Dimensionality Reduction Based On Manifold Visualization

With the development of modern science and technology, A large number of high-dimensional data exsits in computer vision, bioinformatics, machine learning and aerospace fields. High-dimensional data is not only difficult to people intuitively understand, and difficult to find hidden among the high-dimensional data patterns. Data dimension reduction technique is to map the original high-dimensional data to low-dimensional space, as much as possible to maintain the geometric relationship between the data and the distance measure unchanged. Dimensionality reduction algorithm is an important means of dealing with such high-dimensional data and an important tool for feature extraction.Dimension reduction techniques divide into linear dimensionality reduction and nonlinear dimensionality reduction. Manifold learning is a typical non-linear dimension reduction technique. It is to map a set of high-dimensional data space to low dimensional space. Under certain conditions, i.e., the geometric properties of the holding point of the high-dimensional space, its aim is to find a corresponding set of low-dimensional coordinates.This paper focuses on data dimensionality reduction algorithm and its application to start research. The linear dimension reduction algorithm and manifold learning algorithm is studied,Proposing a new manifold learning algorithm. The main work of this paper includes the following aspects:First, The traditional linear dimensionality reduction algorithms and manifold learning algorithm in-depth are studied and discussed, comparing the advantages and disadvantages between them.Secondly, Through simulation experiments on the data set then furtherly illustrates the various inter-dimensionality reduction algorithms, A detailed comparison of the computational complexity of the algorithm.Finally, Propose based on local preserving submanifold visualization methods. Unlike the conventional methods, Learning from ideological expand manifold surfaces in the two-dimensional flat space, proposed a local holding sub-manifold visualization method. Using singular value decomposition and k-means clusting method, manifold data is divided into multi-block submanifolds. Calculate the topology relationship of the center of the first flow shaped cuts with the remaining diced center. Project and expand the manifold cuts one by one in the target low-dimensional target space, maintaining the topology of the above centers. Finally, the experimential results on face data-sets this method is better to keep the structural the extension regulations flutter submanifold.