基于超图正则化非负Tucker分解的图像聚类算法

doi:10.19678/j.issn.1000-3428.0060601

摘要/Abstract

摘要： 针对非负张量分解应用于图像聚类时忽略了高维数据内部几何结构的问题，在经典的张量非负Tucker分解的基础上，添加超图正则项以尽可能多地保留原始数据的内在几何结构信息，提出一种基于超图正则化非负Tucker分解模型HGNTD。通过构造超图刻画数据内部样本间的高阶关系，提高几何结构描述的准确性，针对超图正则化非负张量分解模型，基于交替非负最小二乘法，设计快速有效的超图正则化非负Tucker分解算法求解所给模型，证明算法在非负的条件下是收敛的，最终将算法应用于图像聚类。在Yale和COIL两个常用公开数据集上的实验结果表明，相对于k-means、非负矩阵分解、图正则化非负矩阵分解、非负Tucker分解和图正则化非负Tucker分解等算法，超图正则化非负Tucker分解算法聚类准确度提升了8.6%~11.4%，归一化互信息提升了2.0%~7.5%，具有更好的聚类效果。

关键词: 非负张量分解, Tucker分解, 超图学习, 交替非负最小二乘法, 聚类分析

Abstract: The internal geometry structure of high-dimensional data is ignored when nonnegative tensor decomposition is applied to image clustering.To solve this problem, we propose a Hypergraph regularized Nonnegative Tucker Decomposition(HGNTD) model by adding a hypergraph regularization term to preserve the intrinsic geometric structure information of original data as much as possible.This method is based on the classical nonnegative Tucker decomposition of tensors.Specifically, relying on the hypergraph regularization non-negative tensor decomposition model and based on the Alternating Nonnegative Least Squares(ANLS), a fast and effective hypergraph regularized nonnegative tucker decomposition algorithm is designed to solve the given model.The new algorithm is proven to converge under nonnegative conditions, thereby, it is applied to image clustering.The experimental results on Yale and COIL-100 data sets show that, compared with k-means, Nonnegative Matrix Factorization(NMF), Graph regularized Nonnegative Matrix Factorization(GNMF), Nonnegative Tucker Decomposition(NTD), and Graph regularized Nonnegative Tucker Decomposition(GNTD) algorithms, the clustering accuracy of the new algorithm is improved by approximately 8.6%~11.4%, and the Normalized Mutual Information(NMI) is improved by approximately 2.0%~7.5%.Therefore, it can be said to have a better clustering effect.

Key words: nonnegative tensor decomposition, Tucker decomposition, hypergraph learning, alternating nonnegative least squares, clustering analysis

中图分类号:

TP391

陈璐瑶, 刘奇龙, 许云霞, 陈震. 基于超图正则化非负Tucker分解的图像聚类算法[J]. 计算机工程, 2022, 48(4): 197-205.

CHEN Luyao, LIU Qilong, XU Yunxia, CHEN Zhen. Image Clustering Algorithm Based on Hypergraph Regularized Nonnegative Tucker Decomposition[J]. Computer Engineering, 2022, 48(4): 197-205.

https://www.ecice06.com/CN/Y2022/V48/I4/197

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