Quantifying the Conceptual Error in Dimensionality Reduction

TL;DR

This paper introduces a method to detect and quantify conceptual errors in data dimensionality reduction, emphasizing the preservation of the original data's conceptual structure, which is often overlooked in existing techniques.

Contribution

It provides the theoretical foundation and an experimental evaluation for assessing conceptual errors in data scalings using formal concept analysis.

Findings

The approach effectively detects conceptual errors in various data sets.

Quantification of conceptual errors offers insights into the quality of dimensionality reduction.

Experimental results demonstrate the method's applicability across different data reduction techniques.

Abstract

Dimension reduction of data sets is a standard problem in the realm of machine learning and knowledge reasoning. They affect patterns in and dependencies on data dimensions and ultimately influence any decision-making processes. Therefore, a wide variety of reduction procedures are in use, each pursuing different objectives. A so far not considered criterion is the conceptual continuity of the reduction mapping, i.e., the preservation of the conceptual structure with respect to the original data set. Based on the notion scale-measure from formal concept analysis we present in this work a) the theoretical foundations to detect and quantify conceptual errors in data scalings; b) an experimental investigation of our approach on eleven data sets that were respectively treated with a variant of non-negative matrix factorization.