# pointdensity: Calculate Local Density at Each Data Point In dbscan: Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Related Algorithms

 pointdensity R Documentation

## 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 perform kernel density estimation (KDE) using 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()`.

### 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). Kernel density estimation (KDE) using a uniform kernel, which is just this point count in the eps-neighborhood 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)).

### Value

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

Michael Hahsler

### 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.

`frNN()`, `stats::density()`.

Other Outlier Detection Functions: `glosh()`, `kNNdist()`, `lof()`

### Examples

```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)

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

### Wishart (1969) single link clustering after removing low-density noise
# 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)
```

dbscan documentation built on Oct. 29, 2022, 1:13 a.m.