Tensor Clustering And Regression Modeling And Its Application Research In Consumer Behavior Analysis

The arrival of the era of big data has produced a lot of high-dimensional data.The use of tensors to represent the data can retain the structural information of the data.Therefore,it has been widely used in modern science and commercial applications in recent years.As tensor data becomes more common,the need for reliable tensor data analysis methods is becoming more and more urgent.This thesis mainly analyzes tensor data from two aspects of clustering and regression.Three tensor clustering algorithms are introduced in detail:tensor decomposition-based algorithms CP + k-means,Tucker + k-means and tensor block model.The latter can be regarded as a higher-order extension of the k-means algorithm.By comparing the three algorithms through the method of random tensor simulation,it is found that the tensor block model is superior to the other two methods in terms of estimation accuracy and clustering accuracy.In order to continue to study how to explain the change of data tensor through covariates,we introduced the tensor regression model with covariates in detail.It uses tensor as the response variable and can handle multiple data types such as continuous,count and binary.We reasonably combine the two models of tensor clustering and tensor regression to model user consumption behavior.We constructed the score tensor in three dimensions of “user-item-time”,applied tensor block model to the score tensor,and obtained the clustering of users,items,and time,and the “user-item-time” block with a relatively high level of activity.On this basis,using user gender,age level,shopping level and other characteristics as covariates,applying the tensor regression model to explain consumer behavior through personal characteristics,we can obtain important predictors of item scores for each time period,and we found that even for the same item,the main characteristics that affect its score in different time periods may be different.