Kernel Representation and Similarity Measure for Incomplete Data

• URL: http://arxiv.org/abs/2510.13352v1
• Date: Wed, 15 Oct 2025 09:41:23 GMT
• Title: Kernel Representation and Similarity Measure for Incomplete Data
• Authors: Yang Cao, Sikun Yang, Kai He, Wenjun Ma, Ming Liu, Yujiu Yang, Jian Weng,
• Abstract summary: Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis.<n>Traditional approaches either discard incomplete data or perform imputation as a preprocessing step, leading to information loss and biased similarity estimates.<n>This paper presents a new similarity measure that directly computes similarity between incomplete data in kernel feature space without explicit imputation in the original space.
• Score: 55.62595187178638
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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