A Novel Approach to Regression: Exploring the Similarity Space with Ordinary Least Squares on Database Records

Abstract

The proliferation of textual data, notably in the form of database records, calls for innovative methods of analysis that go beyond traditional numerical techniques. While least squares regression has been a cornerstone in quantitative data analysis, its applicability to textual data remains largely unexplored. This study aims to bridge this gap by introducing a similarity-based least squares method tailored for textual data. Drawing on the principles of similarity measures in text, such as semantic and syntactic closeness, we propose an extension to the conventional least squares framework. Our approach incorporates wordbased similarity metrics into the least squares objective function, enabling the analysis of textual data in a manner coherent with its qualitative nature. The developed methodology is rigorously evaluated using both synthetic and real-world database records, demonstrating its efficacy in uncovering intricate relationships within textual data. Our findings open new avenues for textual data analysis, blending the precision of classical statistical methods with the subtleties of text similarity.

Keywords

• similarity space
• linear regression
• similarity search