Local Outlier Factor Score

Calculate the Local Outlier Factor (LOF) score for each data point using a kd-tree to speed up kNN search.

Usage

lof(x, minPts = 5, ...)

Arguments

x: a data matrix or a dist object.
minPts: number of nearest neighbors used in defining the local neighborhood of a point (includes the point itself).
...: further arguments are passed on to kNN(). Note: sort cannot be specified here since lof() uses always sort = TRUE.

Value

A numeric vector of length nrow(x) containing LOF values for all data points.

Details

LOF compares the local reachability density (lrd) of a point to the lrd of its neighbors. A LOF score of approximately 1 indicates that the lrd around the point is comparable to the lrd of its neighbors and that the point is not an outlier. Points that have a substantially lower lrd than their neighbors are considered outliers and produce scores significantly larger than 1.

If a data matrix is specified, then Euclidean distances and fast nearest neighbor search using a kd-tree is used.

Note on duplicate points: If there are more than minPts duplicates of a point in the data, then LOF the local readability distance will be 0 resulting in an undefined LOF score of 0/0. We set LOF in this case to 1 since there is already enough density from the points in the same location to make them not outliers. The original paper by Breunig et al (2000) assumes that the points are real duplicates and suggests to remove the duplicates before computing LOF. If duplicate points are removed first, then this LOF implementation in dbscan behaves like the one described by Breunig et al.

References

Breunig, M., Kriegel, H., Ng, R., and Sander, J. (2000). LOF: identifying density-based local outliers. In ACM Int. Conf. on Management of Data, pages 93-104. doi:10.1145/335191.335388

Author

Michael Hahsler

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)
  )

### calculate LOF score with a neighborhood of 3 points
lof <- lof(x, minPts = 3)

### distribution of outlier factors
summary(lof)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>  0.8912  0.9628  1.0900  1.2542  1.3972  3.0627 
hist(lof, breaks = 10, main = "LOF (minPts = 3)")


### plot sorted lof. Looks like outliers start around a LOF of 2.
plot(sort(lof), type = "l",  main = "LOF (minPts = 3)",
  xlab = "Points sorted by LOF", ylab = "LOF")


### point size is proportional to LOF and mark points with a LOF > 2
plot(x, pch = ".", main = "LOF (minPts = 3)", asp = 1)
points(x, cex = (lof - 1) * 2, pch = 1, col = "red")
text(x[lof > 2,], labels = round(lof, 1)[lof > 2], pos = 3)