Learning A Self-expressive Network For Scalable Subspace Clustering

Subspace clustering are a class of effective methods used to deal with high-dimensional data clustering problems.These methods use subspaces to model the clustering structure in high-dimensional data.They assume that data points are distributed in several different low-dimensional subspaces and achieve the purpose of clustering by dividing the data points into the subspaces to which they belong.Current subspace clustering methods are usually based on the self-expressive model and spectral clustering.They first utilize the self-expressive model to solve the selfexpressive coefficient matrix,and then obtain the data affinity matrix as the input of the spectral clustering.However,the computational complexity of solving the self-expressive model and running the spectral clustering algorithm is relatively high.Moreover,both self-expressive model and spectral clustering are transductive methods,which do not have generalizability and cannot handle out-of-sample data points efficiently.To deal with these deficiencies,this thesis proposes the following two innovative works:Firstly,this thesis proposes a self-expressive network(SENet),which re-parameterizes the self-expressive model by a specificly designed neural network.The proposed network can predict the self-expressive coefficients with subspace-preserving property,and the trained network can generalize to out-of-sample data.Experiments on synthetic datasets and real datasets verify the effectiveness of the proposed network.Secondly,in replacement of the spectral clustering algorithm,this thesis proposes a subspace classification network(SCN)to produce clustering results as an alternative of the spectral clustering process in the self-expressive model based subspace clustering algorithms.A trained SCN is able to take a single datapoint as input and directly output its clustering result.The training process of this network utilizes the highconfidence positive data pairs mined from the prediction of SENet by Topk filtering.And it also relies on a nuclear norm regularizer to prevent network degradation.Experiments on real datasets verify the generalizability and effectiveness of the proposed network.