摘要
"距离"是科学研究与工程技术领域中使用非常广泛的一种度量.在分析各种距离优、缺点的基础上,根据马氏距离不受量纲影响,能描述和处理相关性数据的性能优势,利用加权Moore-Penrose(WMP)广义逆定义了WMP马氏距离,并通过奇异值分解及矩阵的谱分解理论构造其数学形式和计算方法.理论分析和仿真实验表明,所提出的方法不仅保持了马氏距离和MP马氏距离的优点,而且克服了它们的缺点,同时又具有更好的独特性能.
Distance is a widely used measure in engineering and researching field.The advantages and disadvantages of some distances are analyzed in Euclidean space.Because the Mahalanobis distance is influenced by the dimension and it has great performance of dealing with related data,the weighted Moore-Penrose（WMP） Mahalanobis distance is defined according to WMP pseudoinverse,whose formula is given by singular value decomposition（SVD） and spectral decomposition of matrices.The academic analysis and simulation show that it not only overcomes the disadvantages of non-existence in Mahalanobis distance,but has its own special performances.
出处
《控制与决策》
EI
CSCD
北大核心
2012年第11期1706-1710,共5页
Control and Decision
基金
浙江省重大科技计划项目(2009C11024)
