[Paper Review] A Method for Handling Multi-class Imbalanced Data by Geometry based Information Sampling and Class Prioritized Synthetic Data Generation (GICaPS)

Anima Majumder, Samrat Dutta+2 more|arXiv (Cornell University)|Oct 11, 2020

Imbalanced Data Classification Techniques4 citations

TL;DR

This paper proposes GICaPS, a novel data processing framework for multi-class imbalanced learning that combines geometry-based undersampling and class-prioritized oversampling. By leveraging angular constraints to remove redundant majority-class samples and generating synthetic data in low-overlap regions to respect class boundaries, GICaPS achieves a 99.39% average accuracy on the Shuttle dataset—significantly outperforming SMOTE and ADASYN across ten imbalanced datasets.

ABSTRACT

This paper looks into the problem of handling imbalanced data in a multi-label classification problem. The problem is solved by proposing two novel methods that primarily exploit the geometric relationship between the feature vectors. The first one is an undersampling algorithm that uses angle between feature vectors to select more informative samples while rejecting the less informative ones. A suitable criterion is proposed to define the informativeness of a given sample. The second one is an oversampling algorithm that uses a generative algorithm to create new synthetic data that respects all class boundaries. This is achieved by finding \\emph{no man's land} based on Euclidean distance between the feature vectors. The efficacy of the proposed methods is analyzed by solving a generic multi-class recognition problem based on mixture of Gaussians. The superiority of the proposed algorithms is established through comparison with other state-of-the-art methods, including SMOTE and ADASYN, over ten different publicly available datasets exhibiting high-to-extreme data imbalance. These two methods are combined into a single data processing framework and is labeled as ``GICaPS'' to highlight the role of geometry-based information (GI) sampling and Class-Prioritized Synthesis (CaPS) in dealing with multi-class data imbalance problem, thereby making a novel contribution in this field.

Motivation & Objective

• To address the challenge of multi-class data imbalance in real-world applications such as fraud detection and medical diagnosis, where minority classes are critical but underrepresented.
• To overcome limitations of existing sampling methods like SMOTE and ADASYN, which often generate noisy samples or fail in high-overlap, high-imbalance scenarios.
• To develop a unified framework that combines undersampling and oversampling using geometric principles to preserve informative samples and respect class boundaries.
• To provide a theoretically grounded, implementable method that improves classifier performance on extreme class imbalance (e.g., 10,000:1) without relying on costly reweighting or ensemble techniques.
• To validate the method on diverse, publicly available datasets with high-to-extreme imbalance, demonstrating consistent superiority over state-of-the-art techniques.

Proposed method

• The undersampling method uses the angle between feature vectors to identify and remove redundant majority-class samples, preserving those in distinct orthants to maintain class separability.
• A geometric criterion based on angular deviation from the centroid of the majority class defines sample informativeness, ensuring only less informative samples are removed.
• The oversampling method generates synthetic minority-class samples in regions of low inter-class density, avoiding 'no-man’s land' between classes using Euclidean distance-based boundary detection.
• The framework employs a class-prioritized synthesis strategy that focuses on generating samples near minority-class boundaries to improve generalization and reduce overlap.
• Mathematical formulations define the angular constraint for undersampling and the distance-based no-man’s land detection for oversampling, providing theoretical grounding.
• Pseudocode is provided for both algorithms, enabling reproducible implementation and integration into existing machine learning pipelines.

Experimental results

Research questions

• RQ1 Can geometric relationships between feature vectors be effectively leveraged to identify and remove redundant majority-class samples while preserving informative ones?
• RQ2 Can synthetic data generation be guided by inter-class boundary awareness to avoid creating ambiguous or noisy samples in overlapping regions?
• RQ3 Does combining geometry-based undersampling with class-prioritized oversampling lead to consistent performance gains across diverse, highly imbalanced multi-class datasets?
• RQ4 How does the proposed GICaPS framework compare to SMOTE, ADASYN, and other state-of-the-art methods in terms of accuracy, F-measure, and G-mean on real-world imbalanced datasets?
• RQ5 Can the framework maintain high performance even under extreme class imbalance ratios (e.g., >10,000:1) without relying on cost-sensitive learning or ensemble methods?

Key findings

• GICaPS achieved a 99.39% overall accuracy on the Shuttle dataset—significantly higher than SMOTE (96.59%) and ADASYN (56.27%), demonstrating strong performance on extreme imbalance.
• On the Abalone dataset, GICaPS-O (oversampling only) achieved 96.80% precision and 96.32% F-measure, outperforming SMOTE (75.71% F-measure) and ADASYN (33.5% F-measure).
• In the Pima Indian Diabetes dataset, GICaPS-O achieved 84.15% overall accuracy, surpassing SMOTE (76.40%) and ADASYN (75.45%), with consistent gains in F-measure and G-mean.
• On the Pain dataset, GICaPS achieved 98.80% overall accuracy and 98.79% F-measure, significantly outperforming SMOTE (90.33%) and ADASYN (17.45% F-measure), especially in recall for the minority class.
• The framework consistently outperformed SIMO, WSIMO, SWIM, and MOCAS (NN) across all evaluation metrics, with GICaPS showing the highest G-mean on multiple datasets including Glass (96.7) and Ionosphere (89.43).
• Statistical comparisons in Table VII confirm that GICaPS is statistically superior to all baseline methods, with the highest average performance across OA, F-measure, and G-mean on ten benchmark datasets.