Correlations in NMF Models

Description

basiscor computes the correlation matrix between basis vectors, i.e. the columns of its basis matrix -- which is the model's first matrix factor.

profcor computes the correlation matrix between basis profiles, i.e. the rows of the coefficient matrix -- which is the model's second matrix factor.

Usage

basiscor(x, y, ...)

profcor(x, y, ...)

Arguments

x
a matrix or an object with suitable methods basis or coef.
y
a matrix or an object with suitable methods basis or coef, and dimensions compatible with x. If missing the correlations are computed between x and y=x.
...
extra arguments passed to cor.

Details

Each generic has methods defined for computing correlations between NMF models and/or compatible matrices. The computation is performed by the base function cor.

Methods

  1. basiscorsignature(x = "NMF", y = "matrix"): Computes the correlations between the basis vectors of x and the columns of y.

  2. basiscorsignature(x = "matrix", y = "NMF"): Computes the correlations between the columns of x and the the basis vectors of y.

  3. basiscorsignature(x = "NMF", y = "NMF"): Computes the correlations between the basis vectors of x and y.

  4. basiscorsignature(x = "NMF", y = "missing"): Computes the correlations between the basis vectors of x.

  5. profcorsignature(x = "NMF", y = "matrix"): Computes the correlations between the basis profiles of x and the rows of y.

  6. profcorsignature(x = "matrix", y = "NMF"): Computes the correlations between the rows of x and the basis profiles of y.

  7. profcorsignature(x = "NMF", y = "NMF"): Computes the correlations between the basis profiles of x and y.

  8. profcorsignature(x = "NMF", y = "missing"): Computes the correlations between the basis profiles of x.

Examples



# generate two random NMF models
a <- rnmf(3, 100, 20)
b <- rnmf(3, 100, 20)

# Compute auto-correlations
basiscor(a)

##             [,1]        [,2]         [,3]
## [1,]  1.00000000 0.031692962 -0.130764317
## [2,]  0.03169296 1.000000000  0.005822748
## [3,] -0.13076432 0.005822748  1.000000000

profcor(a)

##             [,1]        [,2]       [,3]
## [1,]  1.00000000  0.01844804 -0.3558334
## [2,]  0.01844804  1.00000000 -0.4002484
## [3,] -0.35583337 -0.40024844  1.0000000

# Compute correlations with b
basiscor(a, b)

##             [,1]       [,2]        [,3]
## [1,] -0.12364568  0.0318066 -0.10049324
## [2,]  0.25546157 -0.2613076  0.10991557
## [3,] -0.09445275  0.1756572  0.01520068

profcor(a, b)

##            [,1]       [,2]         [,3]
## [1,]  0.2791156  0.3824726 -0.179987068
## [2,]  0.1829474 -0.3038400  0.100952866
## [3,] -0.3415462  0.3049951 -0.007022731

# try to recover the underlying NMF model 'a' from noisy data
res <- nmf(fitted(a) + rmatrix(a), 3)

# Compute correlations with the true model
basiscor(a, res)

##             [,1]       [,2]       [,3]
## [1,] -0.31181600  0.8721197  0.2896024
## [2,]  0.06017881 -0.1009603  0.9139113
## [3,]  0.92772281  0.1700795 -0.1742550

profcor(a, res)

##            [,1]        [,2]       [,3]
## [1,] -0.5849075  0.84442507  0.1132048
## [2,] -0.2235612 -0.46983743  0.9746677
## [3,]  0.9477745  0.01338298 -0.5489273

# Compute correlations with a random compatible matrix
W <- rmatrix(basis(a))
basiscor(a, W)

##              [,1]         [,2]        [,3]
## [1,]  0.040376132  0.196558218 -0.19100255
## [2,] -0.008386611 -0.006604350 -0.06910496
## [3,]  0.049164413  0.008146703 -0.06187523

identical(basiscor(a, W), basiscor(W, a))

## [1] FALSE

H <- rmatrix(coef(a))
profcor(a, H)

##            [,1]       [,2]        [,3]
## [1,]  0.4419684  0.4538796  0.01153729
## [2,]  0.2976432  0.3639700 -0.48356340
## [3,] -0.2106585 -0.1186591 -0.10612098

identical(profcor(a, H), profcor(H, a))

## [1] FALSE