Tensor-based Higher-order Multivariate Multi-observation Hidden Markov Models And Their Applications

Spawning by the big data era,data in the Cyber-Physical-Social Systems(CPSSs)hold semantic information highly complex and rich.In this case,it is figuring out a way to extract exactly what benefits us from such data,which are large-scale,multi-source and heterogeneous,say human activity-related research,that has gripped growing research interest and effort.Although typical Hidden Markov Models(HMMs)may model the average application scenarios concerning human activities time-series data,the performance and competence are still constrained by overly idealized prerequisite assumptions to work out applications with relationships intrigued and complicated.A series of tensor-based discrete HMMs,including 1st-Order and Higher-Order Multivariate Multi-Observation HMMs,are put forward in this thesis to break boundaries and limits of the traditional models.Specifically,extending the prerequisite assumptions of classical models relied on and considering the latent high order,multiplicity,and multiobservability of the actual modeling problem.Henceforth theoretical algorithms,compared to regular ones,corresponding to elementary problems of models we brought up are adapted and extended.Also,what has been implemented on those algorithms,say processing the continuous Kronecker product and decomposing the joint probability distribution and other improvement measures,makes them perform better while modeling real-world problems.Algorithms in this thesis,matching the three elementary problems of each model respectively,have been evaluated by launching them on real datasets for applications,like human trajectory prediction and activities of daily living.Results depicted the performance of models involving higher-order and multiplicity gained significantly compared to the usual ones.As such,we validated higher-order models eclipsed 1st-orders with enhanced modeling capability when historical dependencies featured in time-series data.Additionally,the 1st-order models we proposed have overshadowed the usual same-orders likewise.