基于块的二维核四元数主成分分析

doi:10.13190/j.jbupt.2018-045

北京邮电大学学报 ›› 2019, Vol. 42 ›› Issue (1): 53-60.doi: 10.13190/j.jbupt.2018-045

基于块的二维核四元数主成分分析

陈北京^1,2,3, 杨建浩³, 范春年^1,3, 苏庆堂⁴, 王定成^1,3

1. 南京信息工程大学江苏省网络监控工程中心, 南京 210044;
2. 南京信息工程大学江苏省大气环境与装备技术协同创新中心, 南京 210044;
3. 南京信息工程大学计算机与软件学院, 南京 210044;
4. 鲁东大学信息与电气工程学院, 烟台 264025

收稿日期:2018-03-20 出版日期:2019-02-28 发布日期:2019-03-08
作者简介:陈北京(1981-),男,副教授,博士生导师,E-mail:nbutimage@126.com.
基金资助:
国家自然科学基金项目（61572258，61772281，61602253，61672294）；江苏高校优势学科建设工程项目（PAPD）；江苏高校"青蓝工程"项目；江苏省自然科学基金项目（17KJB520021）

Block-Wise Two Dimensional Kernel Quaternion Principal Component Analysis

CHEN Bei-jing^1,2,3, YANG Jian-hao³, FAN Chun-nian^1,3, SU Qing-tang⁴, WANG Ding-cheng^1,3

1. Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science and Technology, Nanjing 210044, China;
2. Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China;
3. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, China;
4. School of Information and Electrical Engineering, Ludong University, Yantai 264025, China

Received:2018-03-20 Online:2019-02-28 Published:2019-03-08

摘要/Abstract

摘要： 核四元数主成分分析（KQPCA）被成功应用于处理非线性四元数信号，然而，核矩阵维数太高使其对角化非常耗时，目前二维形式的KQPCA（2DKQPCA）并没有成功实现.对此，采用基于块处理和并行计算的思想，提出基于块的2DKQPCA（B2DKQPCA），实现真正意义上的2DKQPCA.基于时间复杂度、应用性能和分块矩阵应为四元数Hermitian矩阵的综合考虑，B2DKQPCA重点处理主对角线、反对角线和主对角线旁3个方向的小块.然后，结合B2DKQPCA与RGB-D图像四元数表示方法，将B2DKQPCA应用于RGB-D目标识别领域.在2个公开库上的实验结果表明，提出的基于列向B2DKQPCA的RGB-D识别算法优于现有基于主成分分析算法和基于卷积神经网络的一些算法.

关键词: 核主成分分析, 四元数, 彩色图像, RGB-D目标识别

Abstract: Currently, kernel quaternion principal component analysis (KQPCA) has been proposed and successfully applied to process linear quaternion signals. However, two dimensional version of KQPCA (2DKQPCA) has not been successfully implemented due to the quite time-consuming problem for diagonalizing the high dimensional kernel matrix. So, using the block-based idea and the parallel computing idea, the block-wise 2DKQPCA (B2DKQPCA) is proposed to implement 2DKQPCA really. After the overall consideration of computational complexity, application performance and quaternion Hermitian block, B2DKQPCA mainly processes the blocks of three directions:main-diagonal direction, anti-diagonal direction and side-diagonal direction. Then, B2DKQPCA is applied into RGB-D object recognition by combining B2DKQPCA and quaternion representation of RGB-D images. Experimental results on two publicly available datasets demonstrate that the proposed RGB-D object recognition algorithm based on the column direction B2DKQPCA outperforms some existing algorithms using principal component analysis and some existing algorithms using convolutional neural network.

Key words: kernel principal component analysis, quaternion, color image, RGB-D object recognition

中图分类号:

TN911.22

陈北京, 杨建浩, 范春年, 苏庆堂, 王定成. 基于块的二维核四元数主成分分析[J]. 北京邮电大学学报, 2019, 42(1): 53-60.

CHEN Bei-jing, YANG Jian-hao, FAN Chun-nian, SU Qing-tang, WANG Ding-cheng. Block-Wise Two Dimensional Kernel Quaternion Principal Component Analysis[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2019, 42(1): 53-60.

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基于块的二维核四元数主成分分析

Block-Wise Two Dimensional Kernel Quaternion Principal Component Analysis

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