Hierarchical Information Clustering by Means of Topologically Embedded Graphs

We introduce a graph-theoretic approach to extract clusters and hierarchies in complex data-sets in an unsupervised and deterministic manner, without the use of any prior information. This is achieved by building topologically embedded networks containing the subset of most significant links and analyzing the network structure. For a planar embedding, this method provides both the intra-cluster hierarchy, which describes the way clusters are composed, and the inter-cluster hierarchy which describes how clusters gather together. We discuss performance, robustness and reliability of this method by first investigating several artificial data-sets, finding that it can outperform significantly other established approaches. Then we show that our method can successfully differentiate meaningful clusters and hierarchies in a variety of real data-sets. In particular, we find that the application to gene expression patterns of lymphoma samples uncovers biologically significant groups of genes which play key-roles in diagnosis, prognosis and treatment of some of the most relevant human lymphoid malignancies.我们提出一种图论方法，能够以无监督且确定性的方式，无需任何先验信息，从复杂数据集内提取簇结构与层级关系。该方法通过构建包含最显著连接子集的拓扑嵌入网络，并对网络结构进行分析来实现上述目标。针对平面嵌入场景，该方法可同时提供簇内层级与簇间层级：前者描述簇的内部构成方式，后者阐释簇之间的聚合规律。我们首先通过多个人工数据集对该方法的性能、鲁棒性与可靠性进行验证，结果表明其性能显著优于其他已确立的主流方法。随后我们将该方法应用于多种真实数据集，证明其可有效识别出其中具备实际意义的簇与层级结构。具体而言，我们将该方法应用于淋巴瘤样本的基因表达谱分析时，发现了一批具有重要生物学意义的基因簇，这些基因簇在部分临床相关的人类淋巴系统恶性肿瘤的诊断、预后与治疗中发挥关键作用。