## A Stochastic Framework for Robust Fuzzy Filtering and Analysis of Signals

There are numerous applications across all the spectrum of scientific areas that demand the mathematical studying of signals/data. The two typical study areas of theoretical research on signal/data processing are of modeling (i.e. understanding of signal's behavior) and of analysis (i.e. evaluation of given signal for finding its association to existing signal models). This study presents a unified stochastic framework meant for signal modeling as well as analysis. The signals are modeled via linear-in-parameters models (e.g. a type of Takagi-Sugeno fuzzy model) based on variational Bayes methodology. This gives rise to the ``negative free energy maximizing'' filtering algorithm. The work presented here highlighted that it was analytically possible to maximize the information theoretic quantity, ``mutual information'', exactly in the same manner as maximizing ``negative free energy'' in variational Bayes methodology. This gives rise to the ``variational information maximizing'' analysis algorithm. The robustness of the methodology against data outliers is achieved by modeling the noises with Student-t distributions. The framework takes into account the inputs' noises as well apart from the usually considered output noise. The robustness of the adaptive filtering algorithm against noise is shown by a deterministic analysis where an upper bound on the magnitude of estimation errors is derived.

The work provides several applications scenarios of introduced signals' modeling and analysis framework to solve the practical problems. Some of the challenging practical problems related to signal/data processing have been formulated in a manner that the ``negative free energy maximizing'' filtering and ``variational information maximizing'' analysis algorithms could be directly applied to solve the problems. The studied application examples include robust comparison of objects' geometries in images for child ear biometrics, biomedical signals classification, data smoothing for reflection-mode ultrasound imaging, and modeling related applications. The application examples support the mathematical theory by providing just the ``proof-of-concept''.

The work provides several applications scenarios of introduced signals' modeling and analysis framework to solve the practical problems. Some of the challenging practical problems related to signal/data processing have been formulated in a manner that the ``negative free energy maximizing'' filtering and ``variational information maximizing'' analysis algorithms could be directly applied to solve the problems. The studied application examples include robust comparison of objects' geometries in images for child ear biometrics, biomedical signals classification, data smoothing for reflection-mode ultrasound imaging, and modeling related applications. The application examples support the mathematical theory by providing just the ``proof-of-concept''.

## Related Publications

**M. Kumar, N. Stoll, R. Stoll, and K. Thurow, “A Stochastic Framework for Robust Fuzzy Filtering and Analysis of Signals - Part I,”***IEEE Transactions on Cybernetics*, vol. 46, no. 5, pp. 1118-1131, 2016.**M. Kumar, N. Stoll, R. Stoll, and K. Thurow, “A Stochastic Framework for Robust Fuzzy Filtering and Analysis of Signals - Part II,”***IEEE Transactions on Cybernetics*, vol. 45, no. 3, pp. 486-496, 2015.