Projective Incomplete Multi-View Clustering.

Due to the rapid development of multimedia technology and sensor technology, multi-view clustering (MVC) has become a research hotspot in machine learning, data mining, and other fields and has been developed significantly in the past decades. Compared with single-view clustering, MVC improves clustering performance by exploiting complementary and consistent information among different views. Such methods are all based on the assumption of complete views, which means that all the views of all the samples exist. It limits the application of MVC, because there are always missing views in practical situations. In recent years, many methods have been proposed to solve the incomplete MVC (IMVC) problem and a kind of popular method is based on matrix factorization (MF). However, such methods generally cannot deal with new samples and do not take into account the imbalance of information between different views. To address these two issues, we propose a new IMVC method, in which a novel and simple graph regularized projective consensus representation learning model is formulated for incomplete multi-view data clustering task. Compared with the existing methods, our method not only can obtain a set of projections to handle new samples but also can explore information of multiple views in a balanced way by learning the consensus representation in a unified low-dimensional subspace. In addition, a graph constraint is imposed on the consensus representation to mine the structural information inside the data. Experimental results on four datasets show that our method successfully accomplishes the IMVC task and obtain the best clustering performance most of the time. Our implementation is available at https://github.com/Dshijie/PIMVC.

Efficient Algorithm for Approximating Nash Equilibrium of Distributed Aggregative Games.

In this article, we aim to design a distributed approximate algorithm for seeking Nash equilibria (NE) of an aggregative game. Due to the local set constraints of each player, projection-based algorithms have been widely employed for solving such problems actually. Since it may be quite hard to get the exact projection in practice, we utilize inscribed polyhedrons to approximate local set constraints, which yields a related approximate game model. We first prove that the NE of the approximate game is the ϵ -NE of the original game and then propose a distributed algorithm to seek the ϵ -NE, where the projection is then of a standard form in quadratic optimization with linear constraints. With the help of the existing developed methods for solving quadratic optimization, we show the convergence of the proposed algorithm and also discuss the computational cost issue related to the approximation. Furthermore, based on the exponential convergence of the algorithm, we estimate the approximation accuracy related to ϵ . In addition, we investigate the computational cost saved by approximation in numerical simulation.