Metric for Frobenius Norm

Computes the Frobenius norm of matrix entries

metric_frobenius_norm(estimate, oracle, na.rm = FALSE)

Arguments

estimate	Estimated values from the model.
oracle	Known values used to generate the model.
na.rm	A logical indicating if missing values (including NaN) should be removed. Default: FALSE

Value

A single numeric value.

Details

The Frobenius norm is an extension of the Euclidean norm to \(\mathcal{K}^{n\times n}\).

The metric is computed under: $$\|A\|_{\rm F} = \left(\sum_{i=1}^m \sum_{j=1}^n |a_{ij}|^2\right)^{\frac{1}{2}}$$

Recovery Use

The Frobenius norm is best used to understand differences between the estimated \(\hat\theta\) matrix and the oracle \(\theta\) matrix.

See also

base::norm()

Examples

# Construct data
estimate = matrix(c(1,1,2,4,3,6), nrow = 2, ncol = 3)
truth = matrix(c(1,2,3,4,5,6), nrow = 2, ncol = 3)

# Compute the frobenius norm
metric_frobenius_norm(estimate, truth)
#> [1] 2.44949