利用左Gram矩阵对高维数据进行聚类
Using the left Gram matrix to cluster high dimensional data
摘要：
对于高维数据，N个对象（P >> N）的P个特征表示在一个N × P矩阵X中，我们描述了一种基于归一化左Gram矩阵G = XX '/P的聚类算法。在一定的正则条件下，G中对应于同一类中对象的行收敛到同一个均值向量。通过对行均值进行聚类，该算法不需要通过降维或特征选择技术进行预处理，也不需要调整或超参数值的规范。因为它基于NxN矩阵G，所以它比许多基于聚类特征矩阵X的方法具有更低的计算成本。当与应用于32个基准微阵列数据集的14个其他聚类算法相比时，所提出的算法提供了对底层聚类配置的最准确估计，其最接近的竞争对手的两倍多。
英文摘要：
For high dimensional data, where P features for N objects (P >> N) are represented in an NxP matrix X, we describe a clustering algorithm based on the normalized left Gram matrix, G = XX'/P. Under certain regularity conditions, the rows in G that correspond to objects in the same cluster converge to the same mean vector. By clustering on the row means, the algorithm does not require preprocessing by dimension reduction or feature selection techniques and does not require specification of tuning or hyperparameter values. Because it is based on the NxN matrix G, it has a lower computational cost than many methods based on clustering the feature matrix X. When compared to 14 other clustering algorithms applied to 32 benchmarked microarray datasets, the proposed algorithm provided the most accurate estimate of the underlying cluster configuration more than twice as often as its closest competitors.
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