What Polynomial Regression Reveals About Scientific Data Compression.

Area of Science:

• Data Science
• Scientific Computing
• Applied Mathematics

Background:

• Large-scale scientific simulations and instruments generate massive floating-point datasets.
• Current lossy compression methods reduce data size but can obscure local data characteristics.
• Compression is primarily used for storage efficiency, not for data analysis.

Purpose of the Study:

• To explore piecewise polynomial regression as a structure-aware data compression technique.
• To demonstrate how locally fitted models can expose underlying data structures.
• To shift the perception of compression from mere size reduction to a tool for data understanding.

Main Methods:

• Applying piecewise polynomial regression to segments of floating-point data.
• Analyzing the fitted polynomial models to identify data features.
• Evaluating the compression's effectiveness in preserving and revealing data structure.

Main Results:

• Piecewise polynomial regression effectively reduces data size.
• Locally fitted models highlight data features like trends, changes, and noise.
• This method provides insights into local data behavior obscured by traditional compression.

Conclusions:

• Piecewise polynomial regression offers a structure-aware approach to data compression.
• This technique can serve as a valuable tool for exploring and understanding scientific data.
• The focus is on data interpretability and feature discovery, not solely on compression ratios.