# NOF: Natural Outlier Factor (NOF) algorithm In DDoutlier: Distance & Density-Based Outlier Detection

## Description

Function to calculate the Natural Outlier Factor (NOF) as an outlier score for observations. Suggested by Huang, J., Zhu, Q., Yang, L. & Feng, J. (2015)

## Usage

 `1` ```NOF(dataset) ```

## Arguments

 `dataset` The dataset for which observations have a NOF score returned

## Details

NOF computes the nearest and reverse nearest neighborhood for observations, based on the natural neighborhood algorithm. Density is compared between observations and their neighbors. A kd-tree is used for kNN computation, using the kNN() function from the 'dbscan' package

## Value

 `nb` A vector of in-degrees for observations `max_nb` Maximum in-degree observations in nb vector. Used as k-parameter in outlier detection of NOF `r` The natural neighbor eigenvalue `NOF` A vector of Natural Outlier Factor scores. The greater the NOF, the greater the outlierness

## References

Huang, J., Zhu, Q., Yang, L. & Feng, J. (2015). A non-parameter outlier detection algorithm based on Natural Neighbor. Knowledge-Based Systems. pp. 71-77. DOI: 10.1016/j.knosys.2015.10.014

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# Select dataset X <- iris[,1:4] # Run NOF algorithm outlier_score <- NOF(dataset=X)\$NOF # Sort and find index for most outlying observations names(outlier_score) <- 1:nrow(X) sort(outlier_score, decreasing = TRUE) # Inspect the distribution of outlier scores hist(outlier_score) ```

### Example output

```[1] "r is now: 2"
[1] "r is now: 3"
[1] "r is now: 4"
[1] "r is now: 5"
42       127       144        64        55       113        28        90
1.4568285 1.4551820 1.4432004 1.4098590 1.3595976 1.3496025 1.2933804 1.2905440
103        49       121       125        50        54        16        92
1.2851906 1.2559298 1.2285780 1.2245882 1.2014043 1.1989356 1.1833303 1.1804482
83       100       107        79        60        40        20        23
1.1689806 1.1686685 1.1670581 1.1511226 1.1496940 1.1482661 1.1434154 1.1405675
128        11        31       130       134        14        22       126
1.1299069 1.1257786 1.1228356 1.1197920 1.1167399 1.1123065 1.1069851 1.1054310
117         8        18        80        46       138        99         1
1.1050226 1.1031811 1.1005091 1.0985946 1.0957836 1.0826964 1.0820748 1.0776876
70       110         4        15        47        65        97        98
1.0759488 1.0673490 1.0671666 1.0662943 1.0660229 1.0638617 1.0618035 1.0542436
119        52        61        48       116        95       124         7
1.0528559 1.0523064 1.0462963 1.0462287 1.0458299 1.0454587 1.0443777 1.0353810
13       118        84        45       108       131        58        81
1.0341143 1.0323089 1.0321768 1.0302485 1.0298309 1.0278494 1.0262681 1.0221270
75        33         2       132        51        30         3        37
1.0203894 1.0168846 1.0108023 1.0035592 1.0034935 1.0026185 0.9987692 0.9971942
141        94        82       140        67       112       150         6
0.9938880 0.9905895 0.9896148 0.9872519 0.9847001 0.9792127 0.9790012 0.9759951
12       114       148       135       123       133       102       143
0.9759724 0.9742069 0.9703938 0.9678542 0.9666205 0.9649938 0.9536860 0.9536860
115        34        53       122       139       111        35        69
0.9536113 0.9516014 0.9515444 0.9431567 0.9403054 0.9388869 0.9369747 0.9364066
147         9       149        24        59        43        57        19
0.9347949 0.9329888 0.9328275 0.9324095 0.9273387 0.9247231 0.9244330 0.9232432
88       105        39       120        32        71        77       106
0.9191701 0.9178905 0.9175899 0.9166021 0.9140269 0.9092829 0.9075090 0.9064312
5        27       109        72        78        25       129       101
0.9037674 0.9013173 0.9005028 0.8992171 0.8965279 0.8922238 0.8902182 0.8900310
145        85        66        26        68        17        93        87
0.8872306 0.8864447 0.8829103 0.8822318 0.8819857 0.8797700 0.8767640 0.8751420
41       136        56        73        89        96        63       146
0.8739759 0.8675204 0.8623359 0.8596633 0.8523845 0.8520418 0.8509993 0.8462226
29        74        62        76        91        44        21        38
0.8440434 0.8424309 0.8375984 0.8330724 0.8193339 0.8027794 0.7874575 0.7865786
86       104        10       137       142        36
0.7811683 0.7773199 0.7687574 0.7658661 0.7514867 0.7202985
```

DDoutlier documentation built on May 1, 2019, 10:20 p.m.