Research On Semi-supervised Algorithm For High Dimensional Multi-manifold Data

The essence of manifold learning lies in revealing the inherent low-dimensional mapping hidden in the high-dimensional data space,which can reduce the dimensionality of the sampled high-dimensional data and realize visualization.Along with the development of the manifold learning,some classic algorithms have been proposed,but are basically assume sampling to the high-dimensional data is located in a smooth,single manifold,and sampling data in reality,the internal structure of itself not only complex,but most of them exist in or separation,or intersection,and even more completely overlapping manifold structure.Therefore,the processing of multi-manifold data has become an urgent problem to be solved.This paper makes an in-depth study on the identification and decomposition,dimensionality reduction and visualization of the sampled high-dimensional multi-manifold data,mainly including the following two aspects.(1)The M2 SMPPCA algorithm proposed in this paper is a multi-manifold data recognition and decomposition algorithm based on the idea of semi-supervision.Firstly,the M2 SMPPCA algorithm divides the original multi-manifold data set into small "local data blocks" through the MPPCA algorithm.The label information in the data set is used to "purify" these data blocks,so that the data points in the intersection area of the multi-manifold data can be decomposed as far as possible.Secondly,the M2 SMPPCA algorithm uses the geometric similarity between data points as the basis to judge whether two data points are located in the same sub-manifolds,and then extends the "local data block" to different sub-manifolds.Finally,the basis decomposition results of multiple sub-manifolds are integrated by the co-association matrix to improve the overall robustness of the experiment.Experimental results show that the proposed algorithm has good performance in decomposing intersecting multi-manifold data.(2)the UMD-Isomap algorithm proposed in this paper is a multi-manifold data dimensionality reduction algorithm based on the idea of supervision.The label information in the algorithm is obtained from the original multi-manifold data decomposition result by M2 SMPPCA algorithm.Firstly,UMD-Isomap algorithm proposed a new objective function to realize the mapping from high-dimensional multi-manifold data to low-dimensional space.Then,two methods for solving the objective function are proposed,one is based on SMACOF and the other is based on eigenvalue decomposition.It is proved by experiment that the UMD-Isomap algorithm proposed in this paper can not only reduce the dimensionality of high-dimensional multi-manifold data containing more than three sub-manifolds,but also realize the visualization of multi-manifold data accurately and is easy to choose parameters.The research work in this paper is mainly aimed at high-dimensional multi-manifold data.On the one hand,it provides a new idea for the decomposition of intersecting part of multi-manifold data,and obtains more accurate multi-manifold decomposition results,which greatly improves the accuracy of the algorithm.On the other hand,the proposed objective function enables the high-dimensional multi-manifold data to be embedded into the low-dimensional space more accurately and realizes the data visualization accurately.In addition,it provides a theoretical basis for the application of manifold learning to a wider range of practical life.