Kernel Representation and Similarity Measure for Incomplete Data
This addresses a fundamental challenge in web mining, recommendation systems, and user behavior analysis, offering a novel method for handling incomplete data without information loss or bias.
The paper tackles the problem of measuring similarity between incomplete data by introducing the proximity kernel, a new similarity measure that directly computes similarity in kernel feature space without explicit imputation, and demonstrates superior clustering performance on 12 real-world datasets while maintaining linear time complexity.
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.