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   https://doi.org/10.1145/3623269  

   Hosseiny Marani, Amin ; Baumer, Eric P. ( September 2023 , ACM Computing Surveys)

   Topic modeling includes a variety of machine learning techniques for identifying latent themes in a corpus of documents. Generating an exact solution (i.e., finding global optimum) is often computationally intractable. Various optimization techniques (e.g., Variational Bayes or Gibbs Sampling) are employed to generate topic solutions approximately by finding local optima. Such an approximation often begins with a random initialization, which leads to different results with different initializations. The term “stability” refers to a topic model’s ability to produce solutions that are partially or completely identical across multiple runs with different random initializations. Although a variety of work has been done analyzing, measuring, or improving stability, no single paper has provided a thorough review of different stability metrics nor of various techniques that improved the stability of a topic model. This paper fills that gap and provides a systematic review of different approaches to measure stability and of various techniques that are intended to improve stability. It also describes differences and similarities between stability measures and other metrics (e.g., generality, coherence). Finally, the paper discusses the importance of analyzing both stability and quality metrics to assess and to compare topic models. 

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5. On the stability of strong-stability-preserving modified Patankar–Runge–Kutta schemes

   https://doi.org/10.1051/m2an/2023005  

   Huang, Juntao ; Izgin, Thomas ; Kopecz, Stefan ; Meister, Andreas ; Shu, Chi-Wang ( March 2023 , ESAIM: Mathematical Modelling and Numerical Analysis)

   In this paper, we perform a stability analysis for classes of second and third order accurate strong-stability-preserving modified Patankar–Runge–Kutta (SSPMPRK) schemes, which were introduced in Huang and Shu [ J. Sci. Comput. 78 (2019) 1811–1839] and Huang et al . [ J. Sci. Comput. 79 (2019) 1015–1056] and can be used to solve convection equations with stiff source terms, such as reactive Euler equations, with guaranteed positivity under the standard CFL condition due to the convection terms only. The analysis allows us to identify the range of free parameters in these SSPMPRK schemes in order to ensure stability. Numerical experiments are provided to demonstrate the validity of the analysis. 

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