Tensor Chain Based On Markov Process And Its Application To User Trail Prediction

Today,with the increase of personal mobile devices,people's clothing,food,shelter and transportation are increasingly dependent on the convenience of the Internet,and the user's life track data is fully collected.How to use this data to give users more accurate recommendations for life needs is a very challenging topic in today's era.In this thesis,a tensor chain model based on Markov process is proposed.The tensor is used as a matrix to expand the high-order features of the matrix.The tensor feature decomposition model can fully exploit the potential contact between data.Tensor eigen-decomposition theory can also solve the long-term steady-state distribution of multivariate high-order Markov chains by tensor multi-module multiplication operation,but the traditional method has the disadvantage that the Markov chain order.The scale of increasing the tensor shows an increase in the exponential scale,so there is a physical limit to study the steady-state distribution of high-order multivariate high-order Markov chains.The model proposed in this thesis expresses the high-order transfer tensor as the maximum likelihood estimation method.The linear sum of the low-order metastatic tensors,and then the long-term steady-state distribution is solved for each transfer tensor by multi-mode power method.Finally,these sub-eigentensors are combined to obtain the final steady-state distribution of high-order Markov chain.Then we use the final eigentensor to predict user trails.The tensor chain model based on Markov process makes it feasible to solve the steady-state distribution of multivariate high-order Markov chains.At the same time,the maximum likelihood estimation method avoids the over-fitting problem of high-order Markov chains.Through several experiments we found that our model has better effects on memory occupancy,recommended accuracy,and lower over-fitting rate than traditional Markov models.