基于面积投影的分块鲁棒张量主成分分析算法
Block robust tensor principal component analysis based on area projection
张晓敏 1张超 2石乐岩 1王肖锋3
作者信息
- 1. 天津理工大学天津市先进机电系统设计与智能控制重点实验室,天津 300384
- 2. 彼合彼方机器人(天津)有限公司,天津 300401
- 3. 天津理工大学天津市先进机电系统设计与智能控制重点实验室,天津 300384;天津理工大学机电工程国家级实验教学示范中心,天津 300384
- 折叠
摘要
张量主成分分析算法(tensor principal component analysis,TPCA)作为一种旨在以低维子空间表征高维张量数据的数据降维算法,在多个机器学习领域得到了广泛的应用.由于L1范数丢失了 F范数的旋转不变性,且目前现有的TPCA算法采用单一优化任务,即仅优化投影距离忽略了误差张量的优化任务,因此即使这些算法具有一定程度的鲁棒性,但是仍然表现较弱.为了进一步克服单一优化任务带来的缺陷并且继续保持原有算法具有的性质,在本文中提出了一种多重任务优化的比值型模型.该模型受直角三角形面积公式的启发,通过优化斜边上的高来实现投影距离最大和重构误差最小的多重任务优化,称为面积投影模型.然后本文在此面积投影模型的基础上,采用了 一种分块重组的预处理技术进而提出了分块鲁棒张量主成分分析算法(block tensor PCA with F-norm based on area projection,area-BT PC A-F).该算法不仅保留了 旋转不变性,同时充分考虑了误差张量;针对噪声信息,分块重组处理也大大提升了算法的鲁棒性.最后,通过对含有不同噪声比例的6个彩色数据集进行实验验证,平均重构误差(average reconstruction er-ror,ARCE)实验和分类率实验的结果表明,所提算法相比其他现有TPCA算法而言具有较强的鲁棒性,性能得到了明显的提升.
Abstract
Tensor principal component analysis(TPCA),as a data dimensionality reduction algorithm aimed at representing high-dimensional tensor data in low dimensional subspaces,has been widely applied in multiple machine learning fields.However,the L1-norm loses the rotation invariance and the existing TPCA algorithms adopt a single optimization objective,which only optimizes the projection distances and ignores the optimization of the error tensors.Thus,even though these algorithms have a certain degree of robustness,they still perform weakly.To address these issues,this paper proposes a ratio model for dual-objective optimization.This model is inspired by the formula for the area of a right-angled triangle,which optimizes the height on the hypotenuse to achieve dual-objective optimization with maximum projection distances and minimum reconstruction errors,called the area projection model.Then,based on the projection model,this article adopts a preprocessing technique of blocking recombination and proposes a block tensor PCA with F-norm based on area projection(area-BTPCA-F)algorithm.This algorithm not only preserves rotation invariance,but also fully considers error tensors.In response to noise information,blocking recombination technique has greatly improved the robustness of the algorithm.Finally,experiments on six color datasets with different noise validate the proposed algorithm,showing improvements in average reconstruction error(ARCE)and classification rate.The algorithm demonstrates strong robustness compared to other existing TPCA algorithms.
关键词
张量主成分分析(TPCA)/鲁棒性/特征提取/人脸识别Key words
tensor principal component analysis(TPCA)/robustness/feature extraction/face recogni-tion引用本文复制引用
基金项目
国家重点研发计划(2018AA0103004)
天津市科技计划重大专项(20YFZCGX00550)
出版年
2024
NETL
NSTL
万方数据