colScale normalises a matrix by the sum of each column
rowScale normalises a matrix by the sum of each row
sqrt of both column and row normalisation
Details
Conventionally in connectivity matrices, rows are upstream input
neurons and columns are downstream output neurons. colScaleM will
therefore normalise by the total input onto each downstream neuron while
rowScaleM will normalise by the total output from each upstream
neuron.
These functions will work with dense inputs but are less efficient than
their base R cousins (e.g. scale). As an example, normalising a 4x4k
subset of VNC connectivity data took
colScaleMsparse 3.5mscolScaleMdense 1460msscaledense 365ms
In conclusion sparse matrices with colScaleM/rowScaleM are
the way to go for real connectivity matrices! For large matrices they will
be much faster and for small ones, both methods will be fast anyway.
Note also that these functions were originally called colScale etc
but then the Matrix package added functions of the
same name. The functions in this package differ in two respects from the
Matrix::colScale,rowScale functions. First
they calculate the required row or column sums to perform the scaling.
Second, they handle the inevitable zero sum rows or columns via the default
na.rm argument.
See also
Matrix::colScale on which these are based and,
for the original version,
https://stackoverflow.com/questions/39284774/column-rescaling-for-a-very-large-sparse-matrix-in-r
Examples
library(Matrix)
set.seed(42)
A <- Matrix(rbinom(100,10,0.05), nrow = 10)
rownames(A)=letters[1:10]
colnames(A)=LETTERS[1:10]
colScaleM(A)
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 10 column names ‘A’, ‘B’, ‘C’ ... ]]
#>
#> a 0.2222222 . 0.125 0.1666667 . . 0.1428571 . . 0.125
#> b 0.2222222 0.1428571 . 0.1666667 . . 0.2857143 . . .
#> c . 0.2857143 0.375 . . . 0.1428571 . . .
#> d 0.1111111 . 0.250 0.1666667 0.2222222 0.3333333 . . 0.5 0.250
#> e 0.1111111 . . . . . 0.1428571 . 0.5 0.250
#> f . 0.2857143 . 0.1666667 0.2222222 0.3333333 . 1 . 0.125
#> g 0.1111111 0.2857143 . . 0.1111111 0.3333333 . . . .
#> h . . 0.125 . 0.1111111 . 0.1428571 . . .
#> i 0.1111111 . . 0.1666667 0.2222222 . 0.1428571 . . 0.125
#> j 0.1111111 . 0.125 0.1666667 0.1111111 . . . . 0.125
rowScaleM(A)
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 10 column names ‘A’, ‘B’, ‘C’ ... ]]
#>
#> a 0.3333333 . 0.1666667 0.1666667 . . 0.1666667 . .
#> b 0.3333333 0.1666667 . 0.1666667 . . 0.3333333 . .
#> c . 0.3333333 0.5000000 . . . 0.1666667 . .
#> d 0.1000000 . 0.2000000 0.1000000 0.2000000 0.100 . . 0.1
#> e 0.2000000 . . . . . 0.2000000 . 0.2
#> f . 0.2500000 . 0.1250000 0.2500000 0.125 . 0.125 .
#> g 0.2000000 0.4000000 . . 0.2000000 0.200 . . .
#> h . . 0.3333333 . 0.3333333 . 0.3333333 . .
#> i 0.1666667 . . 0.1666667 0.3333333 . 0.1666667 . .
#> j 0.2000000 . 0.2000000 0.2000000 0.2000000 . . . .
#>
#> a 0.1666667
#> b .
#> c .
#> d 0.2000000
#> e 0.4000000
#> f 0.1250000
#> g .
#> h .
#> i 0.1666667
#> j 0.2000000
geomScaleM(A)
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 10 column names ‘A’, ‘B’, ‘C’ ... ]]
#>
#> a 0.2721655 . 0.1443376 0.1666667 . . 0.1543033
#> b 0.2721655 0.1543033 . 0.1666667 . . 0.3086067
#> c . 0.3086067 0.4330127 . . . 0.1543033
#> d 0.1054093 . 0.2236068 0.1290994 0.2108185 0.1825742 .
#> e 0.1490712 . . . . . 0.1690309
#> f . 0.2672612 . 0.1443376 0.2357023 0.2041241 .
#> g 0.1490712 0.3380617 . . 0.1490712 0.2581989 .
#> h . . 0.2041241 . 0.1924501 . 0.2182179
#> i 0.1360828 . . 0.1666667 0.2721655 . 0.1543033
#> j 0.1490712 . 0.1581139 0.1825742 0.1490712 . .
#>
#> a . . 0.1443376
#> b . . .
#> c . . .
#> d . 0.2236068 0.2236068
#> e . 0.3162278 0.3162278
#> f 0.3535534 . 0.1250000
#> g . . .
#> h . . .
#> i . . 0.1443376
#> j . . 0.1581139