The Study Of Optimization Of Manifold Learning Algorithms Based On Information Geometry

In order to process complex high-dimensional data,embedding the data into lowdimensional space and maintaining the topology of the data is a common practice known as dimensional reduction or Manifold Learning.With the help of Information Geometry tools,this paper studies to optimize Manifold Learning and accomplishes the following:(1)The basic knowledge and principles of Manifold Learning and Information Geometry are introduced.In the aspect of Manifold Learning,the paper mainly introduces principal component analysis,linear discriminant analysis,these two linear dimensional reduction algorithms and local linear embedding,t-distribution Stochastic Neighborhood Embedding and other non-linear dimensionality reduction algorithms,where t-distribution Stochastic Neighborhood Embedding is the core of the discussion below.The aspect of Information Geometry mainly introduces the probability simplex and the tangent space on it,which is the preparatory knowledge that needs to be used below.(2)Focus on Stochastic Neighborhood Embedding and t-distribution Stochastic Neighborhood Embedding,model Manifold Learning.A column of data is modeled as a point on a probability simplex,and a dimensional reduction is then modeled as a point on a probability simplex.In this way,Manifold Learning is re-explained,and various Manifold Learning algorithms are studied under a unified framework.In addition,the quality of Manifold Learning is evaluated by the use of Information Capacity.(3)Based on Information Geometry,a method to improve the quality of dimensional reduction with Information Capacity is proposed.The IC-t SNE algorithm is proposed by combining the Information Capacity method with the t-distribution Stochastic Neighborhood Embedding.The IC-tSNE algorithm is generalized in view of the more obvious effect of Information Capacity in the first few iterations.Finally,experiments were carried out on the MNIST data set and the Swiss Roll data set respectively to verify the validity of the Information Capacity method.