Kernel-change-point-detection

Kernel change point detection is a python library used for anomaly detection on time-series.

Getting started

This library has been tested on Python 3.11 and 3.12.

Setting environement

pip install virtualenv
virtualenv -p <path/to/python3.11> myenv
source myenv/bin/activate

Installation

Once your virtual environment is activated, you can install the Kernel-point-change-detection library directly from Pypi by typing :

pip install kcpdi

This command will install the kcpdi package and all required dependencies. Within your python code, you can then access the library functions by using the following import statement:

import kcpdi

Usage

Our algorithm takes pre-processed (interpolated to a fixed time grid, normalized, etc.) and offline (not streaming) multidimensional time series data and runs linear kernel anomaly/change-point detection on it in order to output a list of likely anomaly/change-points in time. The method is based on results in Arlot et al. (2019).

We have started to develop automated post-hoc visualization tools in order to provide intuitive explicability in the output results in order to attribute a ranked (in terms of importance) list of individual time series for each detected anomaly/change-point. This is because it is otherwise difficult to know 'why' a change-point was detected at a certain point if there are hundreds or thousands of individual concurrent time series. The latter tool is semi-dependent of the anomaly/change-point detection step.

Examples and demonstrators

The following notebook incorporates the most important features:

TADkit link

In order to allow the kernel change-point method to be compatible with the Time-series Anomaly Detection kit TADkit, we have implemented a function kcp_ss which takes the kcp_ds output list of change-points and turns them into scores at all time indices.

We give a score of 1 at each detected change-point. We define a decay_parameter $γ$ (default $γ = 1$). Then :

• For any time index that exactly corresponds to a detected change-point index, its score is 1.

• For any time index $t_x$ before the first detected change-point time index $t_1$, its score is :

$$\left(\frac{1}{2}\right)^{\gamma |t_1 - t_x|}$$

• For any time index $t_x$ after the last detected change-point time index $t_{last}$ its score is :

$$\left(\frac{1}{2}\right)^{\gamma |t_{last} - t_x|}$$

• For any time index $t_x$ between change-point time indices $t_{j}$ and $t_{j+1}$ , its score is the average of the left and right scores :

$$ \frac{1}{2}\left(\left(\frac{1}{2}\right)^{\gamma |t_{j} - t_{x}|} + \left(\frac{1}{2}\right)^{\gamma |t_{j+1}-t_{x}|} \right) $$

Contributors and Support

Responsible : Kevin Bleakley, Sylvain Arlot (INRIA)

Kernel change point detection is a library developed by and supported by the