学习特征权值对K-均值聚类算法的优化

K-均值(K—means)算法聚类的结果依赖于距离度量的选取．传统的K-均值算法选择的相似性度量通常是欧几里德距离的倒数，这种距离通常涉及所有的特征．在距离公式中引入一些特征权参数后，其聚类结果将依赖于这些权值，从而可以通过调整这些权值优化聚类效果．由于K-均值算法是迭代算法，很难直接确定其权值以优化聚类结果，因此提出了一种间接的学习权值算法以改进聚类结果．从数学意义上讲，这种权值学习相当于欧氏空间中对一组点进行了一个线性变换．数值实验证实了算法的有效性．

Optimization of K-means Clustering by Feature Weight Learning

The performance of K-means clustering algorithm depends on the selection of distance metrics. The Euclidean distance is usually chosen as the similarity measure in the conventional K-means clustering algorithm, which usually relates to all attributes. When feature weight parameters are introduced to the distance formula, the performance will depend on the weight values and accordingly can be improved by adjusting weight values. Since K-means algorithm is iterative, it is difficult to optimize clustering results by giving weight values directly. An indirect learning feature weight algorithm is introduced to improve the clustering result. Mathematically it corresponds to a linear transformation for a set of points in the Euclidean space. The numerical experiments prove the validity of this algorithm.