Exploring the Role of Local Centrality in Graph Neural Networks for Point Cloud Classification

This is my final thesis project in the advanced course "Pattern Recognition and Machine Learning" in Fudan University

Overview

I proposes a lightweight approach to enhance Graph Neural Networks (GNNs) for point cloud classification by integrating efficient local centrality measures. The method achieves 91.2% accuracy on ModelNet40 with only 0.27M parameters, demonstrating that carefully designed structural feature learning can maintain competitive performance while significantly reducing model complexity.

Key Contributions

1. Efficient Local Centrality Computation

   • Computes weighted local degree centrality within radius-based neighborhoods
   • Avoids expensive global computations with $O(NlogN)$ complexity
   • Captures higher-order structural information through recursive formulation

2. Structural Edge Convolution Layer

   • Integrates centrality scores into edge feature computation
   • Combines geometric and structural information through adaptive aggregation
   • Prevents over-smoothing while maintaining discriminative features

3. Parameter-Efficient Architecture

   • 0.27M parameters vs. 3.5M for PointNet, 1.8M for DGCNN
   • Multi-scale feature extraction with residual connections
   • Progressive receptive field expansion (r = 0.1, 0.2, 0.4)

Method

Local Centrality Computation

For a point cloud $P \in \mathbb{R}^{N \times 3}$, the weighted local degree centrality is:

$d_i = \sum_{j \in N_r(i)} w_{ij}$, $\quad w_{ij} = \exp(-\Vert p_i - p_j \Vert^2)$

To capture higher-order structure, we use a recursive formulation:

$\tilde{d}_i = d_i + \frac{\alpha}{d_i + \varepsilon} \sum_{j \in N_r(i)} d_j w_{ij}$, $\alpha = 0.5$, $\varepsilon = 10^{-6}$

Structural Edge Features

Edge features are computed with centrality weighting:

$e_{ij} = MLP\big(x_i \Vert (x_j - x_i) \Vert \Vert p_i - p_j \Vert^2\big) \cdot s_i$

where $s_i$ is the normalized centrality score.

Adaptive Feature Aggregation

A learnable combination of max and mean pooling:

$x'_i = w_1 \cdot \max_{j \in N_r(i)} e_{ij} + w_2 \cdot mean_{j \in N_r(i)} e_{ij}$

where $w_1, w_2$ are normalized via softmax.

Experimental Results

ModelNet40 Performance

Method	OA (%)	mAcc (%)	Params (M)
PointNet	89.2	86.2	3.5
PointNet++	90.7	87.8	1.7
Local-Centrality GCN (Ours)	91.2	87.9	0.27

Ablation Study: Centrality Integration Methods

Method	OA (%)	Params (M)
Resconnection GCN	85.5	0.03
Centrality-embedding GCN	86.9	0.04
Large-scale Centrality-embedding	88.6	0.96
Local-Centrality GCN (Ours)	91.2	0.27

Visualization Analysis

Architecture Overview

Figure 1: Overview of our centrality-enhanced architecture for point cloud classification

Figure 2: Detailed structure of the proposed structural edge convolution layer, showing the integration of geometric features with centrality-based attention and adaptive feature aggregation mechanisms

Structural Edge Convolution Layer

Figure 3: Point cloud connection graph after each convolution layer

Connection Graph Evolution

Figure 4: Single point connection graph after centrality-enhanced architecture