FIF : Functional Isolation Forest

This repository hosts Python code of the Functional Isolation Forest algorithms and its extension to Multivariate functional data. Here we provide the source code for the algorithms as well as example notebooks to help get started.

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Installation

To get the latest version of the code:

$ git clone https://github.com/Gstaerman/FIF.git

Algorithm

Functional Isolation Forest is an anomaly detection (and anomaly ranking) algorithm for functional data. It shows a great flexibility to distinguish most of anomaly types of functional data.

Some parameters have to be set by the user :

• innerproduct (one can fix 'auto' and vary alpha parameter to play with FIF)
• D (Dictionary)
• time (vector time of discretization points)

See the documentation of FIF.py to get more informations on innerproduct and dictionary possibilities.

Quick Start :

Create a toy dataset :

import numpy as np
np.random.seed(42)
m =100
n =100
tps = np.linspace(0,1,m)
v = np.linspace(1,1.4,n)
X = np.zeros((n,m))
for i in range(n):
    X[i] = 30 * ((1-tps) ** v[i]) * tps ** v[i]


Z1 = np.zeros((m))
for j in range(m):
    if (tps[j]<0.2 or tps[j]>0.8):
        Z1[j] = 30 * ((1-tps[j]) ** 1.2) * tps[j] ** 1.2
    else:
        Z1[j] = 30 * ((1-tps[j]) ** 1.2) * tps[j] ** 1.2 + np.random.normal(0,0.3,1)
Z1[0] = 0
Z1[m-1] = 0


Z2 = 30 * ((1-tps) ** 1.6) * tps ** 1.6


Z3 = np.zeros((m))
for j in range(m):
    Z3[j] = 30 * ((1-tps[j]) ** 1.2) * tps[j] ** 1.2 + np.sin(2*np.pi*tps[j])

Z4 = np.zeros((m))
for j in range(m):
    Z4[j] = 30 * ((1-tps[j]) ** 1.2) * tps[j] ** 1.2

for j in range(70,71):
    Z4[j] += 2

Z5 = np.zeros((m))
for j in range(m):
    Z5[j] = 30 * ((1-tps[j]) ** 1.2) * tps[j] ** 1.2 + 0.5*np.sin(10*np.pi*tps[j])

X = np.concatenate((X,Z1.reshape(1,-1),Z2.reshape(1,-1),
                     Z3.reshape(1,-1), Z4.reshape(1,-1), Z5.reshape(1,-1)), axis = 0)

And then use FIF to ranking functional dataset :

From FIF import *
np.random.seed(42)
F  = FIForest(X, D="gaussian_wavelets", time=tps, innerproduct="auto", alpha=0.5)
S  = F.compute_paths()

The simulated dataset with the five introduced anomalies (top). The sorted dataset (middle), the darker the color, the more the curves are considered anomalies. The sorted anomaly score of the dataset (bottom).

Dependencies

These are the dependencies to use FIF:

• numpy

Cite

If you use this code in your project, please cite:

Functional Isolation Forest
Guillaume Staerman, Pavlo Mozharovskyi, Stéphan Clémençon, Florence d'Alché-Buc.
(submitted), 2019.
https://arxiv.org/abs/1904.04573