Karayiannis N B, Randolph-Gips M M
Dept. of Electr. and Comput. Eng., Univ. of Houston, TX, USA.
IEEE Trans Neural Netw. 2003;14(1):89-102. doi: 10.1109/TNN.2002.806951.
This paper presents the development of soft clustering and learning vector quantization (LVQ) algorithms that rely on multiple weighted norms to measure the distance between the feature vectors and their prototypes. Clustering and LVQ are formulated in this paper as the minimization of a reformulation function that employs distinct weighted norms to measure the distance between each of the prototypes and the feature vectors under a set of equality constraints imposed on the weight matrices. Fuzzy LVQ and clustering algorithms are obtained as special cases of the proposed formulation. The resulting clustering algorithm is evaluated and benchmarked on three data sets that differ in terms of the data structure and the dimensionality of the feature vectors. This experimental evaluation indicates that the proposed multinorm algorithm outperforms algorithms employing the Euclidean norm as well as existing clustering algorithms employing weighted norms.
本文介绍了基于多个加权范数来测量特征向量与其原型之间距离的软聚类和学习向量量化（LVQ）算法的发展。本文将聚类和LVQ表述为一个重新构造函数的最小化问题，该函数在对权重矩阵施加的一组等式约束下，采用不同的加权范数来测量每个原型与特征向量之间的距离。模糊LVQ和聚类算法是所提出公式的特殊情况。在三个特征向量的数据结构和维度不同的数据集上对所得聚类算法进行了评估和基准测试。该实验评估表明，所提出的多范数算法优于采用欧几里得范数的算法以及现有的采用加权范数的聚类算法。
