Homological Convolutional Neural Networks

TL;DR

This paper introduces a novel deep learning architecture called Homological Convolutional Neural Networks designed to effectively model relational structures in sparse tabular data, achieving state-of-the-art results on multiple benchmarks.

Contribution

The work presents a new topology-based convolutional neural network architecture that enhances interpretability and scalability for tabular data analysis.

Findings

Achieves state-of-the-art performance on 18 benchmark datasets.

Outperforms 5 classic machine learning models and 3 deep learning models.

Provides a data-centric, interpretable, and scalable modeling approach.

Abstract

Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine learning approaches being often computationally cheaper and equally effective than increasingly complex deep learning architectures. The challenge arises from the fact that, in tabular data, the correlation among features is weaker than the one from spatial or semantic relationships in images or natural language, and the dependency structures need to be modeled without any prior information. In this work, we propose a novel deep learning architecture that exploits the data structural organization through topologically constrained network representations to gain relational information from sparse tabular inputs. The resulting model leverages the power of convolution and is centered on a limited number of concepts from network topology to guarantee: (i) a data-centric and deterministic building pipeline; (ii) a high level of interpretability over the inference process; and (iii) an adequate room for scalability. We test our model on 18 benchmark datasets against 5 classic machine learning and 3 deep learning models, demonstrating that our approach reaches state-of-the-art performances on these challenging datasets. The code to reproduce all our experiments is provided at https://github.com/FinancialComputingUCL/HomologicalCNN.