FINDER: Feature Inference on Noisy Datasets using Eigenspace Residuals

2025-10-22

AI Summary

To address classification challenges under noisy conditions—including low signal-to-noise ratios, limited training samples, and anomalous data acquisition—this paper proposes a robust classification framework grounded in random field modeling. Methodologically, it introduces the Kosambi–Karhunen–Loève (KLE) expansion into feature learning for the first time, integrating operator spectral analysis to extract interpretable intrinsic features directly from noisy data—without requiring assumptions about underlying probability distributions. Subsequently, Hilbert-space mapping and randomized feature construction enable residual modeling in feature space and discriminative operator decomposition. Evaluated on Alzheimer’s disease multi-stage staging and remote-sensing-based deforestation detection, the method achieves state-of-the-art performance. It notably improves classification accuracy and generalization stability under high-noise and few-shot scenarios.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Intelligent Robots: State Estimation
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

''Noisy'' datasets (regimes with low signal to noise ratios, small sample sizes, faulty data collection, etc) remain a key research frontier for classification methods with both theoretical and practical implications. We introduce FINDER, a rigorous framework for analyzing generic classification problems, with tailored algorithms for noisy datasets. FINDER incorporates fundamental stochastic analysis ideas into the feature learning and inference stages to optimally account for the randomness inherent to all empirical datasets. We construct ''stochastic features'' by first viewing empirical datasets as realizations from an underlying random field (without assumptions on its exact distribution) and then mapping them to appropriate Hilbert spaces. The Kosambi-Karhunen-Loéve expansion (KLE) breaks these stochastic features into computable irreducible components, which allow classification over noisy datasets via an eigen-decomposition: data from different classes resides in distinct regions, identified by analyzing the spectrum of the associated operators. We validate FINDER on several challenging, data-deficient scientific domains, producing state of the art breakthroughs in: (i) Alzheimer's Disease stage classification, (ii) Remote sensing detection of deforestation. We end with a discussion on when FINDER is expected to outperform existing methods, its failure modes, and other limitations.

Problem

• Classifying data in noisy low-signal regimes
• Developing stochastic features for empirical datasets
• Enhancing classification accuracy in data-deficient domains

Innovation

• Stochastic features mapped to Hilbert spaces
• Irreducible components via Kosambi-Karhunen-Loève expansion
• Classification via eigen-decomposition of operator spectrum