Nystrom low-rank approximation of a kernel matrix

Formula: Q = K_nm * K_mm^- * K_nm', m the retained subset of records

Usage

Nystromap(X, m_index, kernel = "linear", gamma = NULL)

Arguments

X: One record per row.
m_index: 1-based row indices of the retained subset.
kernel: Kernel name: linear, gaussian, polynomial, exponential or sigmoid.
gamma: Kernel bandwidth; None uses 1/p.

Value

List with Q, m, n.

References

Montesinos Lopez, Montesinos Lopez and Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, doi:10.1007/978-3-030-89010-0. Chapter 8: the Nystrom method for compressing a kernel matrix onto a retained subset of records; the implementation delegates to the chapter-8 Nystrom routine verified against the book.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Nystromap(V, V)
#> $Q
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,]    1    2    3    4    5    6    7    8
#> [2,]    2    4    6    8   10   12   14   16
#> [3,]    3    6    9   12   15   18   21   24
#> [4,]    4    8   12   16   20   24   28   32
#> [5,]    5   10   15   20   25   30   35   40
#> [6,]    6   12   18   24   30   36   42   48
#> [7,]    7   14   21   28   35   42   49   56
#> [8,]    8   16   24   32   40   48   56   64
#> 
#> $m
#> [1] 8
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Nystrom kernel approximation, MVSML Chap. 8"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"