基于Hellinger距离的正态云相似性度量方法及应用研究

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Title:

Similarity measurement method for normal cloud based on Hellinger distance and its application

作者:

许昌林^1,2, 徐浩¹

1. 北方民族大学 数学与信息科学学院, 宁夏 银川 750021;
2. 北方民族大学 宁夏智能信息与大数据处理重点实验室, 宁夏 银川 750021

Author(s):

XU Changlin^1,2, XU Hao¹

1. School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China;
2. The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, North Minzu University, Yinchuan, 750021, China

关键词:

知识表示; 正态云; 不确定性; Hellinger距离; 特征曲线; 相似性度量; 协同过滤; 推荐系统

Keywords:

knowledge representation; normal cloud; uncertainty; Hellinger distance; characteristic curve; similarity measurement; collaborative filtering; recommendation system

分类号:

TP311

DOI:

10.11992/tis.202209042

摘要:

针对现有正态云相似性度量计算复杂度较高且区分度不强等问题，本文首先从正态云的特征曲线出发，利用Hellinger距离刻画两个概率分布相似性的特点，提出一种基于Hellinger距离的正态云相似性度量方法，该方法不仅考虑了云概念的数字特征且兼顾了其分布特性，并对相似度量具有的数学性质进行了研究。其次，根据给出的相似度量方法，设计了两种正态云概念的相似度算法。最后，通过数值模拟仿真实验和时间序列数据分类实验对所提出算法的性能进行对比分析，结果表明该算法具有较好的相似度区分能力且分类错误率和CPU时间代价都较低。同时，将本文方法应用于协同过滤推荐系统中，并在MovieLens100k影评数据集上进行了实验，实验结果表明本文方法在用户评分数据极端稀疏的情况下，仍能取得较理想的推荐质量。

Abstract:

To address the problems of high computational complexity and weak discrimination of existing normal cloud model similarity measurement methods, a similarity measurement method for normal clouds based on Hellinger distance is proposed according to the characteristic curve of the normal cloud by taking inspiration from the similarity of two probability distributions described by Hellinger distance. The digital and distribution characteristics of the cloud concept were considered in the proposed method. Furthermore, the mathematical properties of the proposed similarity measurement were studied. Two similarity algorithms were then designed for the normal cloud concept on the basis of the given similarity measurement method. Finally, the performance of the proposed algorithms was compared and analyzed using numerical simulation and classification experiments on time-series data. Results showed that the proposed algorithms have good similarity discrimination capability, and their classification error rate and CPU time cost are low. Moreover, these algorithms were applied to the collaborative filtering recommendation system, and experiments were conducted on the MovieLens100k film review dataset. The experimental results revealed that the proposed methods can continue to achieve ideal recommendation quality even when the user rating data were extremely sparse.