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Group rows of a diagonal matrix using a threshold

Source: R/grouping-functions.R
groupSimilarityMatrix.Rd

This function groups elements (rows or columns) of a diagonal matrix, such as a pairwise correlation matrix or similarity matrix, with a value >= threshold. This creates clusters of elements in which all elements have a value >= threshold with any other element in that cluster. On a correlation matrix (such as created with cor) it will generate small clusters of highly correlated elements. Note however that single elements in one cluster could also have a correlation >= threshold to another element in another cluster. The average similarity to its own cluster will however be higher to that of the other.

Usage

groupSimilarityMatrix(x, threshold = 0.9, full = TRUE, ...)

Arguments

x

symmetrix numeric matrix.

threshold

numeric(1) above which rows in x should be grouped.

full

logical(1) whether the full matrix should be considered, or just the upper triangular matrix (including the diagonal).

...

ignored.

Value

integer same length than nrow(x), grouped elements (rows) defined by the same value.

Details

The algorithm is defined as follows:

  • all pairs of values in x which are >= threshold are identified and sorted decreasingly.

  • starting with the pair with the highest correlation, groups are defined:

  • if none of the two is in a group, both are put into the same new group.

  • if one of the two is already in a group, the other is put into the same group if all correlations of it to that group are >= threshold (and are not NA).

  • if both are already in the same group nothing is done.

  • if both are in different groups: an element is put into the group of the other if a) all correlations of it to members of the other's group are not NA and >= threshold and b) the average correlation to the other group is larger than the average correlation to its own group.

This ensures that groups are defined in which all elements have a correlation >= threshold with each other and the correlation between members of the same group is maximized.

See also

Other grouping operations: groupClosest(), groupConsecutive(), groupSimilarityMatrixTree()

Author

Johannes Rainer

Examples


x <- rbind(
    c(1, 0.9, 0.6, 0.8, 0.5),
    c(0.9, 1, 0.7, 0.92, 0.8),
    c(0.6, 0.7, 1, 0.91, 0.7),
    c(0.8, 0.92, 0.91, 1, 0.9),
    c(0.5, 0.8, 0.7, 0.9, 1)
    )

groupSimilarityMatrix(x, threshold = 0.9)
#> [1] 2 1 3 1 4

groupSimilarityMatrix(x, threshold = 0.1)
#> [1] 1 1 1 1 1

## Add also a correlation between 3 and 2
x[2, 3] <- 0.9
x[3, 2] <- 0.9
x
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  1.0 0.90 0.60 0.80  0.5
#> [2,]  0.9 1.00 0.90 0.92  0.8
#> [3,]  0.6 0.90 1.00 0.91  0.7
#> [4,]  0.8 0.92 0.91 1.00  0.9
#> [5,]  0.5 0.80 0.70 0.90  1.0
groupSimilarityMatrix(x, threshold = 0.9)
#> [1] 2 1 1 1 3

## Add a higher correlation between 4 and 5
x[4, 5] <- 0.99
x[5, 4] <- 0.99
x
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  1.0 0.90 0.60 0.80 0.50
#> [2,]  0.9 1.00 0.90 0.92 0.80
#> [3,]  0.6 0.90 1.00 0.91 0.70
#> [4,]  0.8 0.92 0.91 1.00 0.99
#> [5,]  0.5 0.80 0.70 0.99 1.00
groupSimilarityMatrix(x, threshold = 0.9)
#> [1] 2 2 3 1 1

## Increase correlation between 2 and 3
x[2, 3] <- 0.92
x[3, 2] <- 0.92
x
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  1.0 0.90 0.60 0.80 0.50
#> [2,]  0.9 1.00 0.92 0.92 0.80
#> [3,]  0.6 0.92 1.00 0.91 0.70
#> [4,]  0.8 0.92 0.91 1.00 0.99
#> [5,]  0.5 0.80 0.70 0.99 1.00
groupSimilarityMatrix(x, threshold = 0.9) ## Don't break previous cluster!
#> [1] 3 2 2 1 1