Application of Weibull Distribution to Hidden Markov Model for Non-Negative Factorization Matrix
E. B. Nkemnole, Joshua Olaniyi Bamigbode · European Journal of Theoretical and Applied Sciences · 2024
Probabilistic Nonnegative Matrix Factorizations (NMFs) are very useful in statistics when dealing with stochastic signals such as wave fronts, share prices, and volatility as a Nonnegative Matrix Factorization (NMF) approach. Little attention has been made in the literature to developing NMF algorithms that use moving average to exploit data's temporal dependencies. A hidden Markov model (HMM) using a Weibull distribution as the output density function was created in this study. The Weibull HMM was then reformulated as a probabilistic NMF. This demonstrates the connection between the proposed HMM and NMF, and will lead to a novel probabilistic NMF approach in which the model captures temporal dependencies inherently utilizing moving average. Furthermore, the model parameters were estimated using maximum likelihood estimation (MLE). The model's adaptability was compared to the existing probabilistic NMFs models of gamma and lognormal. Our trials with US COVID-19 data revealed that the proposed technique achieves a superior balance of sparsity, the goodness of fit, and temporal modeling than gamma and lognormal models.