Computer Science and Application
Vol. 09  No. 12 ( 2019 ), Article ID: 33548 , 8 pages
10.12677/CSA.2019.912261

Three-Way Clustering Analysis Based on Voting Theory

Liuquan Gu, Ruilin Chai, Pingxin Wang*

School of Science, Jiangsu University of Science and Technology, Zhenjiang Jiangsu

Received: Dec. 2nd, 2019; accepted: Dec. 13th, 2019; published: Dec. 20th, 2019

ABSTRACT

At present, most of existed clustering methods are two-way clustering which are based on the assumption that a cluster must be represented by a set with crisp boundary. However, assigning uncertain objects into a certain cluster will reduce the accuracy of clustering results. Three-way clustering is an overlapping clustering which describes each cluster by core region and fringe region. It handles the category problem of uncertain objects and reduces the decision risk effectively. This paper mainly introduces a model of three-way clustering, and gives three-way clustering algorithm based on k-means as an example for analysis. Firstly, different clustering results of the same data set are obtained by ensemble clustering. Then, the label matching method is used. Finally, the cluster of objects is determined according to the voting rules. Through the analysis of experimental results, it is verified that the effect of the clustering method has been significantly improved.

Keywords:K-Means, Three-Way Clustering, Label Matching, Voting Rules

Copyright © 2019 by author(s) and Hans Publishers Inc.

1. 引言

2. 相关工作

2.1. 三支聚类

$C\left({m}_{i}\right)\cup F\left({m}_{i}\right)\cup T\left({m}_{i}\right)=U\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(i=1,2,\cdots ,k\right)$ (1)

$\underset{i=1}{\overset{k}{\cup }}\left(C\left({m}_{i}\right)\cup F\left({m}_{i}\right)\right)=U\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(i=1,2,\cdots ,k\right)$ (2)

$C\left({m}_{i}\right)\ne \varphi \text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(i=1,2,\cdots ,k\right)$ (3)

2.2. 匹配原则

Figure 1. Schematic diagram of clustering results

Table 1. Representation of clustering results

2.3. 投票原则

$f\left({x}_{i}\right)=\frac{{m}_{j}}{N}$ (4)

$g\left({x}_{i}\right)=\left\{\begin{array}{ll}{x}_{i}\in C\left({m}_{j}\right),\hfill & \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}f\left({x}_{i}\right)\ge 0.9\hfill \\ {x}_{i}\in F\left({m}_{j}\right),\hfill & 0 (5)

3. 聚类结果评价指标

3.1. 准确率

$\text{ACC}=\frac{1}{N}\underset{i=1}{\overset{k}{\sum }}{M}_{i}$ (6)

3.2. Davies-Bouldin Index

Davies-Bouldin index通过计算每个类簇最大相似度的均值，是一种评估聚类算法优劣的内部聚类评价指标。使用下列公式进行计算

$\text{DBI}=\frac{1}{N}\underset{i=1}{\overset{N}{\sum }}\underset{i\ne j}{\mathrm{max}}\left(\frac{\stackrel{¯}{{S}_{i}}+\stackrel{¯}{{S}_{j}}}{{‖{w}_{i}-{w}_{j}‖}_{2}}\right)$ (7)

$\stackrel{¯}{{S}_{i}}={\left(\frac{1}{{T}_{i}}\underset{j=1}{\overset{{T}_{i}}{\sum }}{|{x}_{j}-{A}_{j}|}^{p}\right)}^{\frac{1}{p}}$ (8)

${x}_{j}$ 代表类簇i中第j个样本点， ${A}_{i}$ 是类簇i的质心， ${T}_{i}$ 是类簇i中样本的个数，p在通常情况下取值为2。

4. 实验数据分析

Table 2. Data used in experiments

Table 3. Experimental results on data sets

5. 结语

Three-Way Clustering Analysis Based on Voting Theory[J]. 计算机科学与应用, 2019, 09(12): 2349-2356. https://doi.org/10.12677/CSA.2019.912261

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16. NOTES

*通讯作者。