Convolutional Manifold Clustering Network

In many real-world applications such as image and video processing,we need to deal with a large amount of high-dimensional data.Such data can often be well approximated by a union of multiple low-dimensional manifolds,where each manifold corresponds to a class or a category.In such cases,it is important to segment the data into multiple groups where each group contains data points from the same manifold.This problem is known as manifold clustering and has become an important topic in unsupervised learning.However,the nonlinear assumption of manifold clustering task and the complex distribution of the manifold topological data make it a challenging problem.Besides,the related work has some problems,such as poor clustering accuracy,need for further fine tuning of the tradeoff parameters,and lack of theoretical justification.Aiming at these problems above,this thesis proposes an efficient approach for manifold clustering,called Local Convex Representation(LCR),in which each data point is represented as a convex combination of other points in the local neighborhood using the local linearity of manifolds.Under some mild conditions,the nonzero coefficients are guaranteed to correspond to the data points lying on the same manifold.Furthermore,the intrinsic dimension estimation of manifolds is introduced for pruning the minor nonzero coefficients to obtain more accurate clustering results Experiments on synthetic data as well as real world data demonstrate promising performance.In addition,with the advantage of multi-level feature learning of deep convolutional network,a deep feature learning-based method combining the stacked convolutional auto-encoders with our proposed manifold clustering algorithm is presented.By introducing the local convex representation coefficients to provide local distance preserving information,a deep version of manifold clustering algorithm named Convolutional Manifold Clustering Network,is implemented.Experiments show its effectiveness.