mdbw {RKUM}

Bandwidth of the Gaussian kernel

Description

A median of the pairwise distance of the data

Usage

mdbw(X)

Arguments

X

a data matrix

Details

While the Gaussian kernel has a free parameter (bandwidth), it still follows a number of theoretical properties such as boundedness, consistenc, universality, robustness, etc. It is the most applicable one. In a Gaussian RBF kernel, we need to select an appropriate a bandwidth. It is well known that the parameter has a strong influence on the result of kernel methods. For the Gaussian kernel, we can use the median of the pairwise distance as a bandwidth.

Value

s

a median of the pairwise distance of the X dataset

Author(s)

Md Ashad Alam <[e-mail]>

References

Md. Ashad Alam, Hui-Yi Lin, HOng-Wen Deng, Vince Calhour Yu-Ping Wang (2018), A kernel machine method for detecting higher order interactions in multimodal datasets: Application to schizophrenia, Journal of Neuroscience Methods, Vol. 309, 161-174.

Md. Ashad Alam, Kenji Fukumizu and Yu-Ping Wang (2018), Influence Function and Robust Variant of Kernel Canonical Correlation Analysis, Neurocomputing, Vol. 304 (2018) 12-29.

Md. Ashad Alam and Kenji Fukumizu (2015), Higher-order regularized kernel canonical correlation analysis, International Journal of Pattern Recognition and Artificial Intelligence, Vol. 29(4) 1551005.

Arthu Gretton, Kenji. Fukumizu, C. H. Teo, L. Song, B. Scholkopf and A. Smola (2008), A Kernel statistical test of independence, in Advances in Neural Information Processing Systems, Vol. 20 585–592.

See Also

See also as lkm, gkm

Examples

##Dummy data:

X <- matrix(rnorm(1000),100)

mdbw(X)