Tensor Model Of Complex Correlated Data And Application Research

In many areas of research,data presents multimodal structure property,this type of data can be expressed clearly and conpletely by tensor.Vectorization of tensor data lose many data structure information,even result in curse of dimensionality and over-fitting.While tensor analysis methods enter tensor data directly,keeping data structure information effectively;models and algorithms based on tensor data,reduce parameter variables,ease overfitting phenomenon of vector methods in model learning process,this means tensor model is more effective for high dimension small sample problem,provide a new idea for analyzing high dimension vector data.Data analysis methods based on tensor have wider applications,so,this paper will discuss tensor models of two types of complex correlated data and their applications,one has natural tensor structure,another can be converted to tensor for processing.Research mainly includes following aspects:1.Tensor model of objects correlated data and application research.Traditional methods destroy structural property of tensor data;tensor can effectively express this type of complex correlated data.Taking social tagging system as background,using tensor and tensor decomposition model to study higher order structural and statistical characteristics of the system.Taking user,resource,tag the three objects as three dimensions,introducing weights to differentiate“user-label-resource" the ternary relation intensity,establishing the three-order weights tensor model,we can get optimal kernel tensor?feature matrix of three dimensions and rating scores of new ternary relations by tensor decomposition,get recommendation list by rating scores,and recommend resources or tags to users.2.Tensor models of attributes correlated data(vector data)and application research.In realistic problems,there are many attribute data which has associated relations,ften handled by vector methods,it will appear overfitting phenomenon when vector dimension is too high,tensor analysis methods ease or avoid occurrence of overfitting by reducing model parameter variables.The paper naturally generalizes to tensor space based on learning methods of vector data,primarily the classification,regression,and feature selection of support vector machine,finally obtain tensor classification model,tensor regression model,and tensor feature selection methods,example comparisons prove that support tensor machine model not only can be used to analyze vector data,but also can alleviate the high dimensional small sample problems effectively.3.Empirical study:network public opinion analysis based on tensor space model By tensor methods,we personalized recommend hot topics of network public opinion to users,and realize the effective identification and automatic classification of network public opinion texts.In the realization of personalized recommendation,using tensor to establish model for user and network public opinion,analyzing interest tendency of user by tensor decomposition,and then recommending hot topics of network public opinion to users individually,experiment results show that introducing weights will increase accuracy of resource recommendation and make personalized recommendation more precise.In the realization of effective identification of network public opinion texts,text is expressed by two order tensor of 20 x 20,constructing tensor classifier to classify network public opinion texts,experiment results show that support tensor machine model has better performance in solving high-dimensional small sample problem and data skew problem of network public opinion texts.It can be seen that tensor space model has wide application value in the field of network public opinion analysis.