correctionKernelMatrix {CEGO} R Documentation

## Correction of a Kernel (Correlation) Matrix

### Description

Convert a non-PSD kernel matrix with chosen approach so that it becomes a PSD matrix. Optionally, the resulting matrix is enforced to have values between -1 and 1 and a diagonal of 1s, with the `repair` parameter. That means, it is (optionally) converted to a valid correlation matrix. Essentially, this is a combination of `correctionDefinite` with `repairConditionsCorrelationMatrix`.

### Usage

```correctionKernelMatrix(mat, method = "flip", repair = TRUE, tol = 1e-08)
```

### Arguments

 `mat` symmetric kernel matrix `method` string that specifies method for correction: spectrum clip `"clip"`, spectrum flip `"flip"`, nearest definite matrix `"near"`, spectrum square`"square"`, spectrum diffusion `"diffusion"`. `repair` boolean, whether or not to use condition repair, so that elements between -1 and 1, and the diagonal values are 1. `tol` torelance value. Eigenvalues between `-tol` and `tol` are assumed to be zero.

### Value

list with corrected kernel matrix `mat`, `isPSD` (boolean, whether original matrix was PSD), transformation matrix `A`, the matrix of eigenvectors (`U`) and the transformation vector (`a`)

### References

Martin Zaefferer and Thomas Bartz-Beielstein. (2016). Efficient Global Optimization with Indefinite Kernels. Parallel Problem Solving from Nature-PPSN XIV. Accepted, in press. Springer.

`correctionDefinite`, `repairConditionsCorrelationMatrix`

### Examples

```x <- list(c(2,1,4,3),c(2,4,3,1),c(4,2,1,3),c(4,3,2,1),c(1,4,3,2))
D <- distanceMatrix(x,distancePermutationInsert)
K <- exp(-0.01*D)
is.PSD(K) #matrix should not be PSD
K <- correctionKernelMatrix(K)\$mat
is.PSD(K) #matrix should now be CNSD
K
```

[Package CEGO version 2.4.2 Index]