AMPD algorithm in Python

Implements a function find_peaks based on the Automatic Multi-scale Peak Detection algorithm proposed by Felix Scholkmann et al. in "An Efficient Algorithm for Automatic Peak Detection in Noisy Periodic and Quasi-Periodic Signals", Algorithms 2012, 5, 588-603

Usage

Install package from source:

pip install git+https://github.com/ig248/pyampd

Import function:

from pyampd.ampd import find_peaks

See notebooks/ampd.ipynb for usage examples.

Specifying maximum scale

To improve run-time on large time-series, it is possible to specify the maximum scale to consider:

peaks = find_peaks(x, scale=100)

will only consider windows up to +-100 point either side of peak candidates.

Adaptive Scale Selection

If the characteristic scale of the signal changes over time, a new algorithm called Adaptive Scale Selection can track the changes in optimal scales and detect peaks accordingly:

peaks = find_peaks_adaptive(x, window=200)

will select the optimal scale at each point using a 200-point running window.

Original implementation

find_peaks is not identical to the algorithm proposed in the original paper (especially near start and end of time series). A performance-optimized version of the original implementation is provided in find_peaks_original.

Tests

Run

pytest

Other implementations

• R: https://cran.r-project.org/web/packages/ampd/index.html
• MATLAB: https://github.com/mathouse/AMPD-algorithm
• Python: https://github.com/LucaCerina/ampdLib

Improvements

This Python implementation provides significant speed-ups in two areas:

1. Efficient tracking of local minima without using random numbers
2. Introduction of maximum window size, reducing algorithm run-time from quadratic to linear in the number of samples.
3. Better handling of peaks near start/end of the series
4. Addition of new Adaptive Scale Selection

ToDo

• It may be possible to avoid repeated comparisons, and reduce worst-case runtime from O(n^2) to O(n log(n)).
• find_peaks_adaptive could benefit from specifying both window and max_scale

References

Original paper: https://doi.org/10.1109/ICRERA.2016.7884365