# R - Outlier Detection Algorithm

I am trying to implement an algorithm for detecting outliers in R and I am pretty new to the language. The outlier algorithm is described in this paper in detail on page 10-11, but to summarize it works like this:

Algorithm – Outlier Detection using K-Nearest Neighbor Data Distributions

1. Find the set S(K) of K nearest neighbors to the test data point O.
2. Calculate the K distances between O and the members of S(K). These distances define fK(d,O).
3. Calculate the K(K-1)/2 distances among the points within S(K). These distances define fK(d,K).
4. Compute the cumulative distribution functions CK(d,O) and CK(d,K), respectively, for fK(d,O) and fK(d,K).
5. Perform the K-S Test on CK(d,O) and CK(d,K). Estimate the p-value of the test.
6. Calculate the Outlier Index = 1-p. If Outlier Index > 0.95, then mark O as an “Outlier”. The Null Hypothesis is rejected. If 0.90 < Outlier Index < 0.95, then mark O as a “Potential Outlier”. If p > 0.10, then the Null Hypothesis is accepted: the two distance distributions are drawn from the same population. Data point O is not marked as an outlier.

I implemented this in the following code but I am unsure if this code is appropriate for R in terms of structure and style (compared with Python). Also, I don't know if there is a more efficient way than the simple step by step way I have done. I added code comments to delineate each step of the algorithm.

outlier_test <- function(data , neighbors){
#Find the set S(K) of K nearest neighbors to the test data point O.
sk <- nn2(data, k=neighbors)$nn.idx #matrix of indices of neighbors #Calculate the K distances between O and the members of S(K). These distances define fK(d,O). outlier_distances <- nn2(data, k=neighbors)$nn.dist #distances between value and its neighbors

#Calculate the K(K-1)/2 distances among the points within S(K). These distances define fK(d,K).
plyr::adply(sk, .margins = 1, function(row) { data[row, ] })

df1<- plyr::alply(sk, .margins=1, function(row){data[row,]})
df1 = plyr::ldply(df1, rbind)
neighbor_distances <- plyr::alply(df1, 1, function(row) c(dist(unlist(row))))

neighbor_distances <- df1 %>%
dplyr::group_by(X1) %>%
do({
row_data <- .
my_dist <- dist(row_data[ ,c(colnames(data),colnames(data))])
as.data.frame(t(as.vector(my_dist)))
}) %>%
dplyr::ungroup() %>%
dplyr::select(-X1) %>%
as.matrix()

#daply(test, .(X1), function(x) as.vector(dist(x))) This  is an alternative way to do the above piping

#Compute the cumulative distribution functions CK(d,O) and CK(d,K), respectively, for fK(d,O)
#and fK(d,K).
# Since ks.test function in R can take vectors of values, we don't need to explicitly find the ECDF of our samples

#Perform the K-S Test on CK(d,O) and CK(d,K). Estimate the p-value of the test.
all_pvalues = sapply(1:nrow(outlier_distances), function(i) ks.test(as.vector(outlier_distances[i,]), as.vector(neighbor_distances[i,]))\$p.value)

#Calculate the Outlier Index = 1-p.
outlier_index = 1-all_pvalues
#If Outlier Index > 0.95, then mark O as an Outlier. The Null Hypothesis is rejected.
#If 0.90 < Outlier Index < 0.95, then mark O as a Potential Outlier.
#If p > 0.10, then the Null Hypothesis is accepted: the two distance distributions are drawn from
#the same population. Data point O is not marked as an outlier
return(outlier_index)
}


• When you refer to columns in a fixed position way such as colnames(data) you should make sure that the data structure you give to the function is as expected