Create a kernel matrix from covariates

nmfkc.kernel constructs a kernel matrix from covariate matrices. It supports Gaussian, Exponential, Periodic, Linear, Normalized Linear, and Polynomial kernels.

Usage

nmfkc.kernel(
  U,
  V = NULL,
  kernel = c("Gaussian", "Exponential", "Periodic", "Linear", "NormalizedLinear",
    "Polynomial"),
  ...
)

Source

Satoh, K. (2024). Applying Non-negative Matrix Factorization with Covariates to the Longitudinal Data as Growth Curve Model. arXiv preprint arXiv:2403.05359. https://arxiv.org/abs/2403.05359

Arguments

U: Covariate matrix \(U(K,N) = (u_1, \dots, u_N)\). Each row may be normalized in advance.
V: Covariate matrix \(V(K,M) = (v_1, \dots, v_M)\), typically used for prediction. If NULL, the default is U.
kernel: Kernel function to use. Default is "Gaussian". Options are "Gaussian", "Exponential", "Periodic", "Linear", "NormalizedLinear", and "Polynomial".
...: Additional arguments passed to the specific kernel function (e.g., beta, degree).

Value

Kernel matrix \(A(N,M)\).

Examples

# install.packages("remotes")
# remotes::install_github("ksatohds/nmfkc")
# Example.
Y <- matrix(cars$dist,nrow=1)
U <- matrix(c(5,10,15,20,25),nrow=1)
V <- matrix(cars$speed,nrow=1)
A <- nmfkc.kernel(U,V,beta=28/1000)
dim(A)
#> [1]  5 50
result <- nmfkc(Y,A,Q=1)
#> Y(1,50)~X(1,1)C(1,5)A(5,50)=XB(1,50)...
#> 0sec
plot(as.vector(V),as.vector(Y))
lines(as.vector(V),as.vector(result$XB),col=2,lwd=2)