Accelerated Sparse Subspace Clustering

State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in practice while the performance of OMP-based schemes are unsatisfactory, especially in settings where data points are highly similar. In this paper, we propose a novel algorithm that exploits an accelerated variant of orthogonal least-squares to efficiently find the underlying subspaces. We show that under certain conditions the proposed algorithm returns a subspace-preserving solution. Simulation results illustrate that the proposed method compares favorably with BP-based method in terms of running time while being significantly more accurate than OMP-based schemes

Accelerated Sampling of Bandlimited Graph Signals

We study the problem of sampling and reconstructing bandlimited graph signals where the objective is to select a subset of nodes of pre-specified cardinality that ensures interpolation of the original signal with the lowest possible reconstruction error. First, we consider a non-Bayesian scenario and propose an efficient iterative sampling procedure that in the noiseless case enables exact recovery of the original signal from the set of selected nodes. In the case of noisy measurements, a bound on the reconstruction error of the proposed algorithm is established. Then, we consider the Bayesian scenario where we formulate the sampling task as the problem of maximizing a monotone weak submodular function, and propose a randomized-greedy algorithm to find a sub-optimal subset. We derive a worst-case performance guarantee on the mean-square error achieved by the randomized-greedy algorithm for general non-stationary graph signals. The efficacy of the proposed methods is illustrated through extensive numerical simulations on synthetic and real-world graphs.Comment: arXiv admin note: text overlap with arXiv:1807.0718

Evolutionary Self-Expressive Models for Subspace Clustering

The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points that lie on a union of low-dimensional evolving subspaces. To learn the parsimonious representation of the data points at each time step, we propose a non-convex optimization framework that exploits the self-expressiveness property of the evolving data while taking into account representation from the preceding time step. To find an approximate solution to the aforementioned non-convex optimization problem, we develop a scheme based on alternating minimization that both learns the parsimonious representation as well as adaptively tunes and infers a smoothing parameter reflective of the rate of data evolution. The latter addresses a fundamental challenge in evolutionary clustering -- determining if and to what extent one should consider previous clustering solutions when analyzing an evolving data collection. Our experiments on both synthetic and real-world datasets demonstrate that the proposed framework outperforms state-of-the-art static subspace clustering algorithms and existing evolutionary clustering schemes in terms of both accuracy and running time, in a range of scenarios

LSTM-Assisted Evolutionary Self-Expressive Subspace Clustering

Massive volumes of high-dimensional data that evolves over time is continuously collected by contemporary information processing systems, which brings up the problem of organizing this data into clusters, i.e. achieve the purpose of dimensional deduction, and meanwhile learning its temporal evolution patterns. In this paper, a framework for evolutionary subspace clustering, referred to as LSTM-ESCM, is introduced, which aims at clustering a set of evolving high-dimensional data points that lie in a union of low-dimensional evolving subspaces. In order to obtain the parsimonious data representation at each time step, we propose to exploit the so-called self-expressive trait of the data at each time point. At the same time, LSTM networks are implemented to extract the inherited temporal patterns behind data in an overall time frame. An efficient algorithm has been proposed based on MATLAB. Next, experiments are carried out on real-world datasets to demonstrate the effectiveness of our proposed approach. And the results show that the suggested algorithm dramatically outperforms other known similar approaches in terms of both run time and accuracy