A Tensorial Auto-regressive Moving Average Model And Its Applications

With the popularization and development of information technology in digital devices,the amount of information in modern society is growing rapidly.High dimensional data analysis and feature representation method is an important exploration and research content in the field of machine learning and pattern recognition technology.In the field of machine learning and pattern recognition technology,a lot of data(such as color image,multispectral image,video,etc.)can be obtained,which are high-dimensional data,namely tensor.In view of these high-dimensional data,traditional methods tend to vectorize them,supplemented by the corresponding classification,regression and other mathematical models.This kind of processing method will lead to the loss of data features and relationships of different dimensions.As a classical time series representation method,auto-regressive moving average model has been widely used in pattern recognition.However,the existing auto-regressive moving average model represents the time series of a single dimension of the data and ignores the relationship of other dimensions of the data.In view of the above problems,this paper studies the tensorial-auto-regressive moving average model and applies it to the classification of high-dimensional data such as images and videos,as well as the short-term traffic flow prediction.Specifically,the work of this thesis mainly includes the following aspects:(1)Image and video classification based on tensorial-auto-regressive moving average model.Traditional image video classification usually does vectorization on high dimensional data,ignoring the relationship between different dimensions of data.Aiming at this problem,this paper proposes an image classification method based on tensorial-auto-regressive moving average model.In this method,the image and video are coded into an ordered tensor data through an auto-regressive sliding average model,and then projected onto a product Grassmann manifold for classification.Experimental results on several datasets show that the proposed method is more effective than other existing classification methods.(2)Short term traffic flow prediction based on tensorial-auto-regressive moving average model.Most of the existing short-term traffic flow prediction methods are based on a single station or a single time series,ignoring the correlation between stations and multi-scale time periods.In this paper,a traffic flow forecasting method based on tensorial-auto-regressive moving average model is proposed.The time series are expressed as low rank tensors by multi-channel delay embedding transformation method,and the tensorial-auto-regressive moving average model is established.The short-term traffic flow forecasting is realized by inverse Tucker decomposition and inverse MDT.The experimental results on the California traffic flow dataset show that the short-term prediction accuracy of the proposed method is better than the existing prediction methods.(3)According to the convergence analysis and complexity analysis of the tensorial-auto-regressive moving average model,the model proposed in this paper has high robustness and computational efficiency.The model not only has application value for image and video classification and short-term traffic flow prediction,but also can be conveniently applied to other classification and regression problems based on tensor data.