Research On Fast Dimensionality Reduction Algorithm

With the arrival of the era of big data,data volume and data dimensionality are constantly increasing.Our computers are faced with great challenges.Although many high-performance computers can deal with such large data,it will cost a lot of time and space.At the same time,because of the curse of dimensionality,the processing result is often unsatisfactory.Therefore,how to do dimensionality reduction on these data has become an urgent problem to be solved.The dimensionality reduction method based on projection is very fast,however,as a linear method,its performance on the nonlinear data is not satisfactory.The manifold learning is a nonlinear method to do dimensionality reduction.It holds the idea that the result of dimensionality reduction should keep the original structure of the data,which has achieved great result on nonlinear data.However,in the process of manifold learning,the parameters of generating manifold are very sensitive,and the speed of manifold learning is very slow.In addition,the method of dimensionality reduction for vector data cannot well exploit the spatial structure information of two-dimensional plane data,which makes the result unsatisfactory.This paper starts from these aspects and studies the background and development history of dimensionality reduction.After that,we put forward two methods to solve these problems respectively.Experiments are carried out on artificial data sets and real data sets respectively.At last,with the experiment results,we analyse the parameters and time complexities of our algorithms.The main contributions are summarized as follows:·We introduce the development experience of the dimensionality reduction method,and detail the linear dimensionality reduction method of the principal component analysis,the nonlinear dimensionality reduction method of local linear embed-ding,the 2DPCA algorithm for reducing the dimension of the plane data and the common convolution neural network for processing image data.· We propose a fast data reduction algorithm SOINN Manifold(Self-Organizing Incremental Neural Network Manifold,named SOINN Manifold)to solve the problem of slow speed and sensitive parameters on manifold learning.We extract a small number of data points to express the manifolds of the original data and then do dimensionality reduction on these data points,which saves a lot of time.On the basis of the generating manifold,we also propose an inner dimension estimation method to improve the result of dimensionality reduction.· We propose a dimension reduction algorithm IOCANet(Incremental Orthogo-nal Component Analysis Network,named IOCANet),which is specially aimed at two-dimensional plane data.We combine the convolution neural network with the dimensionality reduction algorithm and use unsupervised dimensionality re-duction algorithm to automatically generate convolution kernels,which saves a lot of training time and does not need to manually annotate the data.The exper-iment also proves that our algorithm is competitive.