Kernel Representation and Similarity Measure for Incomplete Data

2025-10-15

AI Summary

To address information loss and bias arising from sample discarding or imputation in similarity measurement for incomplete data, this paper proposes the proximity kernel method. It computes similarities directly in a kernel feature space without explicit imputation; introduces data-dependent binning and proximity-based assignment, coupled with a cascaded fallback strategy to estimate missing feature distributions and adaptively model local density variations; and achieves linear-time similarity computation via local-density-aware projection and high-dimensional sparse kernel representation. Extensive clustering experiments on 12 real-world incomplete datasets demonstrate that the proposed method significantly outperforms existing baselines, achieving superior accuracy, strong robustness to missingness patterns, and excellent scalability.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step, leading to information loss and biased similarity estimates. This paper presents the proximity kernel, a new similarity measure that directly computes similarity between incomplete data in kernel feature space without explicit imputation in the original space. The proposed method introduces data-dependent binning combined with proximity assignment to project data into a high-dimensional sparse representation that adapts to local density variations. For missing value handling, we propose a cascading fallback strategy to estimate missing feature distributions. We conduct clustering tasks on the proposed kernel representation across 12 real world incomplete datasets, demonstrating superior performance compared to existing methods while maintaining linear time complexity. All the code are available at https://anonymous.4open.science/r/proximity-kernel-2289.

Problem

• Measuring similarity between incomplete data without imputation
• Handling missing values with cascading fallback distribution estimation
• Projecting data into adaptive high-dimensional sparse representation

Innovation

• Proximity kernel computes similarity without explicit imputation
• Data-dependent binning projects data into sparse representation
• Cascading fallback strategy estimates missing feature distributions