DBSCAN

Description

Fast reimplementation of the DBSCAN (Density-based spatial clustering of applications with noise) clustering algorithm using a kd-tree. The implementation is significantly faster and can work with larger data sets then dbscan in fpc.

Usage

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  dbscan(x, eps, minPts = 5, weights = NULL,
    borderPoints = TRUE, search = "kdtree", bucketSize = 10,
    splitRule = "suggest", approx = 0, ...)

  ## S3 method for class 'dbscan_fast'
predict(object, data, newdata = NULL, ...)

Arguments

x

a data matrix or a dist object.

eps

size of the epsilon neighborhood.

minPts

number of minimum points in the eps region (for core points). Default is 5 points.

weights

numeric; weights for the data points. Only needed to perform weighted clustering.

borderPoints

logical; should border points be assigned. The default is TRUE for regular DBSCAN. If FALSE then border points are considered noise (see DBSCAN* in Campello et al, 2013).

search

nearest neighbor search strategy (one of "kdtree" or "linear", "dist").

bucketSize

max size of the kd-tree leafs.

splitRule

rule to split the kd-tree. One of "STD", "MIDPT", "FAIR", "SL_MIDPT", "SL_FAIR" or "SUGGEST" (SL stands for sliding). "SUGGEST" uses ANNs best guess.

approx

relative error bound for approximate nearest neighbor searching.

object

a DBSCAN clustering object.

data

the data set used to create the DBSCAN clustering object.

newdata

new data set for which cluster membership should be predicted.

...

additional arguments are currently unused.

Details

Note: use dbscan::dbscan to call this implementation when you also use package fpc.

This implementation of DBSCAN implements the original algorithm as described by Ester et al (1996). DBSCAN estimates the density around each data point by counting the number of points in a user-specified eps-neighborhood and applies a used-specified minPts thresholds to identify core, border and noise points. In a second step, core points are joined into a cluster if they are density-reachable (i.e., there is a chain of core points where one falls inside the eps-neighborhood of the next). Finally, border points are assigned to clusters. The algorithm only needs parameters eps and minPts.

Border points are arbitrarily assigned to clusters in the original algorithm. DBSCAN* (see Campello et al 2013) treats all border points as noise points. This is implemented with borderPoints = FALSE.

Setting parameters for DBSCAN: minPts is often set to be dimensionality of the data plus one or higher. The knee in kNNdistplot can be used to find suitable values for eps.

See kNN for more information on the other parameters related to nearest neighbor search.

predict can be used to predict cluster memberships for new data points. A point is considered a member of a cluster if it is within the eps neighborhood of a member of the cluster. Points which cannot be assigned to a cluster will be reported as members of the noise cluster 0.

Value

A object of class 'dbscan_fast' with the following components:

eps

value of the eps parameter.

minPts

value of the minPts parameter.

cluster

A integer vector with cluster assignments. Zero indicates noise points.

Author(s)

Michael Hahsler

References

Martin Ester, Hans-Peter Kriegel, Joerg Sander, Xiaowei Xu (1996). A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. Institute for Computer Science, University of Munich. Proceedings of 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96).

Campello, R. J. G. B.; Moulavi, D.; Sander, J. (2013). Density-Based Clustering Based on Hierarchical Density Estimates. Proceedings of the 17th Pacific-Asia Conference on Knowledge Discovery in Databases, PAKDD 2013, Lecture Notes in Computer Science 7819, p. 160.

See Also

kNNdistplot, dbscan in fpc.

Examples

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data(iris)
iris <- as.matrix(iris[,1:4])

## find suitable eps parameter using a k-NN plot for k = dim + 1
## Look for the knee!
kNNdistplot(iris, k = 5)
abline(h=.4, col = "red", lty=2)

res <- dbscan(iris, eps = .4, minPts = 5)
res

pairs(iris, col = res$cluster + 1L)

## example data from fpc
set.seed(665544)
n <- 100
x <- cbind(
  x = runif(10, 0, 10) + rnorm(n, sd = 0.2),
  y = runif(10, 0, 10) + rnorm(n, sd = 0.2)
  )

res <- dbscan(x, eps = .3, minPts = 3)
res

## plot clusters and add noise (cluster 0) as crosses.
plot(x, col=res$cluster)
points(x[res$cluster==0,], pch = 3, col = "grey")

## predict cluster membership for new data points
## (Note: 0 means it is predicted as noise)
newdata <- x[1:5,] + rnorm(10, 0, .2)
predict(res, x, newdata)

## compare speed against fpc version (if microbenchmark is installed)
## Note: we use dbscan::dbscan to make sure that we do now run the
## implementation in fpc.
## Not run: 
if (requireNamespace("fpc", quietly = TRUE) &&
    requireNamespace("microbenchmark", quietly = TRUE)) {
  t_dbscan <- microbenchmark::microbenchmark(
    dbscan::dbscan(x, .3, 3), times = 10, unit = "ms")
  t_dbscan_linear <- microbenchmark::microbenchmark(
    dbscan::dbscan(x, .3, 3, search = "linear"), times = 10, unit = "ms")
  t_fpc <- microbenchmark::microbenchmark(
    fpc::dbscan(x, .3, 3), times = 10, unit = "ms")

  rbind(t_fpc, t_dbscan_linear, t_dbscan)

  boxplot(rbind(t_fpc, t_dbscan_linear, t_dbscan),
    names = c("fpc", "dbscan (linear)", "dbscan (kdtree)"),
    main = "Runtime comparison in ms")

  ## speedup of the kd-tree-based version compared to the fpc implementation
  median(t_fpc$time) / median(t_dbscan$time)
}
## End(Not run)