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首页> 外文期刊>Mathematical Problems in Engineering >Extrinsic Least Squares Regression with Closed-Form Solution on Product Grassmann Manifold for Video-Based Recognition
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Extrinsic Least Squares Regression with Closed-Form Solution on Product Grassmann Manifold for Video-Based Recognition

机译：产品Grassmann流形上基于视频识别的外在最小二乘回归与闭式解

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摘要

Least squares regression is a fundamental tool in statistical analysis and is more effective than some complicated models with small number of training samples. Representing multidimensional data with product Grassmann manifold has recently led to notable results in various visual recognition tasks. This paper proposes extrinsic least squares regression with ProjectionMetric on product Grassmann manifold by embedding Grassmann manifold into the space of symmetric matrices via an isometric mapping. The proposed regression has closed-form solution which is more accurate compared with numerical solution of previous least squares regression using geodesic distance. Experiments on several recognition tasks show that the proposedmethod achieves considerable accuracy in comparison with some state-of-the-art methods.
机译：最小二乘回归是统计分析的基本工具，比一些训练样本少的复杂模型更有效。用产品Grassmann流形表示多维数据最近在各种视觉识别任务中产生了显著成果。本文通过等轴测图将Grassmann流形嵌入对称矩阵的空间中，在产品Grassmann流形上建议使用ProjectionMetric进行外在最小二乘回归。所提出的回归具有封闭形式的解，与使用测地距离的先前最小二乘回归的数值解相比，它更精确。在多个识别任务上的实验表明，与某些最新方法相比，该方法具有相当高的准确性。

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  • 来源
    《Mathematical Problems in Engineering》 |2018年第3期|6598025.1-6598025.7|共7页
  • 作者

    Wang Yuping; Wang Lichun; Kong Dehui; Yin Baocai;

  • 作者单位

    Beijing Univ Technol, Fac Informat Technol, Beijing Key Lab Multimedia & Intelligent Software, 100 Pingleyuan, Beijing 100124, Peoples R China;

    Beijing Univ Technol, Fac Informat Technol, Beijing Key Lab Multimedia & Intelligent Software, 100 Pingleyuan, Beijing 100124, Peoples R China;

    Beijing Univ Technol, Fac Informat Technol, Beijing Key Lab Multimedia & Intelligent Software, 100 Pingleyuan, Beijing 100124, Peoples R China;

    Beijing Univ Technol, Fac Informat Technol, Beijing Key Lab Multimedia & Intelligent Software, 100 Pingleyuan, Beijing 100124, Peoples R China;

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