NMF 0.17.6

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,]  1.00000  0.08277 -0.09167
## [2,]  0.08277  1.00000 -0.17981
## [3,] -0.09167 -0.17981  1.00000

profcor(a)

##          [,1]     [,2]    [,3]
## [1,]  1.00000  0.05718 -0.0494
## [2,]  0.05718  1.00000 -0.3204
## [3,] -0.04940 -0.32039  1.0000

# Compute correlations with b
basiscor(a, b)

##          [,1]     [,2]     [,3]
## [1,]  0.13191  0.06525  0.05398
## [2,]  0.06914 -0.07215  0.08395
## [3,] -0.11954  0.05423 -0.12475

profcor(a, b)

##        [,1]    [,2]    [,3]
## [1,] 0.2968  0.3300 -0.2138
## [2,] 0.1406 -0.0947 -0.1564
## [3,] 0.2673  0.2512 -0.2651


# 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,] -0.02656  0.94520 -0.04248
## [2,]  0.88282  0.06435 -0.30398
## [3,]  0.02106 -0.14757  0.95249

profcor(a, res)

##          [,1]    [,2]     [,3]
## [1,] -0.02707  0.9365 -0.01096
## [2,]  0.97684  0.2234 -0.50404
## [3,] -0.29382 -0.2544  0.96962


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

##           [,1]      [,2]       [,3]
## [1,] -0.082084 -0.004068  0.1733630
## [2,] -0.150145  0.040432 -0.1231361
## [3,]  0.007276 -0.138978 -0.0008321

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

## [1] FALSE


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

##         [,1]     [,2]    [,3]
## [1,]  0.3823 -0.34576  0.3678
## [2,]  0.2335  0.07934 -0.2875
## [3,] -0.2209 -0.08092  0.2771

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

## [1] FALSE