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Generating Hidden Markov Models from Process Models Through Nonnegative Tensor Factorization

Erik Skau, Andrew Hollis, Stephan Eidenbenz, Kim Rasmussen, Boian Alexandrov

TL;DR

The paper addresses the challenge of monitoring complex industrial processes with scarce observations by fusing SME-derived theoretical process models with minimal Hidden Markov Models. It introduces a coupled nonnegative matrix-tensor factorization framework to construct minimal HMMs from simulated process timelines, enabling stable model selection through ensemble perturbations. Across synthetic and real-data cases, the approach identifies the minimal number of hidden states that faithfully represent the SME-informed process dynamics and demonstrates practical usefulness for model evaluation and monitoring when data are limited. This method offers a principled path to compare competing process models and to rely on SME knowledge to guide probabilistic state representations in practice.

Abstract

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.

Generating Hidden Markov Models from Process Models Through Nonnegative Tensor Factorization

TL;DR

The paper addresses the challenge of monitoring complex industrial processes with scarce observations by fusing SME-derived theoretical process models with minimal Hidden Markov Models. It introduces a coupled nonnegative matrix-tensor factorization framework to construct minimal HMMs from simulated process timelines, enabling stable model selection through ensemble perturbations. Across synthetic and real-data cases, the approach identifies the minimal number of hidden states that faithfully represent the SME-informed process dynamics and demonstrates practical usefulness for model evaluation and monitoring when data are limited. This method offers a principled path to compare competing process models and to rely on SME knowledge to guide probabilistic state representations in practice.

Abstract

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.
Paper Structure (12 sections, 18 equations, 8 figures, 1 algorithm)

This paper contains 12 sections, 18 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. RELATED WORKS
  3. Process Modeling, Hidden Markov Models, and nonnegative Tensor Factorization with Model Selection
  4. Theoretical Process Modeling
  5. Hidden Markov Models
  6. Creating Reference Hidden Markov Models from a Theoretical Process Model
  7. Nonnegative Tensor Factorization and Model Selection
  8. Numerical Experiments
  9. Synthetic Example with Process Model Activities Leading to a Minimal HMM
  10. Synthetic Example with Process Model Activities That Do Not Lead to a Minimal HMM
  11. Real Life Example: HMM of a Dutch Bank Loan Application Process Model
  12. Conclusion

Figures (8)

  • Figure 1: Flow chart illustrating the pipeline to construct a minimal HMM from a theoretical process model.
  • Figure 2: Depiction of an HMM with hidden random variable $X$ and observed random variable $Y$. $pi$ depicts the initial state probability vector. The transition matrix $T$ describes the progression of the hidden random variable at time $t$ to time $t+1$. The emission matrix $E$ describes the probability of each observation based upon the hidden state at each time.
  • Figure 3: Diagram of the steps taken to construct a minimal HMM.
  • Figure 4: Two example process models where the final activities connect to the first activity causing the process models to repeat.
  • Figure 5: Tensor factorization parameter selection and evaluation for simple strictly sequential process.
  • ...and 3 more figures