针对均匀与偏态特征,提出新型归一化方法提升比较一致性。
Normalization in Proportional Feature Spaces
- 从均匀与比例特征空间的对偶性出发,设计非中心化离散度归一化。
- 提出改进的杰卡德相似度,天然包含归一化机制。
- 适用于数据比较、分类任务中特征分布不均的场景。
特征归一化在数据表示、表征、可视化、分析、比较、分类和建模中起着核心作用,其选择需考虑特征类型、后续处理方法及具体问题。本文从均匀与比例(右偏)特征及比较操作的角度,探讨特征归一化的关键问题。讨论了均匀与比例特征空间之间的对偶关系及其比较的一致性条件。提出了基于非中心化离散度的两种归一化方法,并介绍一种内嵌归一化的改进杰卡德相似度。通过初步实验验证所提概念与方法的有效性。
原文摘要 · Abstract (English)
The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of these activities and respective aspects. The selection of an appropriate normalization method needs to take into account the type and characteristics of the involved features, the methods to be used subsequently for the just mentioned data processing, as well as the specific questions being considered. After briefly considering how normalization constitutes one of the many interrelated parts typically involved in data analysis and modeling, the present work addressed the important issue of feature normalization from the perspective of uniform and proportional (right skewed) features and comparison operations. More general right skewed features are also considered in an approximated manner. Several concepts, properties, and results are described and discussed, including the description of a duality relationship between uniform and proportional feature spaces and respective comparisons, specifying conditions for consistency between comparisons in each of the two domains. Two normalization possibilities based on non-centralized dispersion of features are also presented, and also described is a modified version of the Jaccard similarity index which incorporates intrinsically normalization. Preliminary experiments are presented in order to illustrate the developed concepts and methods.
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