# A Bayesian Dynamic Inference Approach Based on Extracted Gray Level Co-Occurrence (GLCM) Features for the Dynamical Analysis of Congestive Heart Failure

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Features Extraction

#### 2.3. Gray-Level Co-Occurrence Matrix (GLCM)

#### 2.4. Feature Ranking Algorithms

#### 2.5. Bayesian Inference Approach

_{1}, X

_{2}, X

_{3}, …, X

_{n}} a set of n dimensional variables, the Bayesian network is defined with couplet $X=\langle G,P\rangle $ represented in angular brackets, where G denotes the DAG and P denotes the set of parameters that quantify the network that contains the probabilities of each possible value of x

_{i}for each variable X

_{i}. Mathematically:

#### 2.6. Mutual Information (MI)

_{1}, X

_{2}, X

_{3}, …. X

_{n}[45] can be computed as:

#### 2.7. Exploratory Analysis of the Unsupervised Network

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GLCM | Gray level co-occurrence |

HRV | Heart rate variability |

PC | Pearson’s correlation |

CHF | Congestive heart failure |

NSR | Normal sinus rhythm |

MI | Myocardial infarction |

SCD | Sudden cardiac death |

CAD | Computed aided diagnostic |

ECG | Electrocardiogram |

EMD | Empirical mode decomposition |

LF | Low frequency |

VLF | Very low frequency |

HF | High frequency |

SDNN | Standard deviation of normal-to-normal beat interval |

LRP | Low risk patients |

AF | Atrial fibrillation |

RMSSD | Root mean square of successive RR differences |

FAWT | Flexible analytic wavelet transforms |

APEnt | Accumulated permutation entropy |

MI | Mutual information |

PC | Pearson’s correlation |

KL | Kullback–Leibler |

EROC | Empirical receiver operating characteristic curve |

NYHA | New York Heart Association |

MFCC | Mel frequency cepstral Coefficients |

SIFT | Scale invariant Feature transform |

EFDs | Elliptic Fourier descriptors |

WPC | Wavelet phase coherence |

DAG | Directed acyclic graph |

## References

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**Figure 1.**Schematic diagram, based on Bayesian inference analysis, of target nodes based on extracted fuzzy entropy features.

**Figure 6.**Significance of the dissimilarity node with all nodes at selected cluster states (≤349,738 (58.62%), ≤882,604 (34.48%), and >882,604 (5.89%)).

Node | Outgoing Force | Incoming Force | Total Force |
---|---|---|---|

Dissimilarity | 0.9330 | 1.0146 | 1.9477 |

Cluster prominance | 1.6428 | 0.0000 | 1.6428 |

Contrast | 0.5446 | 0.6281 | 1.1727 |

Cluster shade | 0.0000 | 0.9330 | 0.9330 |

Correlation | 0.5954 | 0.2848 | 0.8802 |

Energy | 0.5824 | 0.2278 | 0.8102 |

Entropy | 0.1956 | 0.5824 | 0.7779 |

Autocorrelation | 0.2848 | 0.3167 | 0.6015 |

Correlation2 | 0.0000 | 0.5954 | 0.5954 |

Homogenity1 | 0.0000 | 0.1956 | 0.1956 |

**Table 2.**Overall analysis of the highly ranked feature $\text{\u201c}\mathrm{dissimilarity}\text{\u201d}$ (target feature) with other extracted features.

Node | Mutual Information (MI) | Normalized MI | Relative MI | Relative Significance | p-Value |
---|---|---|---|---|---|

Cluster prominence | 1.0146 | 64.01% | 81.33% | 1.0000 | 0.0000 |

Cluster shade | 0.9330 | 58.86% | 74.79% | 0.9196 | 0.0000 |

Contrast | 0.5425 | 34.22% | 43.48% | 0.5347 | 0.0000 |

Autocorrelation | 0.1329 | 8.38% | 10.65% | 0.1310 | 0.00026 |

Energy | 0.0895 | 5.64% | 7.17% | 0.0882 | 0.006164 |

Entropy | 0.0519 | 3.72% | 4.16% | 0.0512 | 0.0795 |

Correlation | 0.0394 | 2.48% | 3.15% | 0.0388 | 0.176 |

Correlation2 | 0.0291 | 1.83% | 2.33% | 0.0287 | 0.3218 |

Homogenity1 | 0.0118 | 0.74% | 0.94% | 0.0116 | 0.7549 |

**Table 3.**Local analysis with target states $\mathrm{dissimilarity}\le 349,738.09\left(\frac{1}{3}\right)58.62\%$.

Node | Binary MI | Relative Binary Significance | Binary Relative Significance | Maximum Bayes Factor | ||
---|---|---|---|---|---|---|

Cluster prominence | 0.7847 | 80.19% | 1.000 | ≤571,475 (1/3) | 92.64% | 1.7059 |

Cluster shade | 0.6640 | 67.86% | 0.8462 | ≤163,215 (1/3) | 98.52% | 1.5657 |

Contrast | 0.3957 | 40.44% | 0.5043 | ≤0.068 (1/3) | 60.29% | 1.7059 |

Autocorrelation | 0.0839 | 8.57% | 0.1069 | ≤0.021 (1/3) | 88.73% | 1.1566 |

Energy | 0.0802 | 8.19% | 0.1021 | ≤45,768 (1/3) | 65.96% | 1.2544 |

Entropy | 0.0481 | 4.92% | 0.0614 | ≤57,145 (1/3) | 73.25% | 1.1640 |

Correlation | 0.0279 | 2.85% | 0.0356 | ≤0.041 (1/3) | 80.88% | 1.0910 |

Correlation2 | 0.0215 | 2.19% | 0.0274 | ≤0.058 (1/3) | 87.33% | 1.0664 |

Homogenity1 | 0.0112 | 1.14% | 0.0143 | >2.201 (1/3) | 9.03% | 1.1640 |

**Table 4.**Local analysis with target states $\mathrm{dissimilarity}\le 882,604.41\left(\frac{2}{3}\right)34.48\%$.

Node | Binary MI | Relative Binary Significance | Binary Relative Significance | Maximum Bayes Factor | ||
---|---|---|---|---|---|---|

Cluster prominence | 0.6966 | 74.95% | 1.000 | ≤1,433,166.15 (2/3) | 97.50% | 2.5705 |

Cluster shade | 0.6150 | 66.17% | 0.84828 | ≤411,098.14 (2/3) | 85.00% | 2.8171 |

Contrast | 0.2993 | 32.20% | 0.4297 | ≤0.105 (2/3) | 84.20% | 1.6841 |

Energy | 0.0441 | 4.74% | 0.0633 | >129,593.07 (2/3) | 11.90% | 1.3809 |

Entropy | 0.0259 | 2.78% | 0.0372 | >156,446.10 (3/3) | 5.92% | 1.3751 |

Autocorrelation | 0.0160 | 1.71% | 0.0229 | >0.041 (3/3) | 6.73% | 1.5628 |

Correlation | 0.0069 | 0.74% | 0.0100 | >0.089 (2/3) | 13.01% | 1.3722 |

Homogenity1 | 0.0063 | 0.67% | 0.0090 | ≤1.241 (1/3) | 56.32 | 1.1265 |

Correlation2 | 0.0055 | 0.58% | 0.0078 | >0.124 (3/3) | 8.28% | 1.3722 |

**Table 5.**Local analysis with target states $\mathrm{dissimilarity}\ge 882,604.41\left(\frac{3}{3}\right)6.89\%$.

Node | Binary MI | Relative Binary Significance | Binary Relative Significance | Maximum Bayes Factor | ||
---|---|---|---|---|---|---|

Cluster shade | 0.3621 | 100% | 1.000 | >411,098 (3/3) | 100% | 14.500 |

Cluster prominence | 0.3230 | 89.21% | 0.8922 | >1,433,166 (3/3) | 100% | 12.888 |

Contrast | 0.2159 | 59.62% | 0.5962 | >0.105 (3/3) | 100% | 6.8235 |

Autocorrelation | 0.0907 | 25.06% | 0.2506 | ≤0.041 (2/3) | 76.47% | 4.032 |

Energy | 0.0287 | 7.94% | 0.0794 | >129,593 (3/3) | 29.41% | 3.411 |

Correlation | 0.0241 | 6.65% | 0.0665 | >0.089 (3/3) | 25.75% | 2.716 |

Correlation2 | 0.0171 | 4.73% | 0.0473 | >0.124 (3/3) | 16.39% | 2.716 |

Entropy | 0.0154 | 4.25% | 0.0426 | >156,446 (3/3) | 12.81% | 2.972 |

Homogenity1 | 0.0033 | 0.90% | 0.0090 | ≤1.241 (1/3) | 62.03% | 1.240 |

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## Share and Cite

**MDPI and ACS Style**

Eltahir, M.M.; Hussain, L.; Malibari, A.A.; K. Nour, M.; Obayya, M.; Mohsen, H.; Yousif, A.; Ahmed Hamza, M.
A Bayesian Dynamic Inference Approach Based on Extracted Gray Level Co-Occurrence (GLCM) Features for the Dynamical Analysis of Congestive Heart Failure. *Appl. Sci.* **2022**, *12*, 6350.
https://doi.org/10.3390/app12136350

**AMA Style**

Eltahir MM, Hussain L, Malibari AA, K. Nour M, Obayya M, Mohsen H, Yousif A, Ahmed Hamza M.
A Bayesian Dynamic Inference Approach Based on Extracted Gray Level Co-Occurrence (GLCM) Features for the Dynamical Analysis of Congestive Heart Failure. *Applied Sciences*. 2022; 12(13):6350.
https://doi.org/10.3390/app12136350

**Chicago/Turabian Style**

Eltahir, Majdy M., Lal Hussain, Areej A. Malibari, Mohamed K. Nour, Marwa Obayya, Heba Mohsen, Adil Yousif, and Manar Ahmed Hamza.
2022. "A Bayesian Dynamic Inference Approach Based on Extracted Gray Level Co-Occurrence (GLCM) Features for the Dynamical Analysis of Congestive Heart Failure" *Applied Sciences* 12, no. 13: 6350.
https://doi.org/10.3390/app12136350