Decision Tree Learning with Spatial Modal Logics

TL;DR

This paper introduces a novel theory and implementation of spatial decision trees using modal spatial logics, demonstrating improved accuracy and interpretability over classical propositional decision trees in image classification tasks.

Contribution

It extends classical decision tree algorithms with a spatial logic framework, enabling better modeling of spatial data in interpretable decision trees.

Findings

Spatial decision trees outperform propositional ones in accuracy.

Spatial models offer higher interpretability.

Experiments show significant performance improvements.

Abstract

Symbolic learning represents the most straightforward approach to interpretable modeling, but its applications have been hampered by a single structural design choice: the adoption of propositional logic as the underlying language. Recently, more-than-propositional symbolic learning methods have started to appear, in particular for time-dependent data. These methods exploit the expressive power of modal temporal logics in powerful learning algorithms, such as temporal decision trees, whose classification capabilities are comparable with the best non-symbolic ones, while producing models with explicit knowledge representation. With the intent of following the same approach in the case of spatial data, in this paper we: i) present a theory of spatial decision tree learning; ii) describe a prototypical implementation of a spatial decision tree learning algorithm based, and strictly extending, the classical C4.5 algorithm; and iii) perform a series of experiments in which we compare the predicting power of spatial decision trees with that of classical propositional decision trees in several versions, for a multi-class image classification problem, on publicly available datasets. Our results are encouraging, showing clear improvements in the performances from the propositional to the spatial models, which in turn show higher levels of interpretability.