摘要
针对现有模式判别分析方法中普遍存在的子空间优化与"小样本"问题,首先剖析总体、类内以及类间三种散布矩阵的零空间的物理含义,深入阐释有效零空间与有效线性判别零空间核心原理;其次,研究始空间中总体、类间散布矩阵与有效零空间、有效值域空间上的总体、类间散布矩阵关于特征值与特征向量之间的关联关系,并且获取类内散布矩阵零空间、值域空间上关于Fisher线性判别率的关键结论;最后,基于有效线性判别零空间理论,设计出一种改进的线性判别子空间模式识别算法,即I-VLDNS。通过相关数据集模拟实验表明,I-VLDNS算法在模式识别分析性能、精确度以及鲁棒性上均得到进一步优化与提高。
In light of the problems of subspace optimisation and 'small sample size'commonly existed in current pattern discriminative analysis methods,in this paper we first analyse the physical meaning of null-space of total scatter matrix,between-class scatter matrix and within-class scatter matrix,and thoroughly explain the core principles of valid null-space and valid linear discriminative null-space. Secondly,we study the association relationship of eigenvalues and eigenvectors with regard to the total scatter matrixes and between-class scatter matrixes of both the original space and the valid null-space and valid range-space,and obtain the key conclusions about Fisher linear discriminative probability of within scatter matrix null-space and within scatter matrix range-space. Finally,based on effective linear discriminative null-space theory,we design an improved linear discriminative subspace pattern recognition algorithm( I-VLDNS). It is demonstrated through correlated dataset simulation experiments that the I-VLDNS gains further optimisation and improvement in analysis performance of pattern recognition,accuracy and robustness.
出处
《计算机应用与软件》
CSCD
2016年第7期172-175,208,共5页
Computer Applications and Software
基金
国家自然科学基金项目(70861001)
广西高等学校立项科研项目(2013LX095)
