Towards the Linear Algebra Based Taxonomy of XAI Explanations

TL;DR

This paper introduces a linear algebra-based taxonomy for local explanations in XAI, aiming to provide a more mathematical and systematic way to classify explanations, especially for data in real n-dimensional space.

Contribution

It proposes a novel linear algebra framework for classifying local explanations in XAI, moving beyond human-centric taxonomies.

Findings

Provides a mathematical taxonomy for local explanations

Facilitates comparison of XAI methods using linear algebra

Focuses on data in real n-dimensional space

Abstract

This paper proposes an alternative approach to the basic taxonomy of explanations produced by explainable artificial intelligence techniques. Methods of Explainable Artificial Intelligence (XAI) were developed to answer the question why a certain prediction or estimation was made, preferably in terms easy to understand by the human agent. XAI taxonomies proposed in the literature mainly concentrate their attention on distinguishing explanations with respect to involving the human agent, which makes it complicated to provide a more mathematical approach to distinguish and compare different explanations. This paper narrows its attention to the cases where the data set of interest belongs to $\mathbb{R} ^n$ and proposes a simple linear algebra-based taxonomy for local explanations.