L(r,c)非负矩阵分解用于图像聚类
L(r,c) Nonnegative Matrix Factorization for Image Clustering
DOI: 10.12677/AAM.2023.123133, PDF,   
作者: 陈运川：贵州师范大学，数学科学学院，贵州 贵阳
关键词: 非负矩阵分解；聚类；L(r；c)函数；鲁棒性；Non-Negative Matrix Factorization； Clustering； L(r；c) Function； Robustness
摘要: 在非负矩阵分解用于聚类的过程中，将每一张大小为r × c灰度图像按列重排成一个样本向量会改变图像数据原有的空间结构，而目标函数直接度量样本向量与重构向量之间的误差会进一步忽略原始图像与重构后图像列之间的相似度。因此，为降低图像数据空间结构的改变对聚类效果的不利影响，本文提出了一种新的损失函数来逐列度量原始图像数据与重构后的图像数据间的误差，并推导了相应的数值算法。数值实验结果表明本文提出的算法有更好的聚类表现，图像表示能力更强。
Abstract: In the process of non-negative matrix factorization for clustering, rearranging each grayscale image with size r × c into a sample vector will change the original spatial structure of the image data, and the objective function directly measures the error between the sample vector and the reconstruc-tion vector to further ignore the similarity between the original image and the reconstructed image column. Therefore, in order to reduce the adverse effect of the change of spatial structure of image data on the clustering effect, a new loss function is proposed to measure the error between the original image data and the reconstructed image data column-by-column, and the corresponding numerical algorithm is derived. Numerical experimental results show that the proposed algorithm has better clustering performance and stronger image representation ability.
文章引用：陈运川. L(r,c)非负矩阵分解用于图像聚类[J]. 应用数学进展, 2023, 12(3): 1306-1316. https://doi.org/10.12677/AAM.2023.123133

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