Network data appears in very diverse applications, like biological, social, or sensor networks. Clustering of network nodes into categories or communities has thus become a very common task in machine learning and data mining. Network data comes with some information about the network edges. In some cases, this network information can even be given with multiple views or layers, each one representing a different type of relationship between the network nodes. Increasingly often, network nodes also carry a feature vector. We propose in this paper to extend the node clustering problem, that commonly considers only the network information, to a problem where both the network information and the node features are considered together for learning a clustering-friendly representation of the feature space. Specifically, we design a generic two-step algorithm for multilayer network data clustering. The first step aggregates the different layers of network information into a graph representation given by the geometric mean of the network Laplacian matrices. The second step uses a neural net to learn a feature embedding that is consistent with the structure given by the network layers. We propose a novel algorithm for efficiently training the neural net via gradient descent, which encourages the neural net outputs to span the leading eigenvectors of the aggregated Laplacian matrix, in order to capture the pairwise interactions on the network, and provide a clustering-friendly representation of the feature space. We demonstrate with an extensive set of experiments on synthetic and real datasets that our method leads to a significant improvement w.r.t. state-of-the-art multilayer graph clustering algorithms, as it judiciously combines nodes features and network information in the node embedding algorithms.

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OrthoNet：多层网络数据群集

网络数据出现在非常多样化的应用程序中，例如生物，社会或传感器网络。因此，将网络节点聚类为类别或社区已成为机器学习和数据挖掘中非常普遍的任务。网络数据附带一些有关网络边缘的信息。在某些情况下，甚至可以为该网络信息提供多个视图或层，每个视图或层代表网络节点之间关系的不同类型。网络节点也越来越多地带有特征向量。我们在本文中提出将通常只考虑网络信息的节点聚类问题扩展到网络信息和节点特征都被一起考虑以学习特征空间的聚类友好表示的问题。特别，我们设计了一种用于多层网络数据聚类的通用两步算法。第一步，将网络信息的不同层聚合为由网络拉普拉斯矩阵的几何平均值给出的图形表示。第二步使用神经网络学习与网络层给出的结构一致的特征嵌入。我们提出了一种通过梯度下降有效训练神经网络的新算法，该算法鼓励神经网络输出跨越聚合拉普拉斯矩阵的前导特征向量，以捕获网络上的成对相互作用，并提供聚类友好表示特征空间。我们通过在合成数据集和真实数据集上进行的大量实验证明，我们的方法可以显着改善WRT