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🌲 Implementation of the Robust Random Cut Forest algorithm for anomaly detection on streams

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# rrcf 🌲🌲🌲
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Implementation of the *Robust Random Cut Forest Algorithm* for anomaly detection by [Guha et al. (2016)](http://proceedings.mlr.press/v48/guha16.pdf).

> S. Guha, N. Mishra, G. Roy, & O. Schrijvers, *Robust random cut forest based anomaly
> detection on streams*, in Proceedings of the 33rd International conference on machine
> learning, New York, NY, 2016 (pp. 2712-2721).

## About

The *Robust Random Cut Forest* (RRCF) algorithm is an ensemble method for detecting outliers in streaming data. RRCF offers a number of features that many competing anomaly detection algorithms lack. Specifically, RRCF:

- Is designed to handle streaming data.
- Performs well on high-dimensional data.
- Reduces the influence of irrelevant dimensions.
- Gracefully handles duplicates and near-duplicates that could otherwise mask the presence of outliers.
- Features an anomaly-scoring algorithm with a clear underlying statistical meaning.

This repository provides an open-source implementation of the RRCF algorithm and its core data structures for the purposes of facilitating experimentation and enabling future extensions of the RRCF algorithm.

## Documentation

Read the docs [here 📖](https://klabum.github.io/rrcf/).

## Installation

Use `pip` to install `rrcf` via pypi:

```shell
$ pip install rrcf
```

Currently, only Python 3 is supported.

### Dependencies

The following dependencies are *required* to install and use `rrcf`:

- [numpy](http://www.numpy.org/) (>= 1.15)

The following *optional* dependencies are required to run the examples shown in the documentation:

- [pandas](https://pandas.pydata.org/) (>= 0.23)
- [scipy](https://www.scipy.org/) (>= 1.2)
- [scikit-learn](https://scikit-learn.org/stable/) (>= 0.20)
- [matplotlib](https://matplotlib.org/) (>= 3.0)

Listed version numbers have been tested and are known to work (this does not necessarily preclude older versions).

## Robust random cut trees

A robust random cut tree (RRCT) is a binary search tree that can be used to detect outliers in a point set. A RRCT can be instantiated from a point set. Points can also be added and removed from an RRCT.

### Creating the tree

```python
import numpy as np
import rrcf

# A (robust) random cut tree can be instantiated from a point set (n x d)
X = np.random.randn(100, 2)
tree = rrcf.RCTree(X)

# A random cut tree can also be instantiated with no points
tree = rrcf.RCTree()
```

### Inserting points

```python
tree = rrcf.RCTree()

for i in range(6):
    x = np.random.randn(2)
    tree.insert_point(x, index=i)
```

```
─+
 ├───+
 │   ├───+
 │   │   ├──(0)
 │   │   └───+
 │   │       ├──(5)
 │   │       └──(4)
 │   └───+
 │       ├──(2)
 │       └──(3)
 └──(1)
```

### Deleting points

```
tree.forget_point(2)
```

```
─+
 ├───+
 │   ├───+
 │   │   ├──(0)
 │   │   └───+
 │   │       ├──(5)
 │   │       └──(4)
 │   └──(3)
 └──(1)
```

## Anomaly score

The likelihood that a point is an outlier is measured by its collusive displacement (CoDisp): if including a new point significantly changes the model complexity (i.e. bit depth), then that point is more likely to be an outlier.

```python
# Seed tree with zero-mean, normally distributed data
X = np.random.randn(100,2)
tree = rrcf.RCTree(X)

# Generate an inlier and outlier point
inlier = np.array([0, 0])
outlier = np.array([4, 4])

# Insert into tree
tree.insert_point(inlier, index='inlier')
tree.insert_point(outlier, index='outlier')
```

```python
tree.codisp('inlier')
>>> 1.75
```

```python
tree.codisp('outlier')
>>> 39.0
```

## Batch anomaly detection

This example shows how a robust random cut forest can be used to detect outliers in a batch setting. Outliers correspond to large CoDisp.

```python
import numpy as np
import pandas as pd
import rrcf

# Set parameters
np.random.seed(0)
n = 2010
d = 3
num_trees = 100
tree_size = 256

# Generate data
X = np.zeros((n, d))
X[:1000,0] = 5
X[1000:2000,0] = -5
X += 0.01*np.random.randn(*X.shape)

# Construct forest
forest = []
while len(forest) < num_trees:
    # Select random subsets of points uniformly from point set
    ixs = np.random.choice(n, size=(n // tree_size, tree_size),
                           replace=False)
    # Add sampled trees to forest
    trees = [rrcf.RCTree(X[ix], index_labels=ix) for ix in ixs]
    forest.extend(trees)

# Compute average CoDisp
avg_codisp = pd.Series(0.0, index=np.arange(n))
index = np.zeros(n)
for tree in forest:
    codisp = pd.Series({leaf : tree.codisp(leaf) for leaf in tree.leaves})
    avg_codisp[codisp.index] += codisp
    np.add.at(index, codisp.index.values, 1)
avg_codisp /= index
```

![Image](https://github.com/kLabUM/rrcf/blob/master/resources/batch.png)

## Streaming anomaly detection

This example shows how the algorithm can be used to detect anomalies in streaming time series data.

```python
import numpy as np
import rrcf

# Generate data
n = 730
A = 50
center = 100
phi = 30
T = 2*np.pi/100
t = np.arange(n)
sin = A*np.sin(T*t-phi*T) + center
sin[235:255] = 80

# Set tree parameters
num_trees = 40
shingle_size = 4
tree_size = 256

# Create a forest of empty trees
forest = []
for _ in range(num_trees):
    tree = rrcf.RCTree()
    forest.append(tree)
    
# Use the "shingle" generator to create rolling window
points = rrcf.shingle(sin, size=shingle_size)

# Create a dict to store anomaly score of each point
avg_codisp = {}

# For each shingle...
for index, point in enumerate(points):
    # For each tree in the forest...
    for tree in forest:
        # If tree is above permitted size, drop the oldest point (FIFO)
        if len(tree.leaves) > tree_size:
            tree.forget_point(index - tree_size)
        # Insert the new point into the tree
        tree.insert_point(point, index=index)
        # Compute codisp on the new point and take the average among all trees
        if not index in avg_codisp:
            avg_codisp[index] = 0
        avg_codisp[index] += tree.codisp(index) / num_trees
```

![Image](https://github.com/kLabUM/rrcf/blob/master/resources/sine.png)

## Obtain feature importance

This example shows how to estimate the feature importance using the dimension of cut obtained during the calculation of the CoDisp.

```python
import numpy as np
import pandas as pd
import rrcf

# Set parameters
np.random.seed(0)
n = 2010
d = 3
num_trees = 100
tree_size = 256

# Generate data
X = np.zeros((n, d))
X[:1000,0] = 5
X[1000:2000,0] = -5
X += 0.01*np.random.randn(*X.shape)

# Compute average CoDisp with the cut dimension for each point
dim_codisp = np.zeros([n,d],dtype=float)
index = np.zeros(n)
for tree in forest:
    for leaf in tree.leaves:
        codisp,cutdim = tree.codisp_with_cut_dimension(leaf)
        
        dim_codisp[leaf,cutdim] += codisp

index[leaf] += 1

avg_codisp = dim_codisp.sum(axis=1)/index

#codisp anomaly threshold and calculate the mean over each feature
feature_importance_anomaly = np.mean(dim_codisp[avg_codisp>50,:],axis=0)
#create a dataframe with the feature importance
df_feature_importance = pd.DataFrame(feature_importance_anomaly,columns=['feature_importance'])
df_feature_importance
```
![Image](https://raw.githubusercontent.com/kLabUM/rrcf/master/feature_importance.png)

## Contributing

We welcome contributions to the `rrcf` repo. To contribute, submit a [pull request](https://help.github.com/en/articles/about-pull-requests) to the `dev` branch.

#### Types of contributions

Some suggested types of contributions include:

- Bug fixes
- Documentation improvements
- Performance enhancements
- Extensions to the algorithm

Check the issue tracker for any specific issues that need help. If you encounter a problem using `rrcf`, or have an idea for an extension, feel free to raise an issue.

#### Guidelines for contributors

Please consider the following guidelines when contributing to the codebase:

- Ensure that any new methods, functions or classes include docstrings. Docstrings should include a description of the code, as well as descriptions of the inputs (arguments) and outputs (returns). Providing an example use case is recommended (see existing methods for examples).
- Write unit tests for any new code and ensure that all tests are passing with no warnings. Please ensure that overall code coverage does not drop below 80%.

#### Running unit tests

To run unit tests, first ensure that `pytest` and `pytest-cov` are installed:

```
$ pip install pytest pytest-cov
```

To run the tests, navigate to the root directory of the repo and run:

```
$ pytest --cov=rrcf/
```

## Citing

If you have used this codebase in a publication and wish to cite it, please use the [`Journal of Open Source Software article`](https://joss.theoj.org/papers/10.21105/joss.01336).

> M. Bartos, A. Mullapudi, & S. Troutman, *rrcf: Implementation of the Robust
> Random Cut Forest algorithm for anomaly detection on streams*,
> in: Journal of Open Source Software, The Open Journal, Volume 4, Number 35.
> 2019

```bibtex
@article{bartos_2019_rrcf,
  title={{rrcf: Implementation of the Robust Random Cut Forest algorithm for anomaly detection on streams}},
  authors={Matthew Bartos and Abhiram Mullapudi and Sara Troutman},
  journal={{The Journal of Open Source Software}},
  volume={4},
  number={35},
  pages={1336},
  year={2019}
}
```

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