直接在核空间计算不完整数据相似性，避免补全带来的信息损失。
Kernel Representation and Similarity Measure for Incomplete Data
- 用自适应分箱和邻近赋值生成高维稀疏表示，捕捉局部密度变化。
- 在12个真实数据集上聚类效果优于现有方法，且时间复杂度线性。
- 适合处理缺失值多的推荐系统与用户行为分析场景。
在网页挖掘、推荐系统与用户行为分析中，衡量不完整数据间的相似性是一项基础挑战。传统方法要么丢弃不完整数据，要么在原始空间进行补全预处理，导致信息损失和相似性估计偏差。本文提出一种近邻核（proximity kernel），可在核特征空间中直接计算不完整数据的相似性，无需在原始空间显式补全。该方法结合数据依赖的分箱策略与邻近赋值，将数据投影到高维稀疏表示，能自适应局部密度变化。针对缺失值处理，提出级联回退策略以估计缺失特征分布。我们在12个真实世界的不完整数据集上进行了聚类实验，结果表明该方法性能优于现有方法，同时保持线性时间复杂度。所有代码已公开于https://anonymous.4open.science/r/proximity-kernel-2289。
原文摘要 · Abstract (English)
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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