一种基于基的曲面聚类方法
A Basis Approach to Surface Clustering
摘要：
提出了一种新的曲面聚类方法。该提案涉及首先使用张量积中的基函数来平滑数据，从而将维度减少到有限数量的系数，然后使用这些估计的系数通过k-means算法对表面进行聚类。扩展的算法聚类张量进行了讨论。我们表明，所提出的算法表现出强一致性的属性，有或没有测量误差，在正确的聚类数据的样本量增加。仿真研究表明，该方法优于基准的k-means算法，使用原始矢量化的数据。最后，以EGG的实际数据为例说明了该方法的实际应用。
英文摘要：
This paper presents a novel method for clustering surfaces. The proposal involves first using basis functions in a tensor product to smooth the data and thus reduce the dimension to a finite number of coefficients, and then using these estimated coefficients to cluster the surfaces via the k-means algorithm. An extension of the algorithm to clustering tensors is also discussed. We show that the proposed algorithm exhibits the property of strong consistency, with or without measurement errors, in correctly clustering the data as the sample size increases. Simulation studies suggest that the proposed method outperforms the benchmark k-means algorithm which uses the original vectorized data. In addition, an EGG real data example is considered to illustrate the practical application of the proposal.
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