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“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 the field of scientific research and engineering.On the basis of analyzing the advantages and disadvantages of various distances and according to the fact that the Mahalanobis distance is not influenced by the dimension, the correlation data can be described and processed The WMP Mahalanobis distance is defined by the generalized inverse of the weighted Moore-Penrose (WMP), and its mathematical form and calculation method are constructed through the singular value decomposition and matrix spectral decomposition theory.Theoretical analysis and simulation results show that the proposed WMP The method not only maintains the advantages of Mahalanobis distance and MP Mahalanobis distance, but also overcomes their shortcomings and at the same time has better unique properties.