# Generating Hidden Markov Models from Process Models Through Nonnegative Tensor Factorization

arXiv: https://arxiv.org/abs/2210.01060 · HTML: https://mlsanity.com/paper/2210.01060/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 79 references that are in the map.
- First posted on arXiv 3 Oct 2022.

## Builds on (most cited first, 10 of 10)

- [Minimal Realization Problems for Hidden Markov Models](https://mlsanity.com/paper/1411.3698/) (2014)
- [Unsupervised Machine Learning Based on Non-Negative Tensor Factorization for Analyzing Reactive-Mixing](https://mlsanity.com/paper/1805.06454/) (2018)
- [A Neural Network for Determination of Latent Dimensionality in Nonnegative Matrix Factorization](https://mlsanity.com/paper/2006.12402/) (2020)
- [Learning Hidden Markov Models from Pairwise Co-occurrences with Application to Topic Modeling](https://mlsanity.com/paper/1802.06894/) (2018)
- [On the Realization of Hidden Markov Models and Tensor Decomposition](https://mlsanity.com/paper/2008.11487/) (2020)
- [Performance Analysis: Discovering Semi-Markov Models From Event Logs](https://mlsanity.com/paper/2206.14415/) (2022)
- [Identification of Anomalous Diffusion Sources by Unsupervised Learning](https://mlsanity.com/paper/2010.02168/) (2020)
- [Distributed non-negative RESCAL with Automatic Model Selection for Exascale Data](https://mlsanity.com/paper/2202.09512/) (2022)
- [Identification of release sources in advection-diffusion system by machine learning combined with Green function inverse method](https://mlsanity.com/paper/1612.03948/) (2016)
- [Determination of Latent Dimensionality in International Trade Flow](https://mlsanity.com/paper/2003.00129/) (2020)

## Built on by (most cited first, 1 of 1)

- [Generative Discrete Event Process Simulation for Hidden Markov Models to Predict Competitor Time-to-Market](https://mlsanity.com/paper/2411.04266/) (2024)

## Abstract (arXiv)

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.