Density-based Spatial Clustering of Applications with Noise (DBSCAN)
Fast reimplementation of the DBSCAN (Density-based spatial clustering of applications with noise) clustering algorithm using a kd-tree.
dbscan(x, eps, minPts = 5, weights = NULL, borderPoints = TRUE, ...) is.corepoint(x, eps, minPts = 5, ...) ## S3 method for class 'dbscan_fast' predict(object, newdata, data, ...)
x |
a data matrix, a data.frame, a dist object or a frNN object with fixed-radius nearest neighbors. |
eps |
size (radius) of the epsilon neighborhood. Can be omitted if
|
minPts |
number of minimum points required in the eps neighborhood for core points (including the point itself). |
weights |
numeric; weights for the data points. Only needed to perform weighted clustering. |
borderPoints |
logical; should border points be assigned to clusters.
The default is |
... |
additional arguments are passed on to the fixed-radius nearest
neighbor search algorithm. See |
object |
clustering object. |
newdata |
new data points for which the cluster membership should be predicted. |
data |
the data set used to create the clustering object. |
The
implementation is significantly faster and can work with larger data sets
than fpc::dbscan() in fpc. Use dbscan::dbscan() (with specifying the package) to
call this implementation when you also load package fpc.
The algorithm
This implementation of DBSCAN follows the original algorithm as described by Ester et al (1996). DBSCAN performs the following steps:
Estimate 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.
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).
Border points are assigned to clusters. The algorithm needs parameters
eps (the radius of the epsilon neighborhood) and minPts (the
density threshold).
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.
Specifying the data
If x is a matrix or a data.frame, then fast fixed-radius nearest
neighbor computation using a kd-tree is performed using Euclidean distance.
See frNN() for more information on the parameters related to
nearest neighbor search.
Any precomputed distance matrix (dist object) can be specified as x.
You may run into memory issues since distance matrices are large.
A precomputed frNN object can be supplied as x. In this case
eps does not need to be specified. This option us useful for large
data sets, where a sparse distance matrix is available. See
frNN() how to create frNN objects.
Setting parameters for DBSCAN
The parameters minPts and eps depend on each other and
changing one typically requires changing the other one as well. The original
DBSCAN paper suggests to start by setting minPts to the
dimensionality of the data plus one or higher. minPts defines the
minimum density around a core point (i.e., the minimum density for non-noise
areas). Increase the parameter to suppress more noise in the data and
require more points to form a cluster. A suitable neighborhood size
parameter eps given a fixed value for minPts can be found
visually by inspecting the kNNdistplot() of the data using
k = minPts - 1 (minPts includes the point itself, while the
k-nearest neighbors distance does not). The k-nearest neighbor distance plot
sorts all data points by their k-nearest neighbor distance. A sudden
increase of the kNN distance (a knee) indicates that the points to the right
are most likely outliers. Choose eps for DBSCAN where the knee is.
Predict cluster memberships
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 (Euclidean distance is used). Points
which cannot be assigned to a cluster will be reported as
noise points (i.e., cluster ID 0).
dbscan() returns an object of class dbscan_fast with the following components:
eps |
value of the |
minPts |
value of the |
cluster |
A integer vector with cluster assignments. Zero indicates noise points. |
is.corepoint() returns a logical vector indicating for each data point if it is a
core point.
Michael Hahsler
Hahsler M, Piekenbrock M, Doran D (2019). dbscan: Fast Density-Based Clustering with R. Journal of Statistical Software, 91(1), 1-30. doi: 10.18637/jss.v091.i01
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), 226-231. https://dl.acm.org/doi/10.5555/3001460.3001507
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. doi: 10.1007/978-3-642-37456-2_14
Other clustering functions:
extractFOSC(),
hdbscan(),
jpclust(),
optics(),
sNNclust()
## Example 1: use dbscan on the iris data set
data(iris)
iris <- as.matrix(iris[, 1:4])
## Find suitable DBSCAN parameters:
## 1. We use minPts = dim + 1 = 5 for iris. A larger value can also be used.
## 2. We inspect the k-NN distance plot for k = minPts - 1 = 4
kNNdistplot(iris, k = 5 - 1)
## Noise seems to start around a 4-NN distance of .7
abline(h=.7, col = "red", lty = 2)
## Cluster with the chosen parameters
res <- dbscan(iris, eps = .7, minPts = 5)
res
pairs(iris, col = res$cluster + 1L)
## Use a precomputed frNN object
fr <- frNN(iris, eps = .7)
dbscan(fr, minPts = 5)
## Example 2: use data from fpc
set.seed(665544)
n <- 100
x <- cbind(
x = runif(10, 0, 10) + rnorm(n, sd = 0.2),
y = runif(10, 0, 10) + rnorm(n, sd = 0.2)
)
res <- dbscan(x, eps = .3, minPts = 3)
res
## plot clusters and add noise (cluster 0) as crosses.
plot(x, col = res$cluster)
points(x[res$cluster == 0, ], pch = 3, col = "grey")
hullplot(x, res)
## Predict cluster membership for new data points
## (Note: 0 means it is predicted as noise)
newdata <- x[1:5,] + rnorm(10, 0, .3)
hullplot(x, res)
points(newdata, pch = 3 , col = "red", lwd = 3)
text(newdata, pos = 1)
pred_label <- predict(res, newdata, data = x)
pred_label
points(newdata, col = pred_label + 1L, cex = 2, lwd = 2)
## Compare speed against fpc version (if microbenchmark is installed)
## Note: we use dbscan::dbscan to make sure that we do now run the
## implementation in fpc.
## Not run:
if (requireNamespace("fpc", quietly = TRUE) &&
requireNamespace("microbenchmark", quietly = TRUE)) {
t_dbscan <- microbenchmark::microbenchmark(
dbscan::dbscan(x, .3, 3), times = 10, unit = "ms")
t_dbscan_linear <- microbenchmark::microbenchmark(
dbscan::dbscan(x, .3, 3, search = "linear"), times = 10, unit = "ms")
t_dbscan_dist <- microbenchmark::microbenchmark(
dbscan::dbscan(x, .3, 3, search = "dist"), times = 10, unit = "ms")
t_fpc <- microbenchmark::microbenchmark(
fpc::dbscan(x, .3, 3), times = 10, unit = "ms")
r <- rbind(t_fpc, t_dbscan_dist, t_dbscan_linear, t_dbscan)
r
boxplot(r,
names = c('fpc', 'dbscan (dist)', 'dbscan (linear)', 'dbscan (kdtree)'),
main = "Runtime comparison in ms")
## speedup of the kd-tree-based version compared to the fpc implementation
median(t_fpc$time) / median(t_dbscan$time)
}
## End(Not run)
## Example 3: manually create a frNN object for dbscan (dbscan only needs ids and eps)
nn <- structure(list(ids = list(c(2,3), c(1,3), c(1,2,3), c(3,5), c(4,5)), eps = 1),
class = c("NN", "frNN"))
nn
dbscan(nn, minPts = 2)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.