kmeans {stats} | R Documentation |
Perform k-means clustering on a data matrix.
kmeans(x, centers, iter.max = 10, nstart = 1, algorithm = c("Hartigan-Wong", "Lloyd", "Forgy", "MacQueen"))
x |
numeric matrix of data, or an object that can be coerced to such a matrix (such as a numeric vector or a data frame with all numeric columns). |
centers |
either the number of clusters, say k, or a set of
initial (distinct) cluster centres. If a number, a random set of
(distinct) rows in x is chosen as the initial centres. |
iter.max |
the maximum number of iterations allowed. |
nstart |
if centers is a number, how many random sets
should be chosen? |
algorithm |
character: may be abbreviated. |
The data given by x
is clustered by the k-means method,
which aims to partition the points into k groups such that the
sum of squares from points to the assigned cluster centres is minimized.
At the minimum, all cluster centres are at the mean of their Voronoi
sets (the set of data points which are nearest to the cluster centre).
The algorithm of Hartigan and Wong (1979) is used by default. Note
that some authors use k-means to refer to a specific algorithm
rather than the general method: most commonly the algorithm given by
MacQueen (1967) but sometimes that given by Lloyd (1957) and Forgy
(1965). The Hartigan–Wong algorithm generally does a better job than
either of those, but trying several random starts (nstart
>
1) is often recommended.
For ease of programmatic exploration, k=1 is allowed, notably
returning the center and withinss
.
Except for the Lloyd–Forgy method, k clusters will always be returned if a number is specified. If an initial matrix of centres is supplied, it is possible that no point will be closest to one or more centres, which is currently an error for the Hartigan–Wong method.
An object of class "kmeans"
which has a print
method and
is a list with components:
cluster |
A vector of integers (from 1:k ) indicating the cluster to
which each point is allocated.
|
centers |
A matrix of cluster centres. |
withinss |
The within-cluster sum of squares for each cluster. |
totss |
The total within-cluster sum of squares. |
tot.withinss |
Total within-cluster sum of squares, i.e., sum(withinss) . |
betweenss |
The between-cluster sum of squares. |
size |
The number of points in each cluster. |
Forgy, E. W. (1965) Cluster analysis of multivariate data: efficiency vs interpretability of classifications. Biometrics 21, 768–769.
Hartigan, J. A. and Wong, M. A. (1979). A K-means clustering algorithm. Applied Statistics 28, 100–108.
Lloyd, S. P. (1957, 1982) Least squares quantization in PCM. Technical Note, Bell Laboratories. Published in 1982 in IEEE Transactions on Information Theory 28, 128–137.
MacQueen, J. (1967) Some methods for classification and analysis of multivariate observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, eds L. M. Le Cam & J. Neyman, 1, pp. 281–297. Berkeley, CA: University of California Press.
require(graphics) # a 2-dimensional example x <- rbind(matrix(rnorm(100, sd = 0.3), ncol = 2), matrix(rnorm(100, mean = 1, sd = 0.3), ncol = 2)) colnames(x) <- c("x", "y") (cl <- kmeans(x, 2)) plot(x, col = cl$cluster) points(cl$centers, col = 1:2, pch = 8, cex=2) kmeans(x,1)$withinss # if you are interested in that ## random starts do help here with too many clusters (cl <- kmeans(x, 5, nstart = 25)) plot(x, col = cl$cluster) points(cl$centers, col = 1:5, pch = 8)