EGGS: Eigen-Gap Guided Search For Automated Spectral Clustering

The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong experience and lead to difficulty in real applications especially when the inter-cluster similarity is high or/and the dataset is large. In addition, we often need to choose different AMC methods for different datasets, which still depends on experience. To solve these two challenging problems, in this paper, we present a simple yet effective method for automated spectral clustering. The main idea is to find the most reliable affinity matrix among a set of candidates given by different AMC methods with different hyperparameters, where the reliability is quantified by the \textit{relative-eigen-gap} of graph Laplacian introduced in this paper. We also implement the method using Bayesian optimization.We extend the method to large-scale datasets such as MNIST, on which the time cost is less than 90s and the clustering accuracy is state-of-the-art. Extensive experiments of natural image clustering show that our method is more versatile, accurate, and efficient than baseline methods.