Non-Conformable Arrays when Doing Matrix Multiplication in R

问题

I am trying to implement Kernel Ridge Regression in R.

The formula is:

alpha <- ((lambda.I + K)^(-1)) * y

Lambda = 0.1. I = identity matrix the same size as K. y is a feature vector that has the same number of rows as K.

So I tried this in R:

I <- diag(nrow(df_matrix)
lambda <- 0.1
alpha <- (lambda * I + df_matrix) ^ (-1) * df_vector

I get the following error

Error in (0.1 * I + df_matrix)^(-1) * df_vector : non-conformable arrays

Here's some information on my dataset

> nrow(df_matrix)
[1] 8222
> ncol(df_matrix)
[1] 8222
> nrow(df_vector)
[1] 8222
> nrow(I)
[1] 8222
> ncol(I)
[1] 8222
> class(df_matrix)
[1] "matrix"
> class(df_vector)
[1] "matrix"

回答1:

I bet you want to have here matrix inversion, which is solve(m), instead of element-wise (m^(-1)). Also, matrix multiplication (%*%) instead of element-wise (*). So, altogether is

alpha <- solve(lambda * I + df_matrix) %*% df_vector

回答2:

You need to use matrix multiplication, %*%. In addition you also need to use solve to compute inverses as raising to the power minus one will just do element wise reciprocals. e.g.:

K <- matrix(runif(9),3)
y <- matrix(runif(3),nrow=3)

solve(lambda*diag(nrow(K))+K) %*% y
            [,1]
[1,]  0.50035075
[2,] -0.04985508
[3,]  0.74944867

回答3:

To transpose a matrix, the matrix has to be quadratic and the determinant has to be different to zero. If you matrix df_matrix fullfil these requirements, then

alpha <- solve(lambda * I + df_matrix) %*% df_vector

来源：https://stackoverflow.com/questions/37183762/non-conformable-arrays-when-doing-matrix-multiplication-in-r