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Jayanta Mukherjee 《Pattern recognition letters》2011,32(6):824-831
In this work, we propose a new class of distance functions called weighted t-cost distances. This function maximizes the weighted contribution of different t-cost norms in n-dimensional space. With proper weight assignment, this class of function also generalizes m-neighbor and octagonal distances. A non-strict upper bound (denoted as Ru in this work) of its relative error with respect to Euclidean norm is derived and an optimal weight assignment by minimizing Ru is obtained. However, it is observed that the strict upper bound of weighted t-cost norm may be significantly lower than Ru. For example, an inverse square root weight assignment leads to a good approximation of Euclidean norm in arbitrary dimension. 相似文献