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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 theprogress of an organization in an industrial process or predict the degradationor aging of machine parts in processes taking place at a remote location.Similar to many data science applications, we usually only have access tolimited raw data, such as satellite imagery, short video clips, event logs, andsignatures captured by a small set of sensors. To combat data scarcity, weleverage the knowledge of Subject Matter Experts (SMEs) who are familiar withthe actions of interest. SMEs provide expert knowledge of the essentialactivities required for task completion and the resources necessary to carryout each of these activities. 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 nonnegative tensor factorization. Our method consolidates: (a) theoreticalprocess models, (b) HMMs, (c) coupled nonnegative matrix-tensor factorizations,and (d) custom model selection. To demonstrate our methodology and itsabilities, we apply it on simple synthetic and real world process models.

Generating Hidden Markov Models from Process Models Through Nonnegative Tensor Factorization