dbscan (version 1.1-3)

pointdensity: Calculate Local Density at Each Data Point

Description

Calculate the local density at each data point as either the number of points in the eps-neighborhood (as used in DBSCAN) or the kernel density estimate (kde) of a uniform kernel. The function uses a kd-tree for fast fixed-radius nearest neighbor search.

Usage

pointdensity(x, eps, type = "frequency",
  search = "kdtree", bucketSize = 10,
  splitRule = "suggest", approx = 0)

Arguments

x

a data matrix.

eps

radius of the eps-neighborhood, i.e., bandwidth of the uniform kernel).

type

"frequency" or "density". should the raw count of points inside the eps-neighborhood or the kde be returned.

search, bucketSize, splitRule, approx

algorithmic parameters for frNN.

Value

A vector of the same length as data points (rows) in x with the count or density values for each data point.

Details

DBSCAN estimates the density around a point as the number of points in the eps-neighborhood of the point (including the query point itself). The kde using a uniform kernel is just this count divided by \(2 eps n\), where \(n\) is the number of points in x.

Points with low local density often indicate noise (see e.g., Wishart (1969) and Hartigan (1975)).

References

WISHART, D. (1969), Mode Analysis: A Generalization of Nearest Neighbor which Reduces Chaining Effects, in Numerical Taxonomy, Ed., A.J. Cole, Academic Press, 282-311.

John A. Hartigan (1975), Clustering Algorithms, John Wiley \& Sons, Inc., New York, NY, USA.

See Also

frNN.

Examples

# NOT RUN {
set.seed(665544)
n <- 100
x <- cbind(
  x=runif(10, 0, 5) + rnorm(n, sd=0.4),
  y=runif(10, 0, 5) + rnorm(n, sd=0.4)
  )
plot(x)

### calculate density
d <- pointdensity(x, eps = .5, type = "density")

### density distribution
summary(d)
hist(d, breaks = 10)

### point size is proportional to Density
plot(x, pch = 19, main = "Density (eps = .5)", cex = d*5)

### Wishart (1969) single link clustering method
# 1. remove noise with low density
f <- pointdensity(x, eps = .5, type = "frequency")
x_nonoise <- x[f >= 5,]

# 2. use single-linkage on the non-noise points
hc <- hclust(dist(x_nonoise), method = "single")
plot(x, pch = 19, cex = .5)
points(x_nonoise, pch = 19, col= cutree(hc, k = 4)+1L)
# }