These functions provide a set of tools to find the best match between the labels used by two different algorithms to cluster the same set of samples.
labelMatcher(tab, verbose = FALSE)
matchLabels(tab)
countAgreement(tab)
labelAccuracy(data, labels, linkage="ward.D2")
bestMetric(data, labels)
remap(fix, vary)The labelMatcher function returns a list of two vectors of the
same length. These contain the matched label-indices, in the order
they were matched by the algorithm.
The matchLabels function is a user-friendly front-end to the
labelmatcher function. It returns a matrix, with the rows and
columns reordered so the labels match.
The countAgreement function returns an integer, the number of
samples with the "same" labels, computed by summing the diagonal of
the reordered matrix produced by matchLabels.
The labelAccuracy function returns a vector indexed by the set
of nine distance metrics hard-coded in the function. Each entry is
the fraction of samples whose hierarchical clusters match the
prespecified labels.
The bestMetric function is a user-friendly front-end to the
labelAccuracy function. It returns the name of the distance
metric whose hierarchical clusters best match the prespecified
labels.
The remap function takes two sets of integer cluster
assignments and returns a new set of labels for the target that best
matches the source.
A contingency table, represented as a square matrix
or table as an R object. Both dimensions represent an
assignment of class labels, with each row and column representing
one of the labels. Entries should be non-negative integer counts of
the number of objects having the labels represented by the row and
column.
A logical value; should the routine print something out periodically so you know it's still working?
A matrix whose columns represent objects to be clustered and whose rows represent the anonymous features used to perform the clustering.
A factor (or character vector) of class labels for the
objects in the data matrix.
A linkage rule accepted by the hclust
function.
A vector of cluater assignments.
A vector of cluater assignments.
Kevin R. Coombes <krc@silicovore.com>
In the most general sense, clustering can be viewed as a function from the space of "objects" of interest into a space of "class labels". In less mathematical terms, this simply means that each object gets assigned an (arbitrary) class label. This is all well-and-good until you try to compare the results of running two different clustering algorithms that use different labels (or even worse, use the same labels -- typically the integers \(1, 2, \dots, K\) -- with different meanings). When that happens, you need a way to decide which labels from the different sets are closest to meaning the "same thing".
That's where this set of functions comes in. The core algorithm is
implemented in the function labelMatcher, which works on a
contingency table whose entries \(N_{ij}\) are the number of samples
with row-label = \(i\) and column-label = \(j\). To find the
best match, one computes (heuristically) the values \(F_{ij}\) that
describe the fraction of all entries in row \(i\) and column \(j\)
represented by \(N_{ij}\). Perfectly matched labels would consist
of a row \(i\) and a column \(j\) where \(N_{ij}\) is the only
nonzero entry in its row and column, so \(F_{ij} = 1\). The largest
value for \(F_{ij}\) (with ties broken simply by which entry is
closer to the upper-left corner of the matrix) defines the best
match. The matched row and column are then removed from the matrix and
the process repeats recursively.
We apply this method to determine which distance metric, when used in hierarchical clustering, best matches a "gold standard" set of class labels. (These may not really be gold, of course; they can also be a set of labels determined by k-means or another clustering algorithm.) The idea is to cluster the samples using a variety of different metrics, and select the one whose label assignments best macth the standard.
factor1 <- sample(c("A", "B", "C"), 30, replace=TRUE)
factor2 <- rep(c("X", "Y", "Z"), each=10)
tab <- table(factor1, factor2)
matchLabels(tab)
labelMatcher(tab)
R <- remap(factor1, factor2)
table(R, factor2) # remapping
table(R, factor1) # cross-comparison
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