OptiMask is a Python package designed for efficiently handling NaN values in matrices, specifically focusing on computing the largest non-contiguous submatrix without NaN. OptiMask employs a heuristic method, relying on numpy and numba for speed and efficiency. In machine learning applications, OptiMask surpasses traditional methods like pandas dropna by maximizing the amount of valid data available for model fitting. It strategically identifies the optimal set of columns (features) and rows (samples) to retain or remove, ensuring that the largest (non-contiguous) submatrix without NaN is utilized for training models.
The problem differs from the computation of the largest rectangles of 1s in a binary matrix (which can be tackled with dynamic programming) and requires a novel approach. The problem also differs from this algorithmic challenge in that it requires rearranging both columns and rows, rather than just columns.
- Largest Submatrix without NaN: OptiMask calculates the largest submatrix without NaN, enhancing data analysis accuracy.
- Efficient Computation: With optimized computation, OptiMask provides rapid results without undue delays.
- Numpy, Pandas and Polars Compatibility: OptiMask adapts to
numpy,pandasandpolarsdata structures.
To employ OptiMask, install the optimask package via pip:
pip install optimaskOptiMask is also available on the conda-forge channel:
conda install -c conda-forge optimaskmamba install optimaskImport the OptiMask class from the optimask package and utilize its methods for efficient data masking:
from optimask import OptiMask
import numpy as np
# Create a matrix with NaN values
m = 120
n = 7
data = np.zeros(shape=(m, n))
data[24:72, 3] = np.nan
data[95, :5] = np.nan
# Solve for the largest submatrix without NaN values
rows, cols = OptiMask().solve(data)
# Calculate the ratio of non-NaN values in the result
coverage_ratio = len(rows) * len(cols) / data.size
# Check if there are any NaN values in the selected submatrix
has_nan_values = np.isnan(data[rows][:, cols]).any()
# Print or display the results
print(f"Coverage Ratio: {coverage_ratio:.2f}, Has NaN Values: {has_nan_values}")
# Output: Coverage Ratio: 0.85, Has NaN Values: FalseThe grey cells represent the NaN locations, the blue ones represent the valid data, and the red ones represent the rows and columns removed by the algorithm:
OptiMask’s algorithm is useful for handling unstructured NaN patterns, as shown in the following example:
OptiMask efficiently handles large matrices, delivering results within reasonable computation times:
from optimask import OptiMask
from optimask.utils import generate_mar
x = generate_mar(m=100_000, n=1_000, ratio=0.02)
%time rows, cols = OptiMask(verbose=True).solve(x)
# CPU times: total: 484 ms
# Wall time: 178 ms
# Trial 1 : submatrix of size 37190x49 (1822310 elements) found.
# Trial 2 : submatrix of size 37147x49 (1820203 elements) found.
# Trial 3 : submatrix of size 37733x48 (1811184 elements) found.
# Trial 4 : submatrix of size 37163x49 (1820987 elements) found.
# Trial 5 : submatrix of size 35611x51 (1816161 elements) found.
# Result: the largest submatrix found is of size 37190x49 (1822310 elements) found.For detailed documentation,API usage, examples and insights on the algorithm, visit OptiMask Documentation.
If you're working with time series data, check out timefiller, another Python package I developed for time series imputation. timefiller is designed to efficiently handle missing data in time series and relies heavily on optimask.
If you use OptiMask in your research or work, please cite it:
@INPROCEEDINGS{Joly2025-vq,
title = "{OptiMask}: Efficiently finding the largest {NaN-free}
submatrix",
booktitle = "Proceedings of the Python in Science Conference",
author = "Joly, Cyril",
abstract = "OptiMask is a heuristic designed to compute the largest, not
necessarily contiguous, submatrix of a matrix with missing
data. It identifies the optimal set of columns and rows to
remove to maximize the number of retained elements.",
publisher = "SciPy",
pages = "67--74",
month = jul,
year = 2025,
copyright = "https://creativecommons.org/licenses/by/4.0/",
conference = "Python in Science Conference, 2025",
location = "Tacoma, Washington"
}This paper is available at https://doi.org/10.25080/uaha7744.