Abstract We introduce an approach to divisive hierarchical clustering that is capable of identifying clusters in nonlinear manifolds. This approach uses the isometric mapping (Isomap) to recursively embed (subsets of) the data in one dimension, and then performs a binary partition designed to avoid the splitting of clusters. We provide a theoretical analysis of the conditions under which contiguous and high-density clusters in the original space are guaranteed to be separable in the one-dimensional embedding. To the best of our knowledge there is little prior work that studies this problem. Extensive experiments on simulated and real data sets show that hierarchical divisive clustering algorithms derived from this approach are effective.

中文翻译：

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聚类的非线性降维

摘要 我们介绍了一种分裂层次聚类方法，该方法能够识别非线性流形中的聚类。这种方法使用等距映射（Isomap）在一维中递归地嵌入数据（的子集），然后执行旨在避免聚类分裂的二进制分区。我们对保证原始空间中连续和高密度集群在一维嵌入中可分离的条件进行了理论分析。据我们所知，研究这个问题的先前工作很少。对模拟和真实数据集的大量实验表明，从这种方法派生的分层分裂聚类算法是有效的。