一种新的求解零空间线性鉴别分析的快速算法

A Novel and Fast Scheme for Null Space Based Linear Discriminant Analysis

利用随机矩阵相乘是最近提出的一种求解零空间线性鉴别分析的算法,但是此算法需要对一个n×n的矩阵进行特征值分解(n指的是训练样本数),使得其算法复杂度依然较高。为了进一步提高零空间线性鉴别分析算法的求解速度,本文提出了一种新的利用随机矩阵相乘的求解零空间线性鉴别分析的快速算法。本文的算法不需要对n×n的矩阵进行特征值分解,使得其算法复杂度比现有的零空间线性鉴别分析求解算法要低得多。理论分析和在人脸数据库上的实验表明,本文算法的计算速度远比现有的零空间线性鉴别分析求解算法要快,但是其识别率与现有的零空间线性鉴别分析求解算法相同。

Recently, a scheme for null space based linear discriminant analysis using random matrix multiplication （NSLDA/RMM） is proposed. The computational complexity of NSLDA/RMM is still relatively high since it need compute the eigenvalue decomposition of an nxn matrix, where n is the number of the training samples. To improve the efficiency of null space based linear discriminant analysis further, we present a new and fast scheme for null space based linear discriminant analysis using random matrix multiplication （FNSLDA/RMM）. FNSLDA/RMM need not compute the eigenvalue decomposition of an n-n matrix. Then the computational complexity of FNSLDA/RMM is much lower than those of the existing schemes for null space based linear discriminant analysis. Theoretical analysis of computational complexity and experiments on face database demonstrate that FNSLDA/RMM is much more efficient than the existing schemes for null space based linear discriminant analysis, but the recognition rates of FNSLDA/RMM and the existing schemes for null space based linear discriminant analysis are the same