  Monitoring of industrial processes is a critical capability in industry and
in government to ensure reliability of production cycles, quick emergency
response, and national security. Process monitoring allows users to gauge the
progress of an organization in an industrial process or predict the degradation
or aging of machine parts in processes taking place at a remote location.
Similar to many data science applications, we usually only have access to
limited raw data, such as satellite imagery, short video clips, event logs, and
signatures captured by a small set of sensors. To combat data scarcity, we
leverage the knowledge of Subject Matter Experts (SMEs) who are familiar with
the actions of interest. SMEs provide expert knowledge of the essential
activities required for task completion and the resources necessary to carry
out each of these activities. Various process mining techniques have been
developed for this type of analysis; typically such approaches combine
theoretical process models built based on domain expert insights with ad-hoc
integration of available pieces of raw data. Here, we introduce a novel
mathematically sound method that integrates theoretical process models (as
proposed by SMEs) with interrelated minimal Hidden Markov Models (HMM), built
via nonnegative tensor factorization. Our method consolidates: (a) theoretical
process models, (b) HMMs, (c) coupled nonnegative matrix-tensor factorizations,
and (d) custom model selection. To demonstrate our methodology and its
abilities, we apply it on simple synthetic and real world process models.
