PySensors is a Scikit-learn style Python package for the sparse placement of sensors, either for reconstruction or classification tasks.

Sparse sensor placement concerns the problem of selecting a small subset of sensor or measurement locations in a way that allows one to perform some task nearly as well as if one had access to measurements at every location.

PySensors provides objects designed for the tasks of reconstruction and classification. See Manohar et al. (2018) for more information about the PySensors approach to reconstruction problems and Brunton et al. (2016) for classification. de Silva et al. (2021) contains a full literature review along with examples and additional tips for using PySensors effectively.

Reconstruction deals with predicting the values of a quantity of interest at different locations other than those where sensors are located. For example, one might predict the temperature at a point in the middle of a lake based on temperature readings taken at various other positions in the lake.

PySensors provides the SSPOR (Sparse Sensor Placement Optimization for Reconstruction) class to aid in the solution of reconstruction problems.

Take representative examples of the types of data to be reconstructed (in this case polynomials)

x = numpy.linspace(0, 1, 1001)
data = numpy.vander(x, 11).T  # Create an array whose rows are powers of x

feed them to a SSPOR instance with 10 sensors, and

model = pysensors.reconstruction.SSPOR(n_sensors=10)
model.fit(data)

Use the predict method to reconstruct a new function sampled at the chosen sensor locations:

f = numpy.abs(x[model.selected_sensors]**2 - 0.5)
f_pred = model.predict(f)

Classification is the problem of predicting which category an example belongs to, given a set of training data (e.g. determining whether digital photos are of dogs or cats). The SSPOC (Sparse Sensor Placement Optimization for Classification) class is used to solve classification problems. Users familiar with Scikit-learn will find it intuitive:

model = pysensors.classification.SSPOC()
model.fit(x, y)  # Learn sensor locations and fit a linear classifier
y_pred = model.predict(x_test[:, model.selected_sensors])  #  Get predictions

See our set of classification examples for more information.

The basis in which measurement data are represented can have a dramatic effect on performance. PySensors implements the three bases most commonly used for sparse sensor placement: raw measurements, SVD/POD/PCA modes, and random projections. Bases can be easily incorporated into SSPOR and SSPOC classes:

basis = pysensors.basis.SVD(n_basis_modes=20)
recon_model = pysensors.reconstruction.SSPOR(basis=basis)
class_model = pysensors.classification.SSPOC(basis=basis)

See this example for further discussion of these options.

The high-level dependencies for PySensors are Linux or macOS and Python 3.6-3.8. pip is also recommended as is makes managing PySensors' other dependencies much easier. You can install it by following the instructions here.

PySensors has not been tested on Windows.

If you are using Linux or macOS you can install PySensors with pip from the command line/terminal:

pip install python-sensors

Note: the name you type in here is python-sensors and is not pysensors.

Once you have run the line above, you are ready to get started with PySensors. Have a look at the examples in our documentation to see what PySensors can do.

First clone this repository:

git clone https://github.com/dynamicslab/pysensors.git

Then, to install the package, run

cd pysensors
pip install .

If you do not have pip you can instead use

python setup.py install

If you do not have root access, you should add the --user option to the install commands above.

The primary PySensors objects are the SSPOR and SSPOC classes, which are used to choose sensor locations optimized for reconstruction and classification tasks, respectively. Other implemented objects include

• basis - submodule implementing different bases in which to represent data
  • Identity - use raw measurement data
  • SVD - efficiently compute first k left singular vectors
  • RandomProjection - Gaussian random projections of measurements
• Convenience functions to aid in the analysis of error as number of sensors or basis modes are varied

PySensors has a documentation site hosted by readthedocs. Examples are available online, as static Jupyter notebooks and as interactive notebooks. To run the example notebooks locally you should install the dependencies in requirements-examples.txt:

pip install -r requirements-examples.txt

You may create an issue for any questions that aren't answered by the documentation or examples.

If you have used PySensors to solve an interesting problem, please consider submitting an example Jupyter notebook showcasing your work!

We welcome contributions to PySensors. To contribute a new feature please submit a pull request. To get started we recommend installing the packages in requirements-dev.txt via

pip install -r requirements-dev.txt

This will allow you to run unit tests and automatically format your code. To be accepted your code should conform to PEP8 and pass all unit tests. Code can be tested by invoking

pytest

We recommend using pre-commit to format your code. Once you have staged changes to commit

git add path/to/changed/file.py

you can run the following to automatically reformat your staged code

pre-commit

Note that you will then need to re-stage any changes pre-commit made to your code.

If you find a bug in the code or want to request a new feature, please open an issue.

We have published a short paper in the Journal of Open Source Software (JOSS). You can find the paper here.

If you use PySensors in your work, please consider citing it using:

de Silva et al., (2021). PySensors: A Python package for sparse sensor placement. Journal of Open Source Software, 6(58), 2828, https://doi.org/10.21105/joss.02828``

Bibtex:

@article{de Silva2021,
  doi = {10.21105/joss.02828},
  url = {https://doi.org/10.21105/joss.02828},
  year = {2021},
  publisher = {The Open Journal},
  volume = {6},
  number = {58},
  pages = {2828},
  author = {Brian M. de Silva and Krithika Manohar and Emily Clark and Bingni W. Brunton and J. Nathan Kutz and Steven L. Brunton},
  title = {PySensors: A Python package for sparse sensor placement},
  journal = {Journal of Open Source Software}
}

• de Silva, Brian M., Krithika Manohar, Emily Clark, Bingni W. Brunton, Steven L. Brunton, J. Nathan Kutz. "PySensors: A Python package for sparse sensor placement." arXiv preprint arXiv:2102.13476 (2021). [arXiv]
• Manohar, Krithika, Bingni W. Brunton, J. Nathan Kutz, and Steven L. Brunton. "Data-driven sparse sensor placement for reconstruction: Demonstrating the benefits of exploiting known patterns." IEEE Control Systems Magazine 38, no. 3 (2018): 63-86. [DOI]
• Brunton, Bingni W., Steven L. Brunton, Joshua L. Proctor, and J Nathan Kutz. "Sparse sensor placement optimization for classification." SIAM Journal on Applied Mathematics 76.5 (2016): 2099-2122. [DOI]
• Clark, Emily, Travis Askham, Steven L. Brunton, and J. Nathan Kutz. "Greedy sensor placement with cost constraints." IEEE Sensors Journal 19, no. 7 (2018): 2642-2656. [DOI]