Analysis And Application Of High Dimension Data Based On Matrix Factor Model

High dimensional matrix data widely exist in many research fields such as economics,finance,image recognition,and meteorology.Analyzing matrix data to reveal its objective laws and characteristic information is of great significance in many scientific research fields.In order to analyze high-dimensional data,recent research has focused on dimensionality reduction of data.Research has shown that matrix factor models can not only extract potential information that drives dynamic changes in highdimensional matrix data,but also maintain the original structure of the matrix during dimensionality reduction.Firstly,this paper introduces the research process of matrix factor model and stock,image two high-dimensional data,and analyzes that matrix factor model can be applied to the research of image and stock data.Then,it introduces in detail what matrix factor models are and estimation methods.Then,the MINIST grayscale image dataset was selected for dimensionality reduction and reconstruction.The dataset contains various handwritten digital images from 0 to 9,60000 training sample sets,and 10000 test sample sets,each image consisting of 28x28 pixels.This article selects 1000 samples from this dataset as the research object,constructs a matrix factor model using the value of each pixel point as a variable,calculates the estimation of the potential factor matrix and the estimation of the dynamic factor matrix,thereby achieving dimensionality reduction of the original image data.From this,the image is reconstructed based on the recognizability conditions,and further obtains a reconstructed image with a resolution coefficient greater than 75%,The reconstructed image still has a good recognition rate under naked eye observation.Therefore,it is proved that using matrix factor models can effectively reduce the dimensionality of image data.After that,we selected 400 days of stock data from 14 listed banks,and used 12 indicators such as opening price,market value,current market value,and maximum price as variables to construct a matrix factor model.We conducted dimensionality reduction processing on the data to solve the problem of stock dimensionality reduction and prediction.We further obtained a4x4x400 matrix time series,and used the matrix autoregressive least squares estimation method to predict the stock data of the next five periods for the dimensionality reduced matrix data.From the perspective of results,this article uses less than 10% of the original data to well predict 70% of the index value.Therefore,matrix factor model and matrix autoregressive model can be effectively applied to stock dimensionality reduction prediction.In this paper,a matrix factor model is applied to dimensionality reduction and reconstruction of grayscale data sets.The reconstructed image still retains the characteristics and information of the original data,and still has a good degree of recognition under visual observation;Using a matrix factor model and a matrix autoregressive model,we conducted a dimensionality reduction prediction on the stock data of 14 listed banks,and applied less than 10% of the original data to well predict 70%of the data.Therefore,the matrix factor model has a good dimensionality reduction effect in image data and stock data.