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Monitoring of industrial processes is a critical capability in industry andin government to ensure reliability of production cycles, quick emergencyresponse, and national security. Process monitoring allows users to gauge theinvolvement of an organization in an industrial process or predict thedegradation or aging of machine parts in processes taking place at a remotelocation. Similar to many data science applications, we usually only haveaccess to limited raw data, such as satellite imagery, short video clips, someevent logs, and signatures captured by a small set of sensors. To combat datascarcity, we leverage the knowledge of subject matter experts (SMEs) who arefamiliar with the process. Various process mining techniques have beendeveloped for this type of analysis; typically such approaches combinetheoretical process models built based on domain expert insights with ad-hocintegration of available pieces of raw data. Here, we introduce a novelmathematically sound method that integrates theoretical process models (asproposed by SMEs) with interrelated minimal Hidden Markov Models (HMM), builtvia non-negative tensor factorization and discrete model simulations. Ourmethod consolidates: (a) Theoretical process models development, (b) Discretemodel simulations (c) HMM, (d) Joint Non-negative Matrix Factorization (NMF)and Non-negative Tensor Factorization (NTF), and (e) Custom model selection. Todemonstrate our methodology and its abilities, we apply it on simple syntheticand real world process models.

Process Modeling, Hidden Markov Models, and Non-negative Tensor Factorization with Model Selection