压缩谱聚类
Compressive Spectral Clustering
摘要：
谱聚类由于其在许多情况下的高性能而成为一种流行的技术。它包括三个主要步骤：创建N个对象之间的相似性图进行聚类，计算其拉普拉斯矩阵的前k个特征向量以定义每个对象的特征向量，并对这些特征运行k-均值以将对象分成k个类。对于大的N和/或k，这三个步骤中的每一个都变得计算密集。我们建议加快最后两个步骤的基础上，在新兴领域的图形信号处理：图形过滤的随机信号，和随机采样的带限图形信号。我们证明，我们的方法，在计算时间的增益，可以达到几个数量级，实际上是一个近似的谱聚类，我们能够控制的错误。我们测试我们的方法在人工和真实世界的网络数据的性能。
英文摘要：
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features to separate objects into k classes. Each of these three steps becomes computationally intensive for large N and/or k. We propose to speed up the last two steps based on recent results in the emerging field of graph signal processing: graph filtering of random signals, and random sampling of bandlimited graph signals. We prove that our method, with a gain in computation time that can reach several orders of magnitude, is in fact an approximation of spectral clustering, for which we are able to control the error. We test the performance of our method on artificial and real-world network data.
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