基于面积投影的分块鲁棒张量主成分分析算法
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天津理工大学

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Block Robust Tensor Principal Component Analysis based on Area Projection
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Tianjin University of Technology

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    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算法以投影距离最大为目标,忽略了误差张量,降低了算法的鲁棒性。为此,针对这些问题,本文提出了一种投影距离最大和重构误差最小双目标优化的面积投影模型,并基于面积投影模型提出了分块鲁棒张量主成分分析算法(Block TPCA with F -norm based on Area Projection, area-BTPCA-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六个彩色数据集进行实验验证,结果表明,本文所提算法在平均重构误差和分类率方面均得到了较好的提升,具有较强的鲁棒性。

    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. Due to the L1-norm lose the rotational invariance and the current TPCA algorithms but only consider the maximum projection distance, ignoring the error tensor, which reduces the robustness of the algorithms. Thus, to address these issues, this paper proposes a dual-objective optimization for maximizing projection distance and minimizing reconstruction error in an area projection model. And then, the area-BTPCA-F algorithm is proposed. The block reorganization processing also significantly improves the robustness of the algorithm against noise. Finally, experiments on six color datasets with different noise validate the proposed algorithm, showing improvements in average reconstruction error and classification rate. The algorithm demonstrates strong robustness.

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  • 收稿日期:2023-08-02
  • 最后修改日期:2023-09-08
  • 录用日期:2023-09-19
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