containing the indices of all data sets where the estimate was wrong (at least one of the zero measures for the elements of an estimated loadings matrix is equal to 0).

Total zero measure, i.e. the average zero measure over all elements of an estimated loadings matrix and over all estimated loadings matrices.

##### References

Hubert, M., Reynkens, T., Schmitt, E. and Verdonck, T. (2016). ``Sparse PCA for High-Dimensional Data with Outliers,'' *Technometrics*, 58, 424--434.

##### Examples

```
# NOT RUN {
P <- cbind(c(1,1), c(0,1))
Plist <- list(matrix(1,2,2), P)
zeroMeasure(Plist, P)
# }
```

*Documentation reproduced from package rospca, version 1.0.4, License: GPL (>= 2)*