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MeanRadius SMOTE Based Graph Neural Network for Imbalanced Node Classification in Fault and Intrusion Detection

This paper proposes the MeanRadius-SMOTE Graph Neural Network (MRS-GNN), a novel framework that addresses class imbalance in fault and intrusion detection by generating synthetic nodes in the embedding space and creating specialized edges to preserve graph topology, thereby significantly improving classification accuracy and AUC-ROC under extreme imbalance conditions.

Original authors: Jagannath E. Nalavade, Ramachandra Pujeri, Rajani Sajjan, Nagesh Jadhav, Amar Buchade, Dattatray Kale

Published 2026-08-24

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CC BY 4.0

Original authors: Jagannath E. Nalavade, Ramachandra Pujeri, Rajani Sajjan, Nagesh Jadhav, Amar Buchade, Dattatray Kale

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the complex machinery of modern industry and the intricate web of global networks, safety depends on the ability to spot the rare and the dangerous before they cause harm. Whether it is a bearing in a factory motor beginning to fail or a subtle pattern of malicious traffic on a computer network, these critical events are often hidden within a vast sea of normal, everyday data. This creates a difficult puzzle for the computer programs designed to watch over these systems. Because failures and attacks are so much rarer than normal operation, the data available to train these programs is heavily skewed. The programs learn to recognize the common, boring patterns of health and safety, but they struggle to identify the rare, dangerous signals because they simply do not have enough examples to study. This is a problem of imbalance, where the few important cases are drowned out by the many unimportant ones.

To solve this, researchers have turned to a type of artificial intelligence known as a graph neural network. Unlike standard computer programs that look at data as a simple list or a grid, these networks treat information as a map of connections. Imagine a system where every piece of data is a point, and the relationships between them are lines connecting those points. This structure allows the computer to understand how different parts of a machine or a network influence one another. However, even these advanced systems stumble when faced with the imbalance problem. If you try to teach them by simply copying the rare examples or by making them pay extra attention to the rare cases, the results are often poor. The copied examples do not fit the complex web of connections, and the extra attention often leads to confusion rather than clarity. The network ends up missing the very faults and intrusions it was built to find.

A team of researchers from universities in India has developed a new approach to fix this specific weakness. They created a framework called the MeanRadius-SMOTE Graph Neural Network, or MRS-GNN, which is designed to generate trustworthy new examples of the rare events without breaking the delicate structure of the data map. Instead of trying to force new data into the raw, messy original format, the researchers first guide the computer to translate the data into a cleaner, more organized internal language. In this simplified space, the computer can see the true shape of the rare events more clearly. It then creates new, synthetic examples of these rare faults by carefully filling in the gaps between existing examples, ensuring that the new data looks and behaves exactly like the real thing.

The most critical part of this new method is how it handles the connections between these new examples and the rest of the system. When a computer creates a fake example, it often leaves it floating alone, disconnected from the network. This is a fatal flaw for a graph-based system, which relies entirely on the lines connecting the points to make sense of the world. The researchers solved this by adding a special module that acts as a bridge builder. This module studies the existing patterns of connection and draws new lines from the synthetic examples to the real data points. It ensures that the new examples are woven seamlessly into the fabric of the network, maintaining the structural integrity of the whole system. This allows the computer to learn from the new examples just as it would from real ones, using the connections to understand the context of the rare events.

The team tested this new framework using data from three well-known sources of mechanical fault information, including datasets from Case Western Reserve University and the University of Paderborn. They simulated extreme conditions where the rare faults were vastly outnumbered by normal operations, creating a scenario where the imbalance was severe. In these difficult tests, the new system proved to be remarkably effective. It achieved a classification accuracy that was more than eighteen percentage points higher than traditional methods that simply copied data or adjusted weights. Furthermore, when measuring the system's ability to distinguish between the rare faults and the normal noise, the new framework reached a score of 0.904, a level of performance that indicates a very high degree of reliability.

The researchers found that this approach worked well even when the number of different types of faults increased, a situation where older methods often fell apart. By keeping the new data connected and true to the original structure, the system avoided the confusion that usually plagues attempts to balance uneven datasets. The study suggests that this method is not limited to mechanical faults but could also be applied to other complex systems, such as detecting intrusions in computer networks or monitoring the stability of power grids. The work demonstrates that by respecting the underlying connections in data and creating new examples with care, it is possible to teach computers to see the rare and dangerous signals that they would otherwise miss, leading to safer and more reliable industrial and digital systems.

Technical Summary: MeanRadius SMOTE Based Graph Neural Network for Imbalanced Node Classification

1. Problem Statement
The paper addresses the critical challenge of class imbalance in semi-supervised node classification tasks within Graph Neural Networks (GNNs), specifically applied to fault diagnosis in mechanical systems and intrusion detection in network security. In these domains, data is heavily skewed: the majority class represents normal operations (healthy bearings or benign traffic), while the minority class represents rare but critical events (faults or cyberattacks).

Standard deep learning models, including GNNs, are biased toward the majority class because their loss functions are dominated by the frequent samples. This leads to poor detection of minority events. Furthermore, traditional oversampling techniques like SMOTE (Synthetic Minority Over-sampling Technique) fail when applied directly to graph data because:

They operate in the original high-dimensional feature space, often generating noisy or out-of-distribution samples.
They ignore the graph topology; simply adding synthetic nodes without defining their connections breaks the structural integrity of the graph, rendering the GNN's message-passing mechanisms ineffective.

2. Methodology: The MRS-GNN Framework
The authors propose the MeanRadius-SMOTE Graph Neural Network (MRS-GNN), a framework designed to synthesize trustworthy node representations while preserving topological integrity. The methodology proceeds through four distinct stages:

Graph Data Generation: Raw one-dimensional time-series signals (e.g., vibration data) are segmented using a sliding window (length 256). Each segment becomes a node. An adjacency matrix is constructed using the Pearson correlation coefficient to measure linear relationships between nodes, followed by a sparsification step to remove noisy edges and prevent oversmoothing.
Feature Extraction: A GNN feature extractor (specifically GraphSage in the proposed architecture) encodes the graph data into a lower-dimensional intermediate embedding space. This step is crucial as it captures both node attributes and local structural information, creating a more coherent distribution for interpolation than the original high-dimensional space.
MeanRadius-SMOTE (MRS-SMOTE): Oversampling occurs within this embedding space, not the raw feature space. The algorithm:
1. Calculates the geometric center ( $Z$ ) of the minority class samples.
2. Computes the average Euclidean radius ( $R$ ) from the center to the samples.
3. Generates synthetic vectors by interpolating between the center and randomly selected minority samples.
4. Creates new sample nodes ( $z_{new}$ ) based on a normal distribution relative to the radius, ensuring the synthetic data remains within the decision boundary of the minority class.
Edge Generator: To address the "isolated island" problem of synthetic nodes, a specialized Edge Generator module is introduced. It learns the authentic edge distribution from the original graph and predicts connections between the new synthetic nodes and existing nodes. The paper proposes two strategies for this:
- MRS-GNNS (Continuous): Predicts edge weights as continuous values (0–1), allowing the edge generator to be optimized jointly with the node classifier via gradient loss.
- MRS-GNNT (Thresholded): Converts predicted weights to binary values (0 or 1) using a threshold $\epsilon$ , optimizing the generator solely on the edge prediction task.

3. Key Contributions

Hybrid Integration: The novel integration of MeanRadius-SMOTE directly into the GNN pipeline, performing oversampling in the intermediate embedding space rather than the raw feature space to improve sample quality and reduce noise.
Topological Integrity: The introduction of an Edge Generator module that ensures synthetic nodes are structurally connected to the original graph, maintaining the continuity required for GNN message passing.
Scalable Framework: A demonstration that the framework is adaptable to various complex systems, moving beyond simple fault diagnosis to potential applications in network intrusion detection and other topological systems.

4. Experimental Results
The framework was validated on three publicly available bearing fault diagnosis datasets: CWRU (Case Western Reserve University), JNU (Jiangnan University), and PU (University of Paderborn).

Performance under Extreme Imbalance: Under severe imbalance conditions (Imbalance Rate/IMR of 0.4), the MRS-GNN variants significantly outperformed baseline methods (Oversampling, SMOTE, Reweight, and GraphSMOTE).
- The MRS-GNNS variant achieved an AUC-ROC of 0.904.
- Classification accuracy improved by more than 18 percentage points compared to baseline oversampling methods on the CWRU dataset.
Robustness: The model maintained stable performance as the number of imbalanced classes increased, whereas traditional methods (SMOTE, Reweight) showed significant degradation.
Base Model Comparison: When tested with different GNN backbones, Graph Attention Networks (GAT) combined with MRS-SMOTE yielded the best performance across all imbalance rates, attributed to the attention mechanism's ability to weigh node importance. GraphSage and GCN also showed improvements but were slightly less effective in highly heterogeneous scenarios compared to GAT.

5. Significance and Claims
The paper claims that MRS-GNN offers a robust solution to the specific limitations of applying oversampling to graph-structured data. By shifting interpolation to the embedding space and explicitly modeling edge generation, the framework resolves the dual issues of sample quality and topological disconnection.

The authors assert that this approach not only enhances fault diagnosis reliability in mechanical systems but also provides a scalable, generalizable solution for other complex systems involving imbalanced node classification, such as power grids, transport networks, and intrusion detection systems. The work positions itself as a bridge between data-level resampling techniques and the structural requirements of Graph Neural Networks.

Technical Summary: MeanRadius SMOTE Based Graph Neural Network for Imbalanced Node Classification

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