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Introducing the Short-Time Fourier Kolmogorov Arnold Network: A Dynamic Graph CNN Approach for Tree Species Classification in 3D Point Clouds

Said Ohamouddou, Mohamed Ohamouddou, Hanaa El Afia, Abdellatif El Afia, Rafik Lasri, Raddouane Chiheb

TL;DR

STFT-KAN is introduced, a novel Kolmogorov-Arnold network that integrates the Short-Time Fourier Transform (STFT), which can replace the standard linear layer with activation in 3D point cloud classification and delivers competitive results compared to leading 3D point cloud learning approaches.

Abstract

Accurate classification of tree species based on Terrestrial Laser Scanning (TLS) and Airborne Laser Scanning (ALS) is essential for biodiversity conservation. While advanced deep learning models for 3D point cloud classification have demonstrated strong performance in this domain, their high complexity often hinders the development of efficient, low-computation architectures. In this paper, we introduce STFT-KAN, a novel Kolmogorov-Arnold network that integrates the Short-Time Fourier Transform (STFT), which can replace the standard linear layer with activation. We implemented STFT-KAN within a lightweight version of DGCNN, called liteDGCNN, to classify tree species using the TLS data. Our experiments show that STFT-KAN outperforms existing KAN variants by effectively balancing model complexity and performance with parameter count reduction, achieving competitive results compared to MLP-based models. Additionally, we evaluated a hybrid architecture that combines MLP in edge convolution with STFT-KAN in other layers, achieving comparable performance to MLP models while reducing the parameter count by 50% and 75% compared to other KAN-based variants. Furthermore, we compared our model to leading 3D point cloud learning approaches, demonstrating that STFT-KAN delivers competitive results compared to the state-of-the-art method PointMLP lite with an 87% reduction in parameter count.

Introducing the Short-Time Fourier Kolmogorov Arnold Network: A Dynamic Graph CNN Approach for Tree Species Classification in 3D Point Clouds

TL;DR

STFT-KAN is introduced, a novel Kolmogorov-Arnold network that integrates the Short-Time Fourier Transform (STFT), which can replace the standard linear layer with activation in 3D point cloud classification and delivers competitive results compared to leading 3D point cloud learning approaches.

Abstract

Accurate classification of tree species based on Terrestrial Laser Scanning (TLS) and Airborne Laser Scanning (ALS) is essential for biodiversity conservation. While advanced deep learning models for 3D point cloud classification have demonstrated strong performance in this domain, their high complexity often hinders the development of efficient, low-computation architectures. In this paper, we introduce STFT-KAN, a novel Kolmogorov-Arnold network that integrates the Short-Time Fourier Transform (STFT), which can replace the standard linear layer with activation. We implemented STFT-KAN within a lightweight version of DGCNN, called liteDGCNN, to classify tree species using the TLS data. Our experiments show that STFT-KAN outperforms existing KAN variants by effectively balancing model complexity and performance with parameter count reduction, achieving competitive results compared to MLP-based models. Additionally, we evaluated a hybrid architecture that combines MLP in edge convolution with STFT-KAN in other layers, achieving comparable performance to MLP models while reducing the parameter count by 50% and 75% compared to other KAN-based variants. Furthermore, we compared our model to leading 3D point cloud learning approaches, demonstrating that STFT-KAN delivers competitive results compared to the state-of-the-art method PointMLP lite with an 87% reduction in parameter count.

Paper Structure

This paper contains 31 sections, 1 theorem, 19 equations, 6 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Dynamic Graph Convolutional Neural Network (DGCNN)
  4. Edge Convolution (EdgeConv)
  5. DGCNN for tree Species classification using LiDAR data
  6. Kolmogorov-Arnold Network
  7. Kolmogorov-Arnold Representation Theorem
  8. Fourier-KAN
  9. Method: STFT-KAN
  10. Motivation
  11. STFT-KAN Layer Formulation
  12. STFT-KAN smooth initialization
  13. Experimental Setup
  14. Adapted DGCNN Architecture (liteDGCNN)
  15. Dataset
  16. ...and 16 more sections

Key Result

Theorem 1

Consider the function: where $\mathbf{x}_w[n]$ is the $n$-th element in the $w$-th window of signal $\mathbf{x}$ over $[a,b]$. Assume: Subsequently, $\phi_{G,w}$ converges uniformly to a univariate function over $[a,b]$ as $G \to \infty$.

Figures (6)

  • Figure 1: Architecture of a STFT-KAN layer, which takes an input $\mathbf{x} \in \mathbb{R}^{4}$ and produces a scalar output $D_{\text{out}} = 1$. The layer operates with a window size $W = 2$, stride $S = 2$, and grid size $G = 2$.
  • Figure 2: Architecture of liteDGCNN. In the architectural diagram, red blocks represent feature tensors, gray dashed blocks denote processing layers, and arrows illustrate the data flow through the network.
  • Figure 3: Sample examples from STPCTLS dataset.
  • Figure 4: Bayesian optimization history and window type impact on the STFT-KAN-based liteDGCNN
  • Figure 5: Parameter importances of STFT-KAN in liteDGCNN
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof