基于块对角线表示的一步多核 K 均值聚类法

IF 3 4区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Expert Systems Pub Date : 2024-09-05 DOI:10.1111/exsy.13720
Cuiling Chen, Zhi Li
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引用次数: 0

摘要

多核 K-means 聚类(MKKC)可以有效地结合多个基本核来生成最优核。现有的许多 MKKC 方法都需要两步操作:学习聚类指标矩阵并对其进行聚类。然而,两步操作的最优聚类结果并不等同于原始问题的最优聚类结果。为了解决这个问题,本文提出了一种新方法,即基于块对角线表示的一步多核均值聚类(OS-MKKC-BD)。通过对指标矩阵及其转置的乘积施加正对角线约束,该方法可以促使指标矩阵成为正对角线。这样,指标矩阵就能产生明确的聚类指标,从而实现一步聚类,避免了两步操作的缺点。此外,利用简单的内核加权策略获得最优内核,提高了最优内核的质量。此外,还设计了一种三步迭代算法来解决相应的优化问题,其中黎曼共轭梯度迭代法用于解决指标矩阵的优化问题。最后,通过在 11 个真实数据集上进行大量实验,并将聚类结果与 10 种 MKC 方法进行比较,得出 OS-MKKC-BD 是有效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
One‐step multiple kernel k‐means clustering based on block diagonal representation
Multiple kernel k‐means clustering (MKKC) can efficiently incorporate multiple base kernels to generate an optimal kernel. Many existing MKKC methods all need two‐step operation: learning clustering indicator matrix and performing clustering on it. However, the optimal clustering results of two steps are not equivalent to those of original problem. To address this issue, in this paper we propose a novel method named one‐step multiple kernel k‐means clustering based on block diagonal representation (OS‐MKKC‐BD). By imposing a block diagonal constraint on the product of indicator matrix and its transpose, this method can encourage the indicator matrix to be block diagonal. Then the indicator matrix can produce explicit clustering indicator, so as to implement one‐step clustering, which avoids the disadvantage of two‐step operation. Furthermore, a simple kernel weighting strategy is used to obtain an optimal kernel, which boosts the quality of optimal kernel. In addition, a three‐step iterative algorithm is designed to solve the corresponding optimization problem, where the Riemann conjugate gradient iterative method is used to solve the optimization problem of the indicator matrix. Finally, by extensive experiments on eleven real data sets and comparison of clustering results with 10 MKC methods, it is concluded that OS‐MKKC‐BD is effective.
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来源期刊
Expert Systems
Expert Systems 工程技术-计算机:理论方法
CiteScore
7.40
自引率
6.10%
发文量
266
审稿时长
24 months
期刊介绍: Expert Systems: The Journal of Knowledge Engineering publishes papers dealing with all aspects of knowledge engineering, including individual methods and techniques in knowledge acquisition and representation, and their application in the construction of systems – including expert systems – based thereon. Detailed scientific evaluation is an essential part of any paper. As well as traditional application areas, such as Software and Requirements Engineering, Human-Computer Interaction, and Artificial Intelligence, we are aiming at the new and growing markets for these technologies, such as Business, Economy, Market Research, and Medical and Health Care. The shift towards this new focus will be marked by a series of special issues covering hot and emergent topics.
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