Improving Spectral Clustering with Deep Embedding and Cluster Estimation Spectral clustering is one of the most popular modern clustering algorithms. It is easy to implement, can be solved efficiently, and very often outperforms other traditional clustering algorithms such as kmeans. However, pectral clustering would be insufficient when dealing with most datasets which have complex statistical properties and quires the user to specify the number of clusters (called k). To address these two problems, in this paper, we propose an approach to extending spectral clustering with deep embedding and estimation of the number of clusters. Specifically, we first generate the deep embedding via learning a deep autoencoder, which transforms the raw data into the lower dimensional representations that suitable for clustering. We then provide an effective method to estimate the number of clusters by learning a softmax autoencoder from the deep embedding. We finally extend spectral clustering with the learned embedding and the estimated number. An extensive experimental study on several image and text datasets illustrates the effectiveness and efficiency of our approach.

Regularized NonNegative Spectral Embedding for Clustering Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix construction, lowdimensional embedding, and KMeans clustering as postprocessing), which may lead to suboptimal results because of the possible mismatch between different stages. In this paper, we propose an endtoend singlestage learning method to clustering called Regularized Nonnegative Spectral Embedding (RNSE) which extends Spectral Clustering with the adaptive learning of similarity matrix and meanwhile utilizes nonnegative constraints to facilitate onestep clustering (directly from data points to clustering labels). Two wellfounded methods, successive alternating projection and strategic multiplicative update, are employed to work out the quite challenging optimization problems in RNSE. Extensive experiments on both synthetic and realworld datasets demonstrate RNSEu0027s superior clustering performance to some stateoftheart competitors.