Source Code for the Paper "Multivariate Functional Linear Discriminant Analysis (MUDRA) for the Classification of Short Time Series with Missing Data"

Installation

We advise to use a virtual environment, either with Conda or VirtualEnv. Then run the following command:

```bash git clone https://github.com/rbordoloi/MUDRA.git cd MUDRA/

If using pip

python -m pip install --upgrade setuptools python -m pip install -r pip/requirements.txt

If using conda

cond env create --name mudra --file=environment.yml python setup.py install --user ```

The sample dataset is included in the datasets directory. To regenerate the dataset from the original source, run datasetGeneration.py.

Example

The class MUDRA is defined like a scikit-learn module, that is

• To import the MUDRA class:

python from MUDRA import MUDRA

The model accepts input X as a pandas DataFrame of shape (n_samples, n_features) and y as list of class labels. Each cell of the DataFrame has a pandas Series object corresponding to the time series for one feature of one sample. Each Series object is indexed by the time points for which observations were recorded. Missing features are denoted by np.nan objects. - To fit the model on training data (X,y) (for r=8, b=9 and 300 iterations for the last optimization step):

python model = MUDRA(r=8, n_iter=300, nBasis=9).fit(X, y)

• To perform dimension reduction on new data (X):

python x = model.transform(X)

• To predict labels on new data (X):

python y = model.predict(X)

• To predict scores on new data (X):

python y = model.predict_proba(X)

Reproduce the results shown in the paper

Please check out the interactive Jupyter notebooks "synthetic.ipynb" and "real.ipynb". After installing Jupyter Notebook, please run the following commands:

bash jupyter notebook real.ipynb jupyter notebook synthetic.ipynb

Citations

If you use MUDRA in academic research, please cite it as follows

``` @article{bordoloi2025multivariate, title={Multivariate functional linear discriminant analysis for partially-observed time series}, author={Bordoloi, Rahul and R{\'e}da, Cl{\'e}mence and Trautmann, Orell and Bej, Saptarshi and Wolkenhauer, Olaf}, journal={Machine Learning}, volume={114}, number={3}, pages={80}, year={2025}, publisher={Springer} }

```

The citation for the ``Articulary Word Recognition'' data set (available in folder "datasets/") is

``` @article{ruizgreat2021, title = {The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances}, volume = {35}, issn = {1573-756X}, doi = {10.1007/s10618-020-00727-3}, number = {2}, journal = {Data Min Knowl Disc}, author = {Ruiz, Alejandro Pasos and Flynn, Michael and Large, James and Middlehurst, Matthew and Bagnall, Anthony}, month = mar, year = {2021}, pages = {401--449}, }

```

Original link to the freely available dataset is here.