gps_cluster

Clustering of GPS-derived velocities using Hierarchical Agglomerative Clustering (HAC, e.g. Simpson et al., 2012). HAC begins with each observation being its own cluster, then sequentially combines similar observations or clusters until all the observations are grouped into a single cluster. Each merging can be represented with a dendrogram. This is essentially a linkage graph with inter-cluster distances in the y-axis. Then using the dendrogram, gap statistics and a priori deformation indicators optimal number of clusters is determined.

Description

The clustering of GPS-derived velocity vectors provides an objective and intuitive starting point for the analysis of block-like deformation and yields a statistically significant number of blocks. Cluster analysis is not a new method, it has applications in various discipline, such as psychology, bioinformatics, and data analysis, but the application is rather recent for continental deformation (Simpson et al., 2012; Savage and Simpson, 2013a,b; Liu et al., 2015; Savage and Wells, 2015; Thatcher et al., 2016; Savage, 2018; Takahashi et al., 2019; Özdemir and Karslıoğlu, 2019).

There are two popular clustering algorithms: k-means and Hierarchical Agglomerative Clustering (HAC). k-means finds cluster centers for a given number of clusters, minimizing the within-cluster dispersion. Its easy implementation, linear execution time scaling with the number of observations, and guaranteed convergence renders it one of the most popular clustering algorithms. k-means perform poorly when clusters are of varying sizes. Furthermore, clustering is sensitive to data outliers and the initial sorting of the data. Therefore, pre-processing and repeat experiments need to be done.

HAC builds a hierarchy of clusters without having a fixed number of clusters. HAC begins with each observation being its own cluster, then sequentially joins near observations (or clusters) until all the observations are grouped into a single cluster. As pairwise distances are calculated at each step, the algorithm is slower compared to k-means and scales with O(n2). However, ”agglomerative clustering can provide a whole hierarchy of possible partitions of the data, which can be easily inspected via dendrograms.” (M ̈uller and Guido, 2016). This is essentially a linkage graph with inter-cluster distances in the y-axis. Then inspection of the dendrogram or variance- reduction measures give an indication for the optimal number of clusters. HAC methods work best with low dimensional data.

Simpson et al. (2012) applied a hierarchical agglomerative clustering approach to GPS velocity vectors in the San Francisco Bay region. The resulting clusters and geologically determined fault-bounded blocks are in good agreement. As the displacements in the Bay Area are predominantly translational, station locations are not taken into account.

Savage and Simpson (2013a,b) applied k-medoids clustering and improved the method by considering station locations on the clustering. After initial clustering of velocities, Euler vectors for each cluster are calculated. Then iteratively, each observation is assigned to that cluster, for which its Euler vector best describes

In this study we used the HAC algorithm.

Installation

In order to set up the necessary environment:

1. review and uncomment what you need in environment.yml and create an environment gps_cluster with the help of conda: conda env create -f environment.yml
2. activate the new environment with: conda activate gps_cluster

NOTE: The conda environment will have gps_cluster installed in editable mode. Some changes, e.g. in setup.cfg, might require you to run pip install -e . again.

Optional and needed only once after git clone:

3. install several pre-commit git hooks with: bash pre-commit install # You might also want to run `pre-commit autoupdate` and checkout the configuration under .pre-commit-config.yaml. The -n, --no-verify flag of git commit can be used to deactivate pre-commit hooks temporarily.

4. install nbstripout git hooks to remove the output cells of committed notebooks with: bash nbstripout --install --attributes notebooks/.gitattributes This is useful to avoid large diffs due to plots in your notebooks. A simple nbstripout --uninstall will revert these changes.

Then take a look into the scripts and notebooks folders.

Dependency Management & Reproducibility

1. Always keep your abstract (unpinned) dependencies updated in environment.yml and eventually in setup.cfg if you want to ship and install your package via pip later on.
2. Create concrete dependencies as environment.lock.yml for the exact reproduction of your environment with: bash conda env export -n gps_cluster -f environment.lock.yml For multi-OS development, consider using --no-builds during the export.
3. Update your current environment with respect to a new environment.lock.yml using: bash conda env update -f environment.lock.yml --prune ## Project Organization

├── AUTHORS.md              <- List of developers and maintainers.
├── CHANGELOG.md            <- Changelog to keep track of new features and fixes.
├── LICENSE.txt             <- License as chosen on the command-line.
├── README.md               <- The top-level README for developers.
├── configs                 <- Directory for configurations of model & application.
├── data
│   ├── external            <- Data from third party sources.
│   ├── interim             <- Intermediate data that has been transformed.
│   ├── processed           <- The final, canonical data sets for modeling.
│   └── raw                 <- The original, immutable data dump.
├── docs                    <- Directory for Sphinx documentation in rst or md.
├── environment.yml         <- The conda environment file for reproducibility.
├── models                  <- Trained and serialized models, model predictions,
│                              or model summaries.
├── notebooks               <- Jupyter notebooks. Naming convention is a number (for
│                              ordering), the creator's initials and a description,
│                              e.g. `1.0-fw-initial-data-exploration`.
├── pyproject.toml          <- Build system configuration. Do not change!
├── references              <- Data dictionaries, manuals, and all other materials.
├── reports                 <- Generated analysis as HTML, PDF, LaTeX, etc.
│   └── figures             <- Generated plots and figures for reports.
├── scripts                 <- Analysis and production scripts which import the
│                              actual Python package, e.g. train_model.py.
├── setup.cfg               <- Declarative configuration of your project.
├── setup.py                <- Use `pip install -e .` to install for development or
|                              or create a distribution with `tox -e build`.
├── src
│   └── gps_cluster         <- Actual Python package where the main functionality goes.
├── tests                   <- Unit tests which can be run with `py.test`.
├── .coveragerc             <- Configuration for coverage reports of unit tests.
├── .isort.cfg              <- Configuration for git hook that sorts imports.
└── .pre-commit-config.yaml <- Configuration of pre-commit git hooks.

Note

This project has been set up using PyScaffold 4.1 and the dsproject extension 0.6.1.