拉格朗日多项式逻辑回归分类算法并行计算优化

摘要

针对拉格朗日多项式逻辑回归算法中逻辑回归参数计算复杂高、耗时长，直接制约其在大数据量遥感图像上应用的问题，提出了基于图形处理器 GPU 对算法进行数据级并行计算处理。算法首先利用已知的训练样本进行多元回归参数估算，然后利用得到的回归参数和光谱数据进行分类，能够获得较高的分类精度，其中算法步骤中的矩阵乘法、矩阵求逆、矩阵特征值计算采用 CULA 库函数并行实现。利用真实场景的高光谱图像对文中提出的并行计算优化方案实验验证，结果表明，该方法能够实现对多元回归参数计算加速200倍左右，对整个拉格朗日多项式逻辑回归分类算法计算加速60倍左右。%Since the computation of regression coefficient of the lagrange multinomial logistic regression algorithm (LORSAL)is time consuming,which make it very hard to apply on large data sets.In this paper,we present parallel optimization of LORSAL algorithm for remote sensing image classification based on GPU.Firstly,the LORSAL estimates the regression coefficient based on labeled training samples.Secondly,it performs classification with the priori regression coefficient and spectral data,which makes it have a relative high accuracy for hyperspectral remote sensing classification.Meanwhile,the CULA routines are used for matrix multiplication,matrix inversion and eigenvalue calculation.The proposed parallel optimization is tested with real hyperspectral remote sensing images.Results show that the computation speed of the proposed method can obtain 200 times for regression coefficient calculation and 60 times for the whole algorithm when compared with the CPU part,respectively.The optimization schemes make it possible for large volume image classification with LORSAL algorithm.