Research On Multi-manifold Learning Algorithm For High Dimensional Data

Manifold learning is an important research direction in the field of machine learning and data mining.The purpose of the research is to reveal the intrinsic low dimensional structure hidden in the high dimensional data set,so as to be able to reconstruct for data visualization and reduce the dimension of nonlinear data.Classical manifold learning algorithms always assume the high-dimensional data in a single batch manifold,but in reality,the complex data can not be a one-time acquisition,and mostly exist in a number of different manifolds,there may be serious overlap between these manifolds.So it is an important task in manifold learning to study the multi-manifold decomposition and incremental learning of multi-manifold data.In this paper,we study the problem of the incremental learning of the well-separated multi-manifolds with same intrinsic dimension and the decomposition of the intersecting multi-manifold,the main contents are as follows:(1)An incremental learning algorithm IMM-ISOMAP for well-separated multi-manifolds with same intrinsic dimension is proposed in view of the present multi-manifold decomposition algorithm which does not generally have the incremental ability.Firstly,dynamic neighborhood algorithm to calculate each new sample of neighborhood information,and then combined with the original submanifolds information,the new samples will be divided into the new submanifold in an extended way,only modify the critical path is affected in the new submanifold,the incremental calculation processing to avoid recalculate all the neighborhood relationship,at the same time we can detect and deal with the "short circuit" or conflict path caused by the new sample.Finally,according to the adjacency relation of each submanifolds,the final low dimensional embedding of the whole sample set is obtained,then the visualization of data set is realized.Through experiments on increasing artificial data and real data,the results show thatthe algorithm we proposed can not only decompose the multi-manifold data effectively,but also the algorithm has the ability of incremental and can be applied to large scale data in the future.(2)In view of the fact that at present there is not a kind of algorithm which can well deal with the data of intersecting multi-manifold,this paper proposes a decomposition algorithm D-MPPCA based on MPPCA model for high dimensional intersecting multi-manifold data.Firstly,we calculate the tangent space and neighborhood information of each sample using dynamic neighborhood algorithm,then the intersecting multi-manifold data is divided into several small disjoint blocks by using the MPPCA.Finally,the intersecting multi-manifold data are decomposed into different independent submanifolds by means of tangent space expansion,the decomposition and recognition of intersecting multi-manifold is realized.Experimental results show that the algorithm can be effectively applied to the artificial intersecting multi-manifold data and the actual high dimensional image data,compared with other algorithms,the recognition accuracy is greatly improved.The above research work has improved the existing manifold learning algorithm in dealing with multi-manifold data,not only the more accurate neighborhood graph is obtained,but also the incremental learning,greatly improve the efficiency of the algorithm.On the other hand,the algorithm can well identify the decomposition of intersecting multi-manifold data,greatly improve the accuracy,and lay a solid foundation for further research work.It is believed that the continuous improvement of this algorithm can provide a new way to reduce the dimension of data and image classification.