Cosine normalization of a kernel matrix

It is equivalent to compute K using the normalization `X/sqrt(sum(X^2))` in Feature Space.

Usage

cosNorm(K)

Arguments

K

Kernel matrix (class "matrix").

Value

Cosine-normalized K (class "matrix").

References

Ah-Pine, J. (2010). Normalized kernels as similarity indices. In Advances in Knowledge Discovery and Data Mining: 14th Pacific-Asia Conference, PAKDD 2010, Hyderabad, India, June 21-24, 2010. Proceedings. Part II 14 (pp. 362-373). Springer Berlin Heidelberg. Link

Examples

dat <- matrix(rnorm(250),ncol=50,nrow=5)
K <- Linear(dat)
cosNorm(K)
#>             [,1]        [,2]        [,3]       [,4]        [,5]
#> [1,]  1.00000000 -0.05614708  0.06373532  0.1948711  0.23277438
#> [2,] -0.05614708  1.00000000  0.20718164 -0.1411817 -0.05666972
#> [3,]  0.06373532  0.20718164  1.00000000 -0.1113739 -0.11711099
#> [4,]  0.19487106 -0.14118167 -0.11137393  1.0000000  0.20354524
#> [5,]  0.23277438 -0.05666972 -0.11711099  0.2035452  1.00000000