# Entropy-Based Machine Learning Model for Fast Diagnosis and Monitoring of Parkinson’s Disease

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## Abstract

**:**

_{RKF}) of ~99.9%. The most important frequency range of rs-EEG for PD-based diagnostics lies in the range of 0–4 Hz, and the most informative signals were mainly received from the right hemisphere of the head. It was also found that A

_{RKF}significantly decreased as the length of rs-EEG segments decreased from 1000 to 150 samples. Using a procedure for selecting the most informative features, it was possible to reduce the computational costs of classification by 11 times, while maintaining an A

_{RKF}~99.9%. The proposed method can be used in the healthcare internet of things (H-IoT), where low-performance edge devices can implement ML sensors to enhance human resilience to PD.

## 1. Introduction

- A comparative analysis of the effectiveness of various methods for calculating entropy for identifying PD was carried out;
- The most significant frequency ranges and EEG channels were identified, as well as their combinations;
- A study was conducted to reduce computational costs by selecting the most significant features and reducing the length of the EEG segments analyzed;
- A method of monitoring a patient’s condition based on entropy values was developed;
- We propose a machine learning model for monitoring the health status of Parkinson’s patients using an IoT environment based on low-performance sensors.

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Signal Preprocessing

- Original (O) signal; frequency ranges: (0–64 Hz);
- Signals reconstructed based on approximation coefficients (cA1–cA4); frequency ranges: (cA1 (0–32 Hz), cA2 (0–16 Hz), cA3 (0–8 Hz), cA4 (0–4 Hz));
- Signals reconstructed based on detail coefficients (cD1–cD4); frequency ranges: (cD1 (32–64 Hz), cD2 (16–32 Hz), cD3 (8–16 Hz), cD4 (4–8 Hz)).

#### 2.3. Feature Generation

#### 2.3.1. SVDEn

_{1}, x

_{2}, … x

_{i}, … x

_{N}] of length N, an embedding matrix A is created as follows:

_{1}, …, λ

_{k}, located on the main diagonal of the matrix, which are called singular values.

_{k}also provides an indication of the complexity of signal dynamics [47]. Singular values can be normalized as:

#### 2.3.2. PermEn

_{i}—the frequency of occurrence of the i-th permutation in embedded matrix A, which is defined in the same way as (1).

#### 2.3.3. SampEn

_{1}, x

_{2}, … x

_{N}] of length N contains several stages. First, the series is divided into template vector ${X}_{i}^{m}$ = [x

_{i}, x

_{i}

_{+1}, … x

_{i}

_{+m−1}] of length m (m < N). Then, the number C (m, r) of pairs of vectors ${X}_{i}^{m}$ and ${X}_{j}^{m}$ (i ≠ j) for which the Chebyshev distance ChebDist[${X}_{i}^{m}$, ${X}_{j}^{m}$] does not exceed r is calculated.

#### 2.3.4. CoSiEn

_{1}, x

_{2}, … x

_{N}] of length N contains several stages. First, the series is divided into template vector ${X}_{i}^{m}$ = [x

_{i}, x

_{i}

_{+1}, … x

_{i}

_{+m−1}] of length m (m < N). Then, the number B (m, r) of pairs of vectors ${X}_{i}^{m}$ and ${X}_{j}^{m}$ (i ≠ j) for which the angular distance AngDist[${X}_{i}^{m}$, ${X}_{j}^{m}$] does not exceed r is calculated.

#### 2.3.5. FuzzyEn

^{m}is expressed through:

#### 2.3.6. PhaseEn

_{1}, x

_{2}, … x

_{N}] of length N, it is necessary to first construct vectors Y and W, which are the coordinates of the points on the second-order difference plot, defined as follows:

_{i}(i = 1…K) is calculated:

_{i}is calculated for each of the K sectors:

#### 2.3.7. AttnEn

_{1}, x

_{2}, … x

_{N}] of length N contains several stages. First, it is necessary to calculate the positions of local minima and maxima within the time series. By local minimum, we mean point x

_{i}for which the inequalities x

_{i}< x

_{i}

_{−1}and x

_{i}< x

_{i}

_{+1}hold, and by local maximum, we mean point x

_{j}for which the inequalities x

_{j}> x

_{j}

_{−1}and x

_{j}> x

_{j}

_{+1}hold. Then, the intervals between two successive peak points (minima and maxima) are calculated. In this case, 4 variants of such intervals are considered: between two maximums (I

_{max-max}), between two minimums (I

_{min-min}), between the maximum and the subsequent minimum (I

_{max-min}), between the minimum and the subsequent maximum (I

_{min-max}).

_{max-max}, I

_{min-min}, I

_{max-min}, I

_{min-max}) for each set, the frequency of occurrence of each interval within the set is calculated, on the basis of which Shannon entropy values are calculated (ShEn

_{max-max}, ShEn

_{min-min}, ShEn

_{max-min}, ShEn

_{min-max}). The AttnEn value is the average of these entropies: AttnEn = (ShEn

_{max-max}+ ShEn

_{min-min}+ ShEn

_{max-min}+ ShEn

_{min-max})/4.

#### 2.4. Assessment of Classification Accuracy

_{RKF}accuracy across the new partitions.

## 3. Experimental Results and Discussion

#### 3.1. Classification Accuracy Using One Method for Calculating the Entropy

_{RKF}) of each entropy feature with different hyperparameters. These entropy features were computed with varying hyperparameter values in this study. Using five non-overlapping segments of 40 subjects (20 PDs and 20 NCs), we extracted entropy features from 200 datasets. In this task, the optimal parameters for each of the entropy calculations were determined.

_{RKF}= 99.9% was demonstrated for FuzzyEn with parameters (m = 1, r = 0.15 × std, r

_{2}= 5). The influence of the r parameter in this case is insignificant. It was observed that the A

_{RKF}value increases as the r

_{2}parameter increases from 1 to 5. The next most accurate entropy method was AttnEn (A

_{RKF}= 97.9%). This method has no hyperparameters. Acceptable accuracy was achieved for PermEn (A

_{RKF}= 95% for m = 5) and SVDEn (A

_{RKF}= 93.6% for m = 3). Both curves have a maximum at intermediate values of the m parameter. The worst results were obtained using the SampEn (A

_{RKF}= 91.5% for m = 2, r = 0.25 × std), PhaseEn (A

_{RKF}= 81.5% for K = 6), and CoSiEn (A

_{RKF}= 81.3% for m = 3, r = 0.05) methods.

#### 3.2. Classification Accuracy Using One Type of Signal

_{RKF}using each type of nine signals (O, cA1–cA4, cD1–cD4) for each of the 14 channels (14 features in total). The values of the optimal entropy parameters correspond to those presented in Section 3.1. Figure 4 shows the dependence of A

_{RKF}on the type of signal.

_{RKF}classification compared to using all 126 features. When using FuzzyEn, the A

_{RKF}value had high values for the following signals: cD2 (A

_{RKF}= 98.9%), cA3 (A

_{RKF}= 98.2%), cA4(A

_{RKF}= 98%). For other entropies, high A

_{RKF}values were observed for signals O, cA1, cA2, cA3, cA4. Perhaps this is due to the presence of a low-frequency component in the range from 0 to 4 Hz in these signals, namely O (0–64 Hz), cA1 (0–32 Hz), cA2 (0–16 Hz), cA3 (0–8 Hz), and cA4 (0–4 Hz), while cD1 (32–64 Hz), cD2 (16–32 Hz), cD3 (8–16 Hz), and cD4 (4–8 Hz) signals contain higher frequency components. Low-frequency rhythms (delta and theta) are usually prominent while the eye is closed and in a resting state compared to waking and alert states (while the eye is open and focused). People with neurological disorders, particularly those with delta and theta rhythms, tend to have these rhythms dominate more than healthy individuals. Due to this, low-frequency rhythms (alpha to gamma) are more accurate in diagnosing Parkinson’s disease than high-frequency rhythms.

_{RKF}= 1 − A

_{RKF}increased by 11 times compared to the result achieved when using all features (Section 3.1). Thus, the use of one frequency range is not enough to achieve maximum classification accuracy A

_{RKF}= 99.9%.

#### 3.3. Classification Accuracy Using a Single Channel

_{RKF}using all nine signal types (nine features in total) corresponding to one of the 14 channels (AF3, F7, F3, FC5, T7, P7, O1, O2, P8, T8, FC6, F4, F8, AF4). The values of the optimal entropy parameters are specified in Section 3.1. In Figure 5, A

_{RKF}is shown in relation to the channel number.

_{RKF}value for most channels was obtained using FuzzyEn for the P8 (A

_{RKF}= 90.8%) and F8 (A

_{RKF}= 88.8%) channels. It is not possible to find pronounced dependencies that are repeated for all entropies. The classification accuracy obtained when using one channel is significantly reduced compared to the results achieved when using all channels: minimum classification error E

_{RKF}increases by ~8 times when using one channel and one type of signal (Section 3.2) and 92 times when using all signals and all channels (Section 3.1). This suggests the need to use multichannel EEG measurement devices to maximize accuracy.

#### 3.4. Classification Accuracy Using One Feature

_{2}= 5. The graphs are grouped by signal types and are divided into two groups:

- Group 1 consists of signals based on detail wavelet coefficients, as follows: cD1 (32–64 Hz), cD2 (16–32 Hz), cD3 (8–16 Hz), and cD4 (4–8 Hz);
- Group 2 consists of the original signal and signals based on approximation wavelet coefficients, as follows: O (0–64 Hz), cA1 (0–32 Hz), cA2 (0–16 Hz), cA3 (0–8 Hz), and cA4 (0–4 Hz).

_{RKF}(A

_{RKF_mean}) is equal to 67.1%, while for the rest of the frequency ranges, A

_{RKF_mean}~63%. Among the signals in the second group (Figure 6b), the most informative is cA3 (0–8 Hz), with an average value of A

_{RKF_mean}= 71.4%, while signals with the presence of higher-frequency components show lower values of A

_{RKF_mean}: 63.2% for O (0–64 Hz), 62.9% for cA1 (0–32 Hz), and 65.8% for cA2 (0–16 Hz). The lower accuracy of A

_{RKF_mean}= 68.2% for cA4 (0–4 Hz) may indicate that the 4–8 Hz range is needed to improve signal classification accuracy. The highest classification accuracy by one feature was obtained for the T8 channel and the cA3 signal: A

_{RKF}= 79.5%.

_{RKF}value from those presented in Figure 6a,b. It can be noted that for most of the channels presented in the table (T8, O2, FC6, F3, AF4), only the low-frequency components of the original signal are the most informative, namely cA3 (0–8 Hz), cA4 (0–4 Hz), and cD4 (4–8 Hz), while for channels F8 and O1, signals with high-frequency components are also informative: O (0–64 Hz) and cD1 (32–64 Hz). It is also worth noting that most of the channels that give the best results were located in the right hemisphere of the head.

## 4. Model Optimization

_{RKF}changes with the number of features computed using FuzzyEn (Section 3.4). In order to do this, we used an iterative approach in which only the first feature gave the maximum value of A

_{RKF}. Next, the A

_{RKF}value was calculated for the combination of two features. The evaluation procedure was repeated with one more of the remaining features added. Figure 7 illustrates the dependence of A

_{RKF}on feature numbers.

_{RKF}is 99.9%, which is the same as that achieved using all 126 features. By minimizing the number of features, it is possible to reduce the computational costs of classification and use lower-performance devices for analysis, such as peripheral IoT devices or embedded analytical modules in EEG signal measurement devices.

_{EEG}) can also be reduced to reduce the amount of data to be processed. In Section 3, we used segments with 1000 counts (~7.8 s). However, it is possible to shorten this length in order to speed up calculations. We achieved this by reducing the most resource-intensive part of the analysis—the calculation of FuzzyEn. Another part of the time is spent filtering the signal using wavelet methods. According to Figure 8, A

_{RKF}accuracy depends on the number of L

_{EEG}readings when using all 126 features (see Section 3.1) or the 11 most informative ones (this section).

_{EEG}of 1000 samples provides a high classification accuracy of 99.9% for both 11 and 126 features. As segment length L

_{EEG}decreases, classification accuracy A

_{RKF}also decreases, but less intensely for 126 features than for 11. For example, a decrease in length even by 20% (up to L

_{EEG}= 800) led to a decrease in accuracy to 99.4% for 126 features and to 98.2% for 11 features. Thus, E

_{RKF}error increased by 6 times for 126 features and by 18 times for 11 features.

_{EEG}and different numbers of features. The calculations were performed on a desktop computer with an Intel i5-7200U (2.5 GHz) processor and 8 GB of RAM.

_{comp}depends linearly on segment length L

_{EEG}, since most of the time is spent calculating entropy features. It took approximately 0.06 s to calculate one feature with a length of L

_{EEG}= 1000. In Figure 9, it can be observed that by reducing the number of features, calculation time can be significantly reduced (for example, with L

_{EEG}= 1000, calculation time varies by 11 times) while maintaining a low classification error (see Figure 8). The reduction in segment length does not significantly improve calculation speed (for example, the speed difference between L

_{EEG}= 1000 and L

_{EEG}= 800 is only 25%), but significantly increases classification error E

_{RKF}.

## 5. Future Work: Smart IoT Environment Concept for Patient Health Monitoring

_{RKF}of ~99.9%. For future research, it is possible to propose the development of a type of Sensor 2.0 which will be implemented in the real device (wireless headset) (Figure 10). EEG signals will be input into the model, and the output will be the degree of disease development. This may be part of a smart IoT environment for patient health monitoring. To implement the EEG signal classification methods proposed in this work, it is proposed that Raspberry Pi Zero W be used.

## 6. Conclusions

_{RKF}of ~99.9%, while reducing data processing time by ~11 times. A study of the dependence of classification accuracy A

_{RKF}on the length of EEG segments (L

_{EEG}) showed a significant decrease in A

_{RKF}with a decrease in L

_{EEG}: from 99.9% for L

_{EEG}= 1000 to 98.3% for L

_{EEG}= 800 when using the 11 best features. At the same time, decreasing the value of L

_{EEG}only slightly reduced computation time, so this approach does not make much practical sense. This also shows the limitations of the method: to obtain a high classification accuracy, it is necessary to use long segments of the EEG signal (1000 samples or ~7.8 s). An optimized model with a small number of features, reducing computational costs, could be used in low-performance devices, and so would be applicable for smart IoT environments with ML sensors.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Dependence of classification accuracy A

_{RKF}on entropy parameters using all 126 features for PermEn (

**a**), PhaseEn (

**b**), SampEn (

**c**), CoSiEn (

**d**), FuzzyEn (

**e**), and SVDEn (

**f**).

**Figure 4.**Dependence of classification accuracy A

_{RKF}on signal type for different entropy calculation methods: PhaseEn (K = 6), SVDEn (m = 3), PermEn (m = 5), AttnEn, CoSiEn (m = 3, r = 0.05), SampEn (m = 2, r = 0.25 × std), and FuzzyEn (m = 1, r = 0.15 × std, r

_{2}= 5).

**Figure 5.**Dependence of classification accuracy A

_{RKF}on the channel number for different entropy calculation methods: PhaseEn (K = 6), SVDEn (m = 3), PermEn (m = 5), AttnEn, CoSiEn (m = 3, r = 0.05), SampEn (m = 2, r = 0.25 × std), and FuzzyEn (m = 1, r = 0.15 × std, r

_{2}= 5).

**Figure 6.**Dependence of classification accuracy A

_{RKF}on channel number for FuzzyEn method (m = 1, r = 0.15 × std, r

_{2}= 5), grouped by signal types: (

**a**) cD1, cD2, cD3, cD4; (

**b**) O, cA1, cA2, cA3, cA4.

**Figure 10.**The concept of a smart IoT environment that can continuously monitor Parkinson’s disease patients.

Entropy Name | Parameter Range |
---|---|

SVDEn | order m = 2…10, delay = 1 |

PermEn | order m = 2…10, delay = 1 |

SampEn | order m = 1…3, tolerance r = 0.05…0.5 × std |

CoSiEn | order m = 2…3, tolerance r = 0.05…0.5 |

FuzzyEn | order m = 1…2, tolerance r = 0.05…0.5 × std, exponent membership function of order r _{2} = 1…5 |

PhaseEn | K = 2…10 |

AttnEn | no parameters |

Channel | Signal Type | A_{RKF}, % |
---|---|---|

T8 | cA3 | 79.5 |

O1 | cA4 | 77.1 |

FC6 | cA4 | 76.9 |

O2 | cA3 | 76.5 |

FC6 | cA3 | 76.2 |

F8 | cA2 | 74.9 |

T8 | cA4 | 74.2 |

F3 | cA3 | 74.2 |

F8 | O | 73.4 |

F8 | cD1 | 73.4 |

O1 | cA3 | 72.4 |

F8 | cA3 | 72.3 |

AF4 | cA3 | 72.1 |

O1 | O | 71.9 |

AF4 | cD4 | 71.6 |

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**MDPI and ACS Style**

Belyaev, M.; Murugappan, M.; Velichko, A.; Korzun, D.
Entropy-Based Machine Learning Model for Fast Diagnosis and Monitoring of Parkinson’s Disease. *Sensors* **2023**, *23*, 8609.
https://doi.org/10.3390/s23208609

**AMA Style**

Belyaev M, Murugappan M, Velichko A, Korzun D.
Entropy-Based Machine Learning Model for Fast Diagnosis and Monitoring of Parkinson’s Disease. *Sensors*. 2023; 23(20):8609.
https://doi.org/10.3390/s23208609

**Chicago/Turabian Style**

Belyaev, Maksim, Murugappan Murugappan, Andrei Velichko, and Dmitry Korzun.
2023. "Entropy-Based Machine Learning Model for Fast Diagnosis and Monitoring of Parkinson’s Disease" *Sensors* 23, no. 20: 8609.
https://doi.org/10.3390/s23208609