## 4 Conclusions  
The dynamics of heart signals are highly complex and nonlinear in nature. To explicate these nonlinear dynamics, we first computed the gray level co-occurrence matrix (GLCM) features to capture these dynamics. We ranked the extracted features based on EROC to determine their importance. The dissimilarity feature yielded the highest EROC value (0.3589), followed by inverse difference (0.3564), cluster prominence (0.3441), and so on. We computed the association and strength of relationships among these features using mutual information (_MI_). The nodes correlation \(\rightarrow\) correlation1 (1.4640) yielded the relationship with the highest strength. We then selected dissimilarity as the target node and computed the significance with other selected states. Finally, we computed the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Node** & **Binary MI** & **Relative Binary Significance** & **Binary Relative Significance** & **Maximum Bayes Factor** \\ \hline Entropy & 0.0259 & 2.78\% & 0.0372 & \textgreater{}156,446.10 (3/3) & 5.92\% & 1.3751 \\ \hline Autocorrelation & 0.0160 & 1.71\% & 0.0229 & \textgreater{}0.041 (3/3) & 6.73\% & 1.5628 \\ \hline Correlation & 0.0069 & 0.74\% & 0.0100 & \textgreater{}0.089 (2/3) & 13.01\% & 1.3722 \\ \hline Homogenity1 & 0.0063 & 0.67\% & 0.0090 & \textgreater{}1.241 (1/3) & 56.32 & 1.1265 \\ \hline Correlation2 & 0.0055 & 0.58\% & 0.0078 & \textgreater{}0.124 (3/3) & 8.28\% & 1.3722 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Node** & **Binary MI** & **Relative Binary Significance** & **Binary Relative Significance** & **Maximum Bayes Factor** \\ \hline Cluster shade & 0.3621 & 100\% & 1.000 & \textgreater{}411,098 (3/3) & 100\% & 14.500 \\ \hline Cluster prominence & 0.3230 & 89.21\% & 0.8922 & \textgreater{}1,433,166 (3/3) & 100\% & 12.888 \\ \hline Contrast & 0.2159 & 59.62\% & 0.5962 & \textgreater{}0.105 (3/3) & 100\% & 6.8235 \\ \hline Autocorrelation & 0.0907 & 25.06\% & 0.2506 & \textgreater{}0.041 (2/3) & 76.47\% & 4.032 \\ \hline Energy & 0.0287 & 7.94\% & 0.0794 & \textgreater{}129,593 (3/3) & 29.41\% & 3.411 \\ \hline Correlation & 0.0241 & 6.65\% & 0.0665 & \textgreater{}0.089 (3/3) & 25.75\% & 2.716 \\ \hline Correlation2 & 0.0171 & 4.73\% & 0.0473 & \textgreater{}0.124 (3/3) & 16.39\% & 2.716 \\ \hline Entropy & 0.0154 & 4.25\% & 0.0426 & \textgreater{}156,446 (3/3) & 12.81\% & 2.972 \\ \hline Homogenity1 & 0.0033 & 0.90\% & 0.0090 & \textgreater{}1.241 (1/3) & 62.03\% & 1.240 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Local analysis with target states dissimilarity \(\geq\) 882, 604.41 (\(\frac{3}{3}\))6.89%. local analysis of dissimilarity at selected states by computing binary mutual information, relative binary significance, and the maximum Bayes factor to further clarify the underlying nonlinear dynamics. The results reveal that the proposed method is more robust as a means of determining the nonlinear dynamics of heart failure signals and will lead to further improvement in prognosis and diagnosis. Currently, we have tested the results on a small dataset with no clinical profiles available. In future, we will test on larger datasets with more clinical details, which present congestive heart failure data and other demographic information. We will also apply more in-depth Bayesian inference analysis to further explain the nonlinear dynamics present in these datasets, to further improve healthcare professionals' decision making and diagnostic capabilities. Data curation, L.H. ; formal analysis, M.M.E., L.H., A.A.M., M.K.N., M.O., H.M., A.Y., and M.A.H. ; investigation, L.H. ; methodology, L.H. and M.K.N. ; project administration, L.H. ; resources, L.H. and A.Y. ; software, L.H. ; supervision, L.H. ; visualization, A.A.M. ; writing--original draft, L.H. ; writing--review and editing, M.M.E., M.O., H.M., and M.A.H. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not Applicable.