| With the gradual progress of information construction and the advent of the era of intelligence,the amount of data generated,acquired,stored and processed in the real world is growing exponentially and rapidly.A large amount of these data contain the characteristic of high dimensionality.These high-dimensional data provide researchers with a wealth of information,but at the same time they also pose great challenges.When processing and analyzing high-dimensional data,the impact of dimensionality cannot be ignored.Dimensionality reduction has become an important step in processing highdimensional data.As a nonlinear dimensionality reduction method,manifold learning,which can excellently capture the nonlinear structure in high-dimensional datasets and obtain a lowdimensional representation,has gained the favor of many researchers.In this Thesis,we conduct a research of dimensionality reduction based on uniform manifold approximation and projection in manifold learning algorithms.The main contributions of this Thesis are as follows.First,to address the neighborhood selection problem in uniform manifold approximation and projection,we propose a neighborhood selection algorithm based on connection strength under multiple neighborhood structures,which takes multiple neighborhood structures into consideration to achieve the expansion of neighborhoods and calculates the connection strength by the information of relevant neighborhoods,and calculates the neighborhood points based on the connection strength to achieve the goal of obtaining more connected neighborhood points,and the algorithm is experimentally analysis.Next,to address the problem that the solution of uniform manifold approximation and projection is more random in the process of solving,and the number of iterations and time is longer.In this Thesis,an isometric uniform manifold approximation and projection algorithm is proposed to obtain the local optimal holding distance by analyzing the optimization structure of uniform manifold approximation and projection,and construct the global optimal distance holding by isometric way,and finally obtain the global stable optimal solution by isomorphic matrix decomposition.Experiments show that this method can well maintain the structure of high-dimensional data in the embedded space,and has certain advantages in evaluation indicators. |
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