Package 'oclust'

Find Initial Gross Outliers

Description

findGrossOuts uses DBSCAN to find areas of high density. Mahalanobis distance to the closest area of high density is calculated for each point. With no elbow specified, the Mahalonis distances are plotted. If the elbow is specified, the indices of the gross outliers are returned.

Usage

findGrossOuts(X, minPts = 10, xlim = NULL, elbow = NULL)

Arguments

X	A data matrix
minPts	The minimum number of points in each region of high density. Default is 10
xlim	A vector of form c(xmin,xmax) to specify the domain of the plot. Default is NULL, which sets xmax to 10% of the data size.
elbow	An integer specifying the location of the elbow in the plot of Mahalanobis distances. Default is NULL, which returns the plot. If elbow is specified, no plot is produced and the gross outliers are returned.

Details

The function plots Mahalanobis distance to the closest centre in decreasing order or returns the indices of the gross outliers. The elbow location of the plot provides a good indication as to where the gross outliers end. Running the function first without an elbow specified will plot the Mahalonobis distances. Running it again with the elbow specified will return the outliers. It is recommended to choose the elbow conservatively. If the MDs decrease smoothly, there are no gross outliers. Set elbow=1.

Value

findGrossOuts returns a vector with the indices of the gross outliers. One fewer point is returned than the elbow specified.

---

Minimum Mahalanobis Distance

Description

minMD calculates the Mahalanobis distance to each cluster and returns the Mahalanobis distance to the closest cluster.

Usage

minMD(X, sigs, mus)

Arguments

X	A matrix or data frame of the data.
sigs	A list of cluster variance matrices
mus	A list of cluster mean vectors

Details

This function is used to help identify initial gross outliers.

Value

minMD returns a vector of length n corresponding to the minimum MD for each point.

---

Mixture of Beta Functions

Description

MixBetaDens generates the pdf and cdf of a mixture of beta functions, and calculates the area under the graph between two points.

Usage

MixBetaDens(
  n,
  p,
  x = seq(0, 15, by = 0.01),
  a = 0,
  b = 1,
  n_g = n_g,
  var = var
)

Arguments

n	The number of observations in the dataset
p	The dimension
x	A vector of x values to evaluate. Default value is seq(0, 15, by=0.01)
a	Lower bound for area evaluation. Default value is 0
b	Upper bound for area evaluation. Default value is 1
n_g	Vector describing the number of observations in each cluster
var	A list of cluster variance matrices

Details

The domain for this function is not [0,1] as is typical with a beta function. The domain encompasses the shifted log-likelihoods generated in oclust.

Value

MixBetaDens returns a list with

pdf	The probability density at each x value
cdf	The cumulative density at each x value
area	The area under the pdf graph between a and b

---

The OCLUST Algorithm

Description

oclust is a trimming method in model-based clustering. It iterates over possible values for the number of outliers and returns the model parameters for the best model as determined by the minimum KL divergence. If kuiper=TRUE, oclust calculates an approximate p-value using the Kuiper test and stops the algorithm if the p-value exceeds the specified threhold.

Usage

oclust(
  X,
  maxO,
  G,
  grossOuts = NULL,
  modelNames = "VVV",
  mc.cores = 1,
  nmax = 1000,
  kuiper = FALSE,
  pval = 0.05,
  B = 100,
  verb = FALSE,
  scale = TRUE
)

Arguments

X	A matrix or data frame with n rows of observations and p columns
maxO	An upper bound for the number of outliers
G	The number of clusters
grossOuts	The indices of the initial outliers to remove. Default is NULL.
modelNames	The model to fit using the gpcm function in the mixture package. Default is "VVV" (unconstrained). If modelNames=NULL, all models are fitted for each subset at each iteration. The BIC chooses the best model for each subset.
mc.cores	Number of cores to use if running in parallel. Default is 1
nmax	Maximum number of iterations for each EM algorithm. Decreasing nmax may speed up the algorithm but lose precision in finding the log-likelihoods.
kuiper	A logical specifying whether to use the Kuiper test (Kuiper, 1960) to stop the algorithm when p-value exceeds the specified threshold. Default is FALSE.
pval	The p-value for the Kuiper test. Default is 0.05.
B	Number of samples to calculate the approximate p-value. Default is 100.
verb	A logical specifying whether to print the current iteration number. Default is FALSE
scale	A logical specifying whether to centre and scale the data. Default is TRUE

Details

Gross outlier indices can be found with the findGrossOuts function.

N. H. Kuiper, Tests concerning random points on a circle, in: Nederl. Akad. Wetensch. Proc. Ser. A, Vol. 63, 1960, pp. 38–47.

Value

oclust returns a list of class oclust with

data	A list containing the raw and scaled data
numO	The predicted number of outliers
outliers	The most likely outliers in the optimal solution in order of likelihood
class	The classification for the optimal solution
model	The model selected for the optimal solution
G	The number of clusters
pi.g	The group proportions for the optimal solution
mu	The cluster means for the optimal solution
sigma	The cluster variances for the optimal solution
KL	The KL divergence for each iteration, with the first value being for the initial dataset with the gross outliers removed
allCand	All outlier candidates in order of likelihood

Examples

## Not run: 
#simulate 4D dataset
library(mvtnorm)
set.seed(123)
data<-rbind(rmvnorm(250,rep(-3,4),diag(4)),
           rmvnorm(250,rep(3,4),diag(4)))
#add outliers
noisy<-simOuts(data=data,alpha=0.02,seed=123)

#Find gross outliers
findGrossOuts(X=noisy,minPts=10)

#Elbow between 5 and 10. Specify limits of graph
findGrossOuts(X=noisy,minPts=10,xlim=c(5,10))

#Elbow at 9
gross<-findGrossOuts(X=noisy,minPts=10,elbow=9)

#run algorithm
result<-oclust(X=noisy,maxO=15,G=2,grossOuts = gross,
modelNames = "EEE",mc.cores=1,nmax=50,kuiper=FALSE,
verb=TRUE,scale=TRUE)

## End(Not run)

---

Plots results of the ‘oclust’ algorithm.

Description

Plots results of the ‘oclust’ algorithm.

Usage

## S3 method for class 'oclust'
plot(
  x,
  what = c("classification", "KL", "pval"),
  dimens = NULL,
  xlab = NULL,
  ylab = NULL,
  ylim = NULL,
  addEllipses = TRUE,
  ...
)

Arguments

x	An ‘oclust’ class object obtained by using oclust
what	A string specifying the type of graph. The options are: "classification" a plot of the classifications for the optimal solution. For data with p>2, if more than two "dimens" are specified, a pairs plot is produced. If two "dimens" are specified, a coordinate projection plot is produced with the specified "dimens". Ellipses corresponding to covariances of mixture components are also drawn if "addEllipses = TRUE". "KL" a plot of Kullback-Leibler divergence for each number of outliers. "pval" a plot of approximate p-value for each number of outliers.
dimens	a vector specifying the dimensions of the coordinate projections
xlab, ylab	optional argument specifying axis labels for the classsification plot
ylim	optional limits of the y axis of the BIC and KL plots
addEllipses	logical indicating whether to include ellipses corresponding to the covariances of the mixture components
...	other graphical parameters

---

Print oclust

Description

Prints list of available components for ‘oclust’ class objects.

Usage

## S3 method for class 'oclust'
print(x, ...)

Arguments

x	An ‘oclust’ class object obtained by using oclust
...	additional print parameters

---

Prints the summary of key results for ‘oclust’ class objects.

Description

Prints the summary of key results for ‘oclust’ class objects.

Usage

## S3 method for class 'summary.oclust'
print(x, digits = getOption("digits"), ...)

Arguments

x	An ‘oclust’ class object obtained by using oclust
digits	number of digits to print
...	additional print arguments

---

Simulate Outliers

Description

simOuts generates uniform outliers in each dimension in (min- 2.range, max+ 2.range)

Usage

simOuts(data, alpha, seed = 123)

Arguments

data	The data in data frame form
alpha	The proportion of outliers to add in terms of the original data size
seed	Set the seed for reproducibility

Value

simOuts returns a data frame with the generated outliers appended to the original data.

---

Summarizes key results for ‘oclust’ class objects.

Description

Summarizes key results for ‘oclust’ class objects.

Usage

## S3 method for class 'oclust'
summary(object, ...)

Arguments

object	An ‘oclust’ class object obtained by using oclust
...	additional summary arguments

---