A guide to studying population dynamics with topological data analysis. We aim at correctly identifying two clusters in an ensemble of time series describing the adult population of the Tribolium flour beetle. We compare our approach to a baseline approach where we cluster the unmodified time series.
See the accompanying blog post for further details.
Here, we simulate the evolution of the adult population of Tribolium flour beetles. This approach is reasonable and justified as there exist mathematical models describing the population dynamics of Tribolium flour beetles adequately. The beetles' life cycle consists of larva, pupa, and adult stages, with the transition between each stage lasting approximately two weeks. Remarkably, Tribolium flour beetles become cold-hearted in face of overpopulation as they turn cannibalistic by eating unhatched eggs and pupae.
We use tools provided by topological data analysis to create several features. For each time series, these features are combined into one vector. The collection of those can then be clustered. The general pipeline is as follows: First, we embed each time series describing an adult population into a higher dimensional space. Next, we calculate the persistence diagrams and extract features from them. More details are given in the blog post and jupyter notebook.
For both the baseline and our approach, we use k-means to find clusters within the simulated data.
We show that an approach using TDA features outperforms the baseline. This even holds true in the presence of high environmental uncertainty.
Spin up a virtual environment and install the required libraries:
virtualenv -p python3.7 env
pip install -r requirements.txt
To make plotly play nice with JupyterLab one also needs to run:
# Avoid "JavaScript heap out of memory" errors during extension installation
# (OS X/Linux)
export NODE_OPTIONS=--max-old-space-size=4096
# (Windows)
set NODE_OPTIONS=--max-old-space-size=4096
# Jupyter widgets extension
jupyter labextension install @jupyter-widgets/[email protected] --no-build
# FigureWidget support
jupyter labextension install [email protected] --no-build
# and jupyterlab renderer support
jupyter labextension install [email protected] --no-build
# JupyterLab chart editor support (optional)
jupyter labextension install [email protected] --no-build
# Build extensions (must be done to activate extensions since --no-build is used above)
jupyter lab build
# Unset NODE_OPTIONS environment variable
# (OS X/Linux)
unset NODE_OPTIONS
# (Windows)
set NODE_OPTIONS=