## Density-based Outlier Detection Algorithms

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A MATLAB version of DDOutlier

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## Story

An R package called DDOutlier [4] contains many density-based outlier detection algorithms. I find the package by accident in the searching for the sophisticated outlier detection methods. It proves the codes together with the associated papers, which are what I need. Then, I start to find a similar package in the MATLAB.

The MATLAB will never provide any algorithms that have not been proved stable and useful. It is an excellent advantage of the MATLAB. One will not worry that a function from MathWorks, Inc. has already been shown containing errors by other scientists. The MATLAB supports density-based methods from the bottom. It proves a function called ‘knnsearch’ and other associated functions.

## DDOutlier written in MATLAB

The MATLAB version of DDOutlier proves an interface to operate the neighbors or reverse neighbors of a data point. The neighborhood is the keystone of density-based outlier detection algorithms. In the meantime, the buffer in the DDOutlier package prevents frequently search the database. It is self-maintained. The user will not worry about them when operating the neighborhood.

## Supported algorithms

The MATLAB version directly supports two outlier detection algorithms:

1. Local Outlier Factor (LOF) in function LOFs.m, which is from [1].

2. Natural Outlier Factor (NOF) in function NOFs.m from [2] and [3].

Note that the R version of DDOutlier [4] supports many other algorithms.

## Functions in the package:

1. LRD.m : Local Reachability density [1].
2. NIS.m : Natural Influence Space [2].
3. NN.m : kth neighborhood [1].
4. NaNSearching.m : find the searching range when all the nature neighbors are found [3].
5. dataSet.m : store your data and buffer.
6. distance.m : calculate the distance of two data points if at least one of them considers another as friends.
7. kDistObj.m : generate a buffer for a specific searching range. Please use ‘clean all’ to clean it.
8. k_distance.m : calculate the k-distance [1].
9. matlabKNN.m : a function will generate the same output as KNN functions in R.
10. rNN.m : kth-reverse-neighborhood [2].
11. reach_distance.m : reachability distance [1].
12. rnbs.m : the times that one point is contained by the neighborhood of other points.

## Usage

A sample example can be found in tests.m. Remember to use ‘clean all’ to clean all the persist variables in the package. The package supports other distance metrics; however, only the euclidean metric is tested. So, it temporarily prevents outlier metric. The user is welcome to alter the code in dataSet.m for using other distance metrics.

## References

[1] Breunig, Markus M., et al. “LOF: identifying density-based local outliers.” ACM sigmod record. Vol. 29. No. 2. ACM, 2000.APA

[2] Huang, Jinlong, et al. “A non-parameter outlier detection algorithm based on Natural Neighbor.” Knowledge-Based Systems 92 (2016): 71-77.

[3] Zhu, Qingsheng, Ji Feng, and Jinlong Huang. “Natural neighbor: A self-adaptive neighborhood method without parameter K.” Pattern Recognition Letters 80 (2016): 30-36.APA

### 引用

Blue Bird (2022). Density-based Outlier Detection Algorithms (https://github.com/BlueBirdHouse/DDoutlier), GitHub. 取得済み .

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