Activity monitoring – the detection of fraud involving mobile phones and proximity-based methods

Two major approaches of proximity-based methods are distance-based and density-based outlier detection algorithms.

The NL algorithm

The summarized pseudocodes of the NL algorithm are as follows:

The NL algorithm

The FindAllOutsM algorithm

The following are the summarized pseudocode of the FindAllOutsM algorithm:

The FindAllOutsM algorithm

The FindAllOutsD algorithm

The summarized pseudocodes of the FindAllOutsD algorithm are as follows:

The FindAllOutsD algorithm

The distance-based algorithm

The summarized pseudocodes of the distance-based outlier detection algorithm are as follows, given a dataset D, size of the input dataset n, threshold r (r > 0), and The distance-based algorithm:

The distance-based algorithm

A The distance-based algorithm outlier is defined as a data point, o, and subjected to this formula:

The distance-based algorithm

Let's now learn the pseudocodes for a variety of distance-based outlier detection algorithms, which are summarized in the following list. The input parameters are k, n, and D, which represent the neighbors' number, outlier number to be identified, and input dataset, respectively. A few supporter functions also are defined. Nearest (o, S, k) returns k nearest objects in S to o, Maxdist (o, S) returns the maximum distance between o and points from S, and TopOutlier (S, n) returns the top n outliers in S according to the distance to their kth nearest neighbor.

The distance-based algorithm

The Dolphin algorithm

The Dolphin algorithm is a distance-based outlier detection algorithm. The summarized pseudocodes of this algorithm are listed as follows:

The Dolphin algorithm
The Dolphin algorithm
The Dolphin algorithm

The R implementation

Look up the file of R codes, ch_07_proximity_based.R, from the bundle of R codes for the preceding algorithms. The codes can be tested with the following command:

> source("ch_07_proximity_based.R")

Activity monitoring and the detection of mobile fraud

The purpose of outlier detection is to find the patterns in source datasets that do not conform to the standard behavior. The dataset here consists of the calling records, and the patterns exist in the calling records.

There are many special algorithms developed for each specific domain. Misuse of a mobile is termed as mobile fraud. The subject under research is the calling activity or call records. The related attributes include, but are not limited to, call duration, calling city, call day, and various services' ratios.

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