基于块的二维核四元数主成分分析

Block-Wise Two Dimensional Kernel Quaternion Principal Component Analysis

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.

Currently,kernel quaternion principal component analysis(KQPCA)has been proposed and successfully applied to process linear quaternion signals.However,two dimensional version of KQPCA(2 DKQPCA)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 2 DKQPCA(B2 DKQPCA)is proposed to implement 2 DKQPCA really.After the overall consideration of computational complexity,application performance and quaternion Hermitian block,B2 DKQPCA mainly processes the blocks of three directions:main-diagonal direction,anti-diagonal direction and side-diagonal direction.Then,B2 DKQPCA is applied into RGB-D object recognition by combining B2 DKQPCA 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 B2 DKQPCA outperforms some existing algorithms using principal component analysisand some existing algorithms using convolutional neural network.