Research On Clustering Problem Of High-Dimensional Multi-manifold Data

Since manifold learning was first proposed in 2000,it has been widely used in the dimensionality reduction of high-dimensional data and the visualization of data because of the assumption that the data has the property of local Euclidean space.At present,classic manifold learning methods are aimed at uniform,single manifold,non-intersecting simple structure data,and the actual data distribution may be complex with uneven,multi-manifold,and intersecting regions Structured high-dimensional data,And these data are widely present in the fields of finance,medical treatment,astronomy,etc.Therefore,it is of great practical significance to carry out related research on multi-manifold data.This paper studies the classification of multi-manifold data.It is embodied as follows:(1)This paper proposes a DC_MPPCA algorithm based on density and data geometry structure of intersecting multi-manifold clustering method.This algorithm aims at the problem that the density-based multi-manifold clustering algorithm cannot handle intersecting multi-manifolds.When constructing the data relationship between points based on density,the MPPCA algorithm is used to divide the multi-manifold data to ensure different manifolds.The samples on are in different blocks,and then judge whether each block is located on the same manifold,thus classifying the data of intersecting multi-manifolds.The algorithm has achieved good experimental results on artificial data and real data.(2)Tensor Voting is a local-based method that can accurately describe the geometric structure of intersecting multi-manifold data.This paper proposes the TMMC algorithm based on Tensor Voting.This algorithm can not only effectively identify the intersecting area in multi-manifold data,but also divide the points in the intersecting area into the corresponding non-intersecting areas through the center point of the intersecting area.,And then the normal vector of each point can be accurately solved.Finally,we solve the tangent space deviation between adjacent points to construct the geometric similarity matrix of the data,and use the idea of spectral clustering to classify intersecting multi-manifold data Come on.The algorithm can accurately describe and effectively solve the problem of intersecting multi-manifolds.Experiments on artificial data and real data verify the effectiveness of the algorithm.(3)Designed a "manufacturing visualization display system based on MATLAB".The system is embedded with a variety of classic artificial data sets and manifold learning algorithms,which can not only be visualized,but also be compared with individual algorithms.In addition,the system is highly scalable.Both the data set and the algorithm can be added on demand,and it has certain human-computer interaction functions.