Automated Detection of Cannabis-Induced Alteration in Cardiac Autonomic Regulation of the Indian Paddy-Field Workers Using Empirical Mode Decomposition, Discrete Wavelet Transform and Wavelet Packet Decomposition Techniques with HRV Signals

Abstract

Early detection of the dysfunction of the cardiac autonomic regulation (CAR) may help in reducing cannabis-related cardiovascular morbidities. The current study examined the occurrence of changes in the CAR activity that is associated with the consumption of bhang, a cannabis-based product. For this purpose, the heart rate variability (HRV) signals of 200 Indian male volunteers, who were categorized into cannabis consumers and non-consumers, were decomposed by Empirical Mode Decomposition (EMD), Discrete Wavelet transform (DWT), and Wavelet Packet Decomposition (WPD) at different levels. The entropy-based parameters were computed from all the decomposed signals. The statistical significance of the parameters was examined using the Mann–Whitney test and t-test. The results revealed a significant variation in the HRV signals among the two groups. Herein, we proposed the development of machine learning (ML) models for the automatic classification of cannabis consumers and non-consumers. The selection of suitable input parameters for the ML models was performed by employing weight-based parameter ranking and dimension reduction methods. The performance indices of the ML models were compared. The results recommended the Naïve Bayes (NB) model developed from WPD processing (level 8, db02 mother wavelet) of the HRV signals as the most suitable ML model for automatic identification of cannabis users.

1. Introduction

Cannabis is a dioecious annual plant, which is used to develop various therapeutic agents for the treatment of pain, nausea, and insomnia in cancer patients and anorexia in acquired immune deficiency syndrome (AIDS) patients [1]. However, the cannabis plant is also used to derive various recreational products like bhang, ganja, and charas. Cannabis-based recreational products are believed to have low toxicity, and their consumption is increasing day by day [2]. As per the reported literature, cannabis has become the most highly used psychotropic recreational compound across the globe, following alcohol and tobacco [1]. Many states of the USA have legalized the non-medical use of cannabis and have allowed companies to sell cannabis to adults who are older than 21 years old [3]. However, many recent reports have revealed the occurrence of a variety of unfavorable health effects of cannabis, including cardiovascular diseases [4]. Hence, it is important to identify the effect of cannabis intake on the cardiovascular activities of cannabis users. It is a well-known fact that the modulation in cardiac autonomic regulation (CAR) provides prognostic information about cardiovascular diseases [5]. This is attributed to the innervations of the sympathetic and vagal nerves of the ANS to the heart [6]. The functioning of the ANS can be understood non-invasively by analyzing the RR interval/HRV signals, derived from the electrocardiogram (ECG) signals [7]. Researchers have proposed both linear and nonlinear techniques for the processing of the HRV signals [8]. However, decomposition-based methods (e.g., EMD, DWT, and WPD) are getting more attention from researchers nowadays because of the nonlinear and non-stationary behavior of the HRV signals [8,9,10].

The EMD technique is a popular nonlinear signal decomposition technique, which was first proposed by Huang et al. (1998) [11]. It divides the input signal into mono-component functions called intrinsic mode functions (IMFs) and simplifies the further processing of the signals [8]. Several researchers have proposed that subtle variations within the HRV signals can be identified easily using EMD [8]. Pachori et al. (2015) performed the EMD analysis of the HRV signals for the automated detection of diabetes [12]. The EMD-based decomposition of the HRV signals produced six IMFs. The IMFs were used to extract two time-domain parameters and three frequency-domain parameters [12]. The clinically significant variations were obtained between the diabetic and control groups, suggesting the applicability of the EMD method in the automated identification of diabetic patients. Djelaila et al. (2016) used EMD analysis of HRV signals and calculated the power spectral density (PSD) of the IMFs for the detection of cardiac arrhythmia [13]. Acharya et al. (2017) reported EMD-based processing of HRV signals to facilitate the automated detection of congestive heart failure (CHF) disease [8]. Each of the HRV signals was decomposed into six IMFs, and 13 types of entropies were extracted from them. The extracted parameters were ranked using five ranking methods, and the highly-rated variables were classified using probabilistic neural networks and support vector machines. The normal and the CHF classes could be classified with the accuracy, sensitivity, and specificity of 97.64%, 97.01%, and 98.24%, respectively. Thus, the authors recommended that the proposed automated method could be employed to recognize the persons suffering from CHF, which will help the clinicians to plan their treatment.

In the last few decades, studies have also been carried out on wavelet (DWT and WPD)-based decomposition of the HRV signals [14,15]. The DWT represents a widely used wavelet-based decomposition method that simultaneously enables the time and frequency domain analyses of the signals [16]. Acharya et al. (2015) employed DWT-based processing of HRV signals for automated diagnosis of diabetes [10]. The HRV signals were extracted from 30 volunteers (15 controls and 15 diabetics). The decomposition of the HRV signals was performed using DWT (level 5, db08 mother wavelet). The parameters, namely, energy, sample entropy, approximation entropy, kurtosis, and skewness, were extracted from the wavelet coefficients, and the ranking of the parameters was carried out. The classification of diabetic and control groups could be performed with a maximum accuracy of 92.02% using the decision tree (DT) algorithm. Thus, the authors recommended that DWT can be considered as a potential candidate for the processing of the HRV signals. The WPD technique represents an extension of the DWT technique. It decomposes a signal like that of DWT. However, the difference lies in the fact that both the approximation and the detail coefficients of WPD participate in decomposition, unlike DWT, where only the approximate coefficient is decomposed at each level. Suparerk Janjarasjitt (2017) proposed WPD (level 3, db02 mother wavelet)-based processing of HRV data for detecting congestive heart failure (CHF) [15]. The spectral exponent of the HRV data was computed and the author could correctly discriminate the CHF patients from the people who were having a normal sinus rhythm. Therefore, WPD has been suggested as a potential method for the processing of the HRV signals. Recently, Geng et al. (2020) used WPD for the parameter extraction of HRV signals along with the Hilbert Huang Transform (HHT) and the Singular Value Decomposition (SVD) techniques for the development of an automatic sleep-staging decision support system [9]. The parameters extracted using WPD exhibited the highest classification accuracy for the random forest (RF) classifier suggesting the superiority of WPD compared to HHT and SVD methods of parameter extraction for HRV signals.

Although the above-mentioned nonlinear signal decomposition methods have been used by many researchers in the processing of HRV signals to carry out the detection of various diseases, no studies could be found that have implemented them for the detection of any alteration in the CAR due to cannabis consumption. Taking motivation from the above-mentioned facts, the current article proposes the decomposition of the HRV signals using the EMD, DWT, and WPD methods to identify variations in the CAR activity in a habitual bhang (a cannabis product)-consuming population. Furthermore, an ML-based model for automatic detection of cannabis users has also been designed. In this manuscript, bhang has been represented as cannabis unless otherwise mentioned.

2. Results

2.1. EMD-Based Analysis of the HRV Signals

EMD has been reported to be an efficient method for the processing of nonlinear and non-stationary data [8]. This may be attributed to its adaptive nature [11]. The HRV signals were subjected to EMD-based decomposition. The decomposition resulted in the generation of at least seven IMFs for each of the HRV signals. Hence, seven IMFs were considered for further analysis [12]. The typical IMFs for HRV signals belonging to Category-C and Category-B have been shown in Figure 1.

The extraction of 11 entropy-based parameters (described in Section 4.3) was carried out from each of the IMFs. The extracted parameters were named XY, where X represents the IMF name and Y indicates the base name of the parameter. Out of the 77 parameters extracted from 7 IMFs, 49 parameters were found to have non-normal distribution, and the remaining 28 parameters exhibited normal distribution as per the Shapiro–Wilk Test. The Mann–Whitney U test (with a critical p-value of 0.05) was used to analyze the statistical importance of the IMF parameters having non-Gaussian distribution. It revealed that the IMF7SpE parameter was significantly different (p-value ≤ 0.05) among Category-C and Category-B. The statistical importance testing using the t-test for the parameters having Gaussian distribution suggested four significantly different parameters among Category-C and Category-B. The statistically different parameters include IMF5SVDE, IMF5SpE, IMF5FI, and IMF5HjC. The median (MD) ± standard deviation (SD), and the25th and 75th percentile values of these parameters, have been tabulated in

Table 1. Characteristics of statistically important IMF-derived parameters.

Parameters	Statistical Test Name	Category-C			Category-B			p-Value
		MD ± SD	25th	75th	MD ± SD	25th	75th
IMF5SVDE	t-test	0.329 ± 0.064	0.288	0.377	0.355 ± 0.054	0.318	0.385	0.010
IMF5SpE	t-test	4.088 ± 0.450	3.756	4.380	4.245 ± 0.523	3.825	4.555	0.049
IMF5FI	t-test	0.884 ± 0.029	0.862	0.902	0.872 ± 0.025	0.858	0.889	0.011
IMF5HjC	t-test	0.076 ± 0.021	0.063	0.092	0.085 ± 0.018	0.071	0.096	0.012
IMF7SpE	Mann-Whitney U	2.420 ± 0.774	2.065	2.847	2.680 ± 0.604	2.359	3.163	0.004

.

Among all the extracted entropy-based parameters, the parameters that ranked within the top 10 by the weight-based parameter ranking methods and the parameters suggested by the dimensionality reduction methods were used as input for developing nine ML models as discussed in Section 4.5.2. As a result, 135 ML (9 ML models × 15 weight-based selection methods) models were developed from 15 weight-based parameter ranking methods, and 45 ML (9 ML models × 5 dimensionality reduction methods) models were obtained from 5 dimensionality reduction methods. The most accurate ML models (out of the nine ML models) along with their performance measures generated from each parameter selection method are shown in

Table 2. Performance matrix of the machine learning models.

Input Selection Methods	Feature Selection Methods	Classifier	Accuracy (%)	AUC	Precision (%)	F-Measure (%)	Sensitivity (%)	Specificity (%)
Weight-based (Top 10 important parameters)	CSS	FLM	61.00 ± 10.49%	0.641 ± 0.122	60.82 ± 9.93%	62.00 ± 10.81%	65.00 ± 16.50%	57.00 ± 17.67%
	CM PCA	GLM	61.00 ± 11.01%	0.618 ± 0.119	61.51 ± 12.96%	61.28 ± 11.86%	63.00 ± 16.36%	59.00 ± 15.95%
	CM ICA	GBT	61.00 ± 12.65%	0.620 ± 0.120	62.80 ± 12.95%	61.03 ± 12.38%	62.00 ± 15.49%	60.00 ± 22.11%
	CM SVD	GBT	60.00 ± 10.27%	0.657 ± 0.104	60.34 ± 11.56%	59.77 ± 11.17%	60.00 ± 13.33%	60.00 ± 14.14%
	Correlation	RF	62.50 ± 9.50%	0.651 ± 0.133	67.60 ± 13.48%	57.26 ± 11.19%	51.00 ± 12.87%	74.00 ± 15.06%
	Deviation	GBT	67.00 ± 10.06%	0.680 ± 0.123	70.79 ± 12.86%	65.57 ± 9.48%	63.00 ± 11.60%	71.00 ± 18.53%
	GI	LR	61.00 ± 4.59%	0.622 ± 0.079	62.28 ± 8.07%	60.49 ± 6.14%	61.00 ± 12.87%	61.00 ± 13.70%
	IG	GBT	67.00 ± 9.78%	0.694 ± 0.104	71.45 ± 15.07%	64.83 ± 12.18%	64.00 ± 20.66%	70.00 ± 21.08%
	IGR	LR	58.00 ± 9.78%	0.628 ± 0.133	59.22 ± 10.93%	57.33 ± 12.12%	59.00 ± 18.53%	57.00 ± 19.47%
	PCA	FLM	64.00 ± 9.37%	0.672 ± 0.132	63.42 ± 9.97%	66.25 ± 8.68%	71.00 ± 12.87%	57.00 ± 18.89%
	Relief	GBT	65.00 ± 11.30%	0.698 ± 0.117	68.56 ± 14.11%	62.92 ± 11.60%	60.00 ± 14.14%	70.00 ± 17.64%
	Rule	GBT	62.50 ± 11.61%	0.661 ± 0.153	62.70 ± 11.32%	61.79 ± 12.92%	62.00 ± 16.19%	63.00 ± 14.18%
	SVM	FLM	59.50 ± 13.43%	0.614 ± 0.154	59.25 ± 11.98%	57.66 ± 15.18%	57.00 ± 18.89%	62.00 ± 12.29%
	TI	DL	60.50 ± 12.12%	0.631 ± 0.144	57.90 ± 10.34%	64.21 ± 14.10%	74.00 ± 21.19%	47.00 ± 17.67%
	Uncertainty	SVM	61.00 ± 9.66%	0.618 ± 0.144	59.98 ± 8.02%	63.09 ± 9.85%	68.00 ± 15.49%	54.00 ± 15.06%
Dimension Reduction	PCA	GBT	58.00 ± 11.11%	0.609 ± 0.117	60.30 ± 17.06%	58.06 ± 10.35%	58.00 ± 12.29%	58.00 ± 18.74%
	ICA	SVM	60.50 ± 9.85%	0.613 ± 0.139	60.99 ± 11.44%	62.08 ± 9.50%	66.00 ± 17.13%	55.00 ± 19.58%
	Kernel PCA	GBT	64.00 ± 14.68%	0.656 ± 0.156	66.38 ± 17.96%	60.12 ± 17.62%	56.00 ± 19.55%	72.00 ± 14.76%
	SVD	RF	58.00 ± 9.49%	0.551 ± 0.142	67.58 ± 23.68%	38.56 ± 18.28%	28.00 ± 15.49%	28.00 ± 15.49%
	SOM	RF	62.00 ± 7.89%	0.647 ± 0.102	61.32 ± 9.76%	60.77 ± 13.44%	62.00 ± 18.74%	62.00 ± 12.29%

[17].

The GBT models generated using the ten important parameters obtained from the “Deviation” and “IG” parameter ranking methods exhibited an accuracy of 67.00 ± 10.06 and 67.00 ± 9.78%, respectively. Although the mean value of the accuracy was the same in both the models, the standard deviation (SD) of the IG-based GBT model was relatively lower than that of the Deviation-based GBT model. Hence, the IG-based GBT model was selected as the most suitable model for automatic identification of cannabis consumers using EMD-based processing of the HRV signals. The GBT model is an ensemble of either classification or regression trees, which uses boosting to provide the results with progressively improved estimations [18]. The proposed GBT model generated 20 classification trees to provide the final classification result. A typical classification tree among them has been shown in Figure 2.

2.2. DWT-Based Analysis of the HRV Signals

DWT is a popular joint time-frequency analysis method that helps to detect subtle variations in the signals [10]. The DWT-based decomposition of the HRV signals was performed from level 2 up to level 8 using Daubechies (db02, db04, db06, and db08) mother wavelets [10]. Hence, 28 different sets of DWT wavelet coefficients were generated in our study. The representative DWT coefficients generated for level 6 decomposition (using db02 mother wavelet) of HRV signals that belonged to Category-C and Category-B, respectively, have been shown in Figure 3.

A total of 11 entropy-based parameters were extracted from each wavelet coefficient. The extracted parameters were named as PQ, where P corresponded to the base name of the parameter and Q indicated the index of the wavelet coefficients. The index of the wavelet coefficients started from 0, i.e., the 1st wavelet coefficient was assigned with the index number 0. For each of the parameters extracted from the 28 different sets of DWT wavelet coefficients, the nature of distribution was found using the Shapiro–Wilk test. The results suggest that the majority of the parameters have non-Gaussian distribution, and the Mann–Whitney U test was performed to test their statistical significance. The parameters having Gaussian distribution were subjected to the t-test to examine their statistical importance. The MD ± SD, and the 25th and 75th percentile values of the statistically important parameters that were extracted from only db02 mother wavelet-based level 2 decomposition, have been provided in

Table 3. Characteristics of statistically important parameters extracted from db02 mother wavelet-based level 2 decomposition of the HRV signals using DWT.

Parameters	Statistical Test Name	Category-C			Category-B			p-Value
		MD ± SD	25th	75th	MD ± SD	25th	75th
SVDE1	t-test	1.399 ± 0.084	1.326	1.459	1.369 ± 0.070	1.317	1.412	0.016
SpE1	t-test	6.808 ± 0.323	6.556	7.061	6.728 ± 0.292	6.512	6.839	0.039
FI1	t-test	0.200 ± 0.073	0.143	0.258	0.221 ± 0.060	0.185	0.266	0.013
HjC1	Mann-Whitney U	1.843 ± 0.074	1.78	1.885	1.856 ± 0.495	1.817	1.886	0.019
HjM1	Mann-Whitney U	1.024 ± 0.017	1.015	1.035	1.019 ± 0.010	1.013	1.025	0.014
PFD1	t-test	1.022 ± 0.001	1.021	1.023	1.023 ± 0.001	1.022	1.023	0.003
PFD2	t-test	1.018 ± 0.001	1.018	1.020	1.019 ± 0.001	1.018	1.02	0.023

as a typical representation.

The parameters were examined for their relevance in the development of ML models using weight-based ranking and dimensionality reduction methods. In the case of the ranking methods, the parameters which ranked within the top 10 were considered relevant. The relevant parameters were used as inputs for the development of the ML models. The accuracies and AUCs of the most efficient ML models developed from the various levels of decomposition of the HRV signals have been provided in

Table 4. Classification and AUC accuracies of the best ML models generated from DWT-based processing of HRV signals at different decomposition levels.

Classification accuracies of the best ML models generated from DWT-based processing of HRV signals at different decomposition levels
Mother Wavelet	Model Details	Decomposition Level
		Level 2	Level 3	Level 4	Level 5	Level 6	Level 7	Level 8
db02	Parameter selection method	Uncertainty	Relief	Uncertainty	SOM	SVM	IG	SVM
	ML Model	GBT	GBT	GBT	RF	GLM	NB	SVM
	Accuracy	62.00 ± 9.49%	64.50 ± 6.85%	65.00 ± 11.30%	64.50 ± 6.85%	61.50 ± 11.07%	64.50 ± 9.26%	66.00 ± 12.65%
db04	Parameter selection method	CSS	Kernel PCA	CSS	CSS	CSS	CSS	CSS
	ML Model	GBT	RF	GBT	GBT	GBT	GBT	GBT
	Accuracy	62.00 ± 9.49%	64.50 ± 6.85%	65.00 ± 11.30%	64.50 ± 6.85%	61.50 ± 11.07%	64.50 ± 9.26%	66.00 ± 12.65%
db06	Parameter selection method	TI	GI	CSS	CSS	CSS	Kernel PCA	CSS
	ML Model	GBT	GBT	GBT	GBT	RF	GBT	GBT
	Accuracy	65.50 ± 13.01%	67.00 ± 8.88%	67.00 ± 6.32%	66.50 ± 5.30%	68.50 ± 8.51%	67.00 ± 12.95%	65.50 ± 8.32%
db08	Parameter selection method	GI	Rule	CSS	Rule	GI	Uncertainty	GI
	ML Model	GBT	GBT	NB	GBT	GBT	GBT	GBT
	Accuracy	71.00 ± 8.43%	65.50 ± 8.64%	67.00 ± 10.59%	69.50 ± 14.03%	68.00 ± 9.19%	67.50 ± 11.84%	73.00 ± 5.87%
AUC of the best ML models generated from DWT-based processing of HRV signals at different decomposition levels
Mother Wavelet	Model Details	Decomposition Level
		Level 2	Level 3	Level 4	Level 5	Level 6	Level 7	Level 8
db02	Parameter selection method	Uncertainty	Relief	Uncertainty	SOM	SVM	IG	SVM
	ML Model	GBT	GBT	GBT	RF	GLM	NB	SVM
	AUC	0.683 ± 0.141	0.661 ± 0.119	0.687 ± 0.141	0.643 ± 0.104	0.661 ± 0.128	0.665 ± 0.084	0.676 ± 0.064
db04	Parameter selection method	CSS	Kernel PCA	CSS	CSS	CSS	CSS	CSS
	ML Model	GBT	RF	GBT	GBT	GBT	GBT	GBT
	AUC	0.617 ± 0.149	0.681 ± 0.097	0.651 ± 0.135	0.691 ± 0.066	0.652 ± 0.095	0.708 ± 0.125	0.719 ± 0.119
db06	Parameter selection method	TI	GI	CSS	CSS	CSS	Kernel PCA	CSS
	ML Model	GBT	GBT	GBT	GBT	RF	GBT	GBT
	AUC	0.692 ± 0.135	0.705± 0.092	0.712 ± 0.091	0.701 ± 0.106	0.742 ± 0.097	0.698 ± 0.126	0.674 ± 0.107
db08	Parameter selection method	GI	Rule	CSS	Rule	GI	Uncertainty	GI
	ML Model	GBT	GBT	NB	GBT	GBT	GBT	GBT
	AUC	0.726 ± 0.098	0.685± 0.141	0.657 ± 0.135	0.724 ± 0.140	0.723 ± 0.096	0.710 ± 0.115	0.797 ± 0.102

, [17]. The GBT model generated during level 8 decomposition (using db08 as the mother wavelet) exhibited the highest accuracy of 73.00 ± 5.87. The top 10 important parameters suggested by the “GI” parameter ranking method were used as the input parameters for the development of this GBT model.

2.3. WPD-Based Analysis of the HRV Signals

The WPD method is a generalization of the DWT technique, where both the approximation and the detail coefficients participate in the decomposition process [19]. The HRV signals were subjected to WPD-based decomposition up to level 8 using Daubechies (db02, db04, db06, and db08) mother wavelets [10]. The typical WPD coefficients generated from level 2 decomposition of the HRV signals (using db02 mother wavelet) that belonged to Category-C and Category-B have been shown in Figure 4.

The extraction and naming of 11 entropy-based parameters were carried out from each of the WPD coefficients, which was similar to that of the DWT-based processing of HRV signals. The Shapiro-Wilk test revealed that majority of the parameters exhibited a non-normal behavior. Hence, their statistical importance was analyzed using the Mann–Whitney U test. The parameters that suggested normal behavior were analyzed for their statistical importance using the t-test. The results of the statistical test suggested several parameters varied significantly among Category-C and Category-B (p-value ≤ 0.05). The MD ± SD, and the 25th and 75th percentile values of the statistically important parameters extracted from db02 mother wavelet-based level 2 decomposition using WPD, have been provided in

Table 5. Characteristics of statistically important parameters extracted from db02 mother wavelet-based level 2 decomposition of the HRV signals using WPD.

Parameters	Category-C			Category-B			p-Value
	MD ± SD	25th	75th	MD ± SD	25th	75th
PFD0	1.040 ± 0.003	1.039	1.043	1.042 ± 0.003	1.04	1.044	0.015
SVDE1	1.344 ± 0.084	1.28	1.397	1.305 ± 0.075	0.103	0.168	0.023
SpE1	5.839 ± 0.334	5.585	6.078	5.743 ± 0.306	5.543	5.869	0.023
FI1	0.243 ± 0.070	0.1988	0.2963	0.276 ± 0.062	0.219	0.31	0.025
HjC1	1.822 ± 0.855	1.749	1.875	1.847 ± 0.057	1.803	1.873	0.021
PFD1	1.048 ± 0.002	1.046	1.049	1.050 ± 0.003	1.047	1.051	0.004
SVDE2	1.362 ± 0.061	1.318	1.409	1.341 ± 0.068	1.292	1.388	0.002
SpE2	6.218 ± 0.388	5.936	6.541	6.060 ± 0.374	5.8	6.356	0.008
FI2	0.226 ± 0.050	0.188	0.266	0.246 ± 0.056	0.207	0.286	0.007
HjC2	1.720 ± 0.144	1.633	1.803	1.782 ± 0.107	1.683	1.836	0.003
HjM2	1.045 ± 0.046	1.031	1.089	1.039 ± 0.041	1.027	1.078	0.024
PFD2	1.048 ± 0.002	1.046	1.05	1.050 ± 0.003	1.047	1.052	0.018
HjC3	1.756 ± 0.143	1.628	1.835	1.805 ± 0.109	1.718	1.86	0.003
HjM3	1.037 ± 0.038	1.018	1.076	1.023 ± 0.028	1.017	1.042	0.008

as a typical representation.

The judgment of the relevance of the parameters using ranking and dimensionality reduction methods as well as the development of the ML models was carried out similarly to that of DWT-based processing of the HRV signals. The accuracies and AUCs of the most efficient ML models developed from each decomposition level in WPD-based processing of the HRV signals have been provided in

Table 6. Classification and AUC accuracies of the best ML models generated from WPD-based processing of HRV signals at different decomposition levels.

Classification accuracies of the best ML models generated from WPD-based processing of HRV signals at different decomposition levels
Mother Wavelet	Model Details	Decomposition Level
		Level 2	Level 3	Level 4	Level 5	Level 6	Level 7	Level 8
db02	Parameter selection method	CSS	Kernel PCA	GI	CSS	IG	SVM	SVM
	ML Model	RF	SVM	GBT	NB	FLM	SVM	NB
	Accuracy	64.50 ± 7.98%	66.00 ± 9.37%	73.00 ± 5.87%	67.00 ± 10.85%	71.50 ± 10.01%	74.00 ± 9.66%	75.00 ± 13.94%
db04	Parameter selection method	CM PCA	IG	IG	IG	GI	IG	SVM
	ML Model	RF	RF	RF	GBT	GBT	GBT	SVM
	Accuracy	67.00 ± 5.87%	70.00 ± 9.43%	67.00 ± 12.52%	70.00 ± 9.43%	68.50 ± 9.73%	69.50 ± 9.85%	72.00 ± 7.15%
db06	Parameter selection method	CM PCA	CSS	IGR	IG	Correlation	SVM	SOM
	ML Model	GBT	GBT	GBT	GBT	GBT	NB	RF
	Accuracy	66.00 ± 11.01%	68.00 ± 13.58%	64.00 ± 11.01%	70.50 ± 9.85%	46.00 ± 8.43%	67.00 ± 12.95%	68.00 ± 12.52%
db08	Parameter selection method	TI	SVM	SVM	GI	IG	CSS	GI
	ML Model	GBT	GBT	GBT	GBT	LR	GBT	GBT
	Accuracy	66.00 ± 8.43%	68.00 ± 11.35%	68.50 ± 12.92%	64.00 ± 11.25%	67.50 ± 8.25%	70.50 ± 8.32%	73.00 ± 5.87%
AUC accuracies of the best ML models generated from WPD-based processing of HRV signals at different decomposition levels
Mother Wavelet	Model Details	Decomposition Level
		Level 2	Level 3	Level 4	Level 5	Level 6	Level 7	Level 8
db02	Parameter selection method	CSS	Kernel PCA	GI	CSS	IG	SVM	SVM
	ML Model	RF	SVM	GBT	NB	FLM	SVM	NB
	AUC	0.690 ± 0.131	0.681 ± 0.135	0.797 ± 0.102	0.669 ± 0.161	0.726 ± 0.112	0.731 ± 0.064	0.797 ± 0.130
db04	Parameter selection method	CM PCA	IG	IG	IG	GI	IG	SVM
	ML Model	RF	RF	RF	GBT	GBT	GBT	SVM
	AUC	0.694 ± 0.091	0.708 ± 0.071	0.706 ± 0.138	68.00 ± 7.89%	0.711 ± 0.097	0.734 ± 0.128	0.780 ± 0.087
db06	Parameter selection method	CM PCA	CSS	IGR	IG	Correlation	SVM	SOM
	ML Model	GBT	GBT	GBT	GBT	GBT	NB	RF
	AUC	0.669 ± 0.124	0.732 ± 0.123	0.687 ± 0.153	0.727 ± 0.124	0.408 ± 0.102	0.693 ± 0.160	0.698 ± 0.136
db08	Parameter selection method	TI	SVM	SVM	GI	IG	CSS	GI
	ML Model	GBT	GBT	GBT	GBT	LR	GBT	GBT
	AUC	0.719 ± 0.113	0.651 ± 0.124	0.722 ± 0.138	0.681 ± 0.156	0.706 ± 0.069	0.711 ± 0.103	0.797 ± 0.102

. The NB model generated during level 8 decomposition (db02 mother wavelet) exhibited the highest accuracy of 75.00 ± 13.94% among all the ML models that were developed using WPD-based processing of the HRV signals. This model used the top 10 important parameters ranked by the “SVM” method as the input parameters.

3. Discussion

Cannabis refers to one of the ancient annual plants that are found mainly in Central Asia. It has been reported that cannabis plants were cultivated in China as much as 10,000 years ago for food and medical applications [20]. The ancient use of cannabis is also evident from the mythological scriptures. In Hindu mythology, cannabis (bhang) has been designated as the favorite food of Lord Shiva, and it is used as a beverage in many ceremonies like Shivaratri, Holi, etc. However, cannabis-based products are also consumed as popular illicit drugs due to their psychoactive behavior. In the last 50 years, the recreational intake of cannabis by adolescents and young adults has increased exponentially. As per Hall et al. (2009), the recreational cannabis intake by college students was first observed in 1979 in the USA, and it has gradually spread to the entire globe [21]. Cohen et al. (2019) have reported that ~4% of the entire population of the globe consume cannabis. Consumption is more in the USA compared to other rich countries in Europe [22]. The authors have revealed that ~11% of the US population have taken cannabis at least once in their lifetime. This might be because of the legalization of recreational cannabis use by adults in various states of the USA since 2012 [23]. However, various adverse health effects of recreational cannabis intake have been found in regular cannabis users [22]. This has been evident from the increased emergency department visits and hospitalizations by regular cannabis users. Among the various adverse health effects of cannabis consumption, the risk of addiction remains the primary concern [24]. It has both short-term as well as long-term influences on the functioning of the brain. The short-term effect depends on the way that cannabis is consumed. When a person smokes cannabis, the psychoactive compound (i.e., tetrahydrocannabinol (THC)) reaches the lungs directly, from where it quickly partitions into the bloodstream. The compound is then easily transported to the brain and other organs. On the other hand, THC is passed to the brain at a slower rate of up to 30 min to 1 h when it is consumed as a food or drink. The psychoactive compound acts on the brain cell receptors, thereby inducing short-term effects like altered sense, delusion, psychosis, and hallucination. The long-term effects of cannabis consumption on the brain include the decline in intelligence quocient (IQ) level and verbal ability, and the risk of anxiety and depression. The physical effects of cannabis on breathing, pregnancy, and vomiting, etc., have also been reported in addition to the mental effects.

The adverse effects of cannabis consumption on cardiovascular activities were also acknowledged more than four decades ago [25]. Some of the common and acute effects include an increment in heart rate and blood pressure that causes an enhancement in the workload of cardiac muscles. Kalla et al. analyzed the National Inpatient Sample (NIS) database of patients to understand the prevalence of cardiovascular diseases in people who regularly consumed cannabis [26]. They found that diseases like a cardiac failure and coronary artery disease were more in cannabis users than in the general population. Van Keer reported a case of complete heart block in a 19 year-old boy after the intake of cannabis [27]. The treatment of the patient was started using IV isoprenaline, and the occurrence of bradycardia was resolved within 24 h. Based on the outcomes, the boy was advised to stop consuming cannabis and the author recommended that the doctors in the emergency department should be aware of the potential cardiovascular effects of cannabis intake. Although many such cardiovascular complications have been reported in cannabis takers [4,28], the underlying mechanisms causing such effects are still very little known [25]. Hence, it is the need of the hour to understand the modulation in cardiovascular activity that is caused by cannabis consumption.

An understanding of the CAR provides valuable diagnostic information about the cardiovascular activity. This is because the rhythmic contraction of the heart is primarily regulated by the ANS through its nerve innervations (both vagal and sympathetic) into the heart. The ANS activity results in the alteration of the time duration between the consecutive RR intervals (also regarded as the HRV signals) [29]. Hence, the HRV signals have been widely used in the last few decades for diagnosing any imbalance in the CAR activity due to any external stimuli or diseases [8]. Usually, the processing of the HRV signals is performed using the time domain (statistical, geometric), frequency domain (e.g., FFT, AR), or the nonlinear methods (e.g., Poincare plot, recurrence quantification analysis (RQA), correlation dimension, and detrended fluctuation analysis (DFA)) [30]. However, several recent studies have proposed the use of signal decomposition-based techniques like EMD, DWT, and WPD for the analysis of the HRV signals [8,9,10]. This may be attributed to their ability to evaluate the original signatures that are present within the nonlinear and non-stationary HRV signals [8,31]. Hence, EMD, DWT, and WPD-based processing of the HRV signals were performed in the current study to examine the existence of any alteration in the CAR activity due to cannabis consumption. The EMD method resulted in the generation of at least seven IMFs from each HRV signal. Hence, only the first seven IMFs of each HRV signal were chosen as the input signals for the feature extraction process [12]. The selection of the appropriate mother wavelet plays a vital role in the wavelet analysis of the signals. Singh et al. (2006) have advocated the use of the Daubechies series of the mother wavelet for the processing of the HRV signals due to its ability to clearly reveal the properties of the transient and other components of the HRV signals [32]. Hence, Daubechies (db) wavelet was used as the mother wavelet for the processing of the HRV signals using DWT and WPD. The level of decomposition of the HRV signals was varied from 2 to 8 for identifying the most suitable level of decomposition.

The entropy-based parameters were extracted from the IMFs and the wavelet coefficients to obtain useful information related to the corresponding HRV signals. The reason behind the extraction of the entropy-based parameters may be attributed to the fact that entropy reveals the rate of generation of the information in a dynamical system and is extensively used as a complexity measure in the biomedical signal analysis [8,33]. Apart from this, the entropy-based parameters also help to quantify the degree of regularity in the signal by examining the repetitive patterns [34].

It is customary to use hypothesis testing as a tool for establishing whether there is a significant difference between the data of two populations using samples of a relatively lower size [35]. The t-test method was used for hypothesis testing when the parameter followed the normal distribution. However, most of the IMF and wavelet coefficient-derived entropy parameters did not exhibit the normal distribution (evident from the Shapiro—Wilk test). Hence, the Mann–Whitney U test (with a critical p-value = 0.05) was used to identify the significantly varying parameters for such parameters, which is a nonparametric statistical method. This method does not require the normal distribution of the parameters [36]. The results of the t-test and Mann–Whitney U test revealed many statistically significant parameters. This corresponds to the existence of variation in the characteristics of the HRV signals obtained from Category-C and Category-B. The variation in the HRV signal behavior might be due to the alteration in the CAR activity induced by cannabis intake. This is because HRV signals are regarded as a non-invasive indicator of CAR [37]. The analysis of these HRV signals using time and frequency methods by our group [38] has revealed an increase in sympathetic activity and a corresponding reduction in parasympathetic activity due to the regular intake of cannabis. This information further supported the hypothesis regarding the alteration of CAR activity due to the regular consumption of cannabis.

The ML models are currently extensively studied for the development of automated decision support systems for biomedical applications [39]. Many youths across the globe are getting addicted to cannabis products and may suffer from various health issues in the future. The development of automated cannabis user detection can help the healthcare givers to detect the changes in cardiac electrophysiology at an early stage. Accordingly, healthcare givers can counsel cannabis users to refrain from its consumption. Hence, the current study is an attempt to develop an ML model that can be used for the automated detection of the bhang-consuming population from their HRV signals. Although the efficiency of our developed ML models based on signal decomposition techniques may not be high, it will help researchers to do further research in this direction to develop robust automated cannabis-user detection systems that will contribute to the computer-aided prognosis of cannabis-induced ailments.

A small and efficient set of signal parameters is important for the development of an ML model [40]. This is because the optimal number of parameters reduces the complexity of the feature space that helps the model to achieve better performance. It also reduces the noise of the target signal [40]. Therefore, 15 weight-based parameter ranking methods and 5 dimensionality reduction methods were applied for the identification of the reduced set of the appropriate parameters to develop the ML models. The important parameters revealed by each method were used to train and validate nine ML models. The most accurate models developed from the EMD, DWT, and WPD decomposition methods have been summarized in Table 2, Table 4 and Table 6, respectively. The accuracy (75.00 ± 13.94%) of the NB model generated from the WPD-based processing of the HRV signals outperformed the highest accuracies of the best GBT models, i.e., 73.00 ± 5.87% and 67.00 ± 9.78%, generated by the DWT and EMD-based processing of the HRV signals, respectively. The other performance measures for this model were the AUC of 0.797 ± 0.130, precision (%) of 76.66 ± 15.22%, the F-measure (%) of 73.90 ± 15.22%, sensitivity (%) of 72.00 ± 16.87%, and specificity (%) of 78.00 ± 13.98%. Most of these measures were also superior to the other models. Hence, the NB model generated from WPD-based decomposition (db02 mother wavelet) of HRV signals at level 8 has been proposed for the automated identification of the bhang consuming population.

An in-depth review of the recent literature on the effects of cannabis on cardiovascular health was conducted. A comparative analysis of the studies has been summarized below in

Table 7. Recent studies on the effects of cannabis on cardiovascular health.

Author, Year	Signals Used	Processing Methods or Parameters Extracted	Statistical Methods Used	Classifiers Used	Inference
DeAngelis et al. (2020) [41]	Blood pressure, heart rate, mean arterial pressure	Systolic blood pressure; diastolic blood pressure, heart rate and mean arterial pressure	Independent-sample t-test and chi-square test	-	Reduced positive (euphoria) and negative (stress, anxiety) affective reactions to acute stress have been linked to chronic cannabis use, suggesting dysregulation of emotions.
Rompala et al. (2021) [42]	HRV signal at rest and during auditory startle, hair hormone levels and neurobehavioral traits	HF power components of HRV and gene expressions	Generalized linear model	-	Cannabis intake causes increased cortisol, anxiety, aggression, and hyperactivity in young children.
Lee et al. (2021) [43]	Echocardiogram, Heart rate and body temperature	Estimation of stroke volume, ejection fraction, fractional shortening, and cardiac output.	Student’s t-test	-	Maternal intake of cannabis during pregnancy harms fetal growth, causing cardiac dysfunction in the offspring
Majhi et al. (2022) [44]	ECG Signals	Statistical and Entropy features	Mann–Whitney U test	ML Models (NB, GLM, LR, FLM, DL, DT, RF, GBT, and SVM)	Statistical and entropy features extracted from ECG segments effectively separate women who use cannabis from those who don’t.
Razanouski et al. (2022) [45]	Heart rate, blood pressure and HRV signal	Time-domain parameters	-	-	Increase in parasympatheitic activity due to increased dosage of cannabis
Our Study	HRV Signals	Signal Decomposition methods (EMD, DWT and WPD) and Entropy computation	Shapiro–Wilk test, Mann–Whitney U test and t-test	ML Models (NB, GLM, LR, FLM, DL, DT, RF, GBT, and SVM)	Detected significant variation in the HRV signals among the regular cannabis users and non-users. Further, ML models for automatic classification of the cannabis-induced changes in HRV signals have been proposed.

.

4. Materials and Methods

4.1. Acquisition of the ECG Signals and Extraction of the HRV Signals

The present study involved the analysis of the HRV signals of 200 paddy-field workers who had given consent to volunteer in this study. All of them were residents of the Sambalpur district in Odisha, India [38]. Written consent from the volunteers was taken as per the World Health Organization (WHO) guidelines. Initially, there were 218 paddy-field workers, out of which 207 paddy-field workers gave written permission for their voluntary participation in the study after detailed information about the study was provided to them. Out of the 207 interested volunteers, 200 volunteers were chosen for this study based on our inclusion criteria of 18–60 years of age and no occurrence of cardiovascular diseases [38]. Prior ethical approval was received from the Institute Ethical Committee (IEC) of NIT Rourkela, India (Ref.# NIRTKL/IEC/FORM-2/002; dated 16/8/2017) to acquire the ECG signals. The ECG signals were acquired using an ECG machine (VESTA 121i ECG machine, RMS Pvt. Ltd., India) for 5 min in the lead-I configuration. The sampling rate of the ECG machine was 500.6 Hz. The acquired signals were divided into two categories, i.e., Category-C (control group) and Category-B (bhang consuming group) [38]. Each of the categories comprised 100 signals. The ECG signals were processed through the Biomedical Workbench toolkit of LabVIEW (V2017, National Instruments, USA) and were further analyzed using the Pan–Tompkins algorithm to extract the RR interval signals (also known as HRV Signals). The ECG Feature Extractor tool of the Biomedical Workbench toolkit initially performs the signal enhancement through bandpass filtering (10–25 Hz). The employment of the bandpass filter allows for the extraction of the QRS complexes from the ECG signals. After the filtering process, the processed signal is rectified by squaring the signal. The combined processing technique allows the ECG Feature Extractor tool to extract the R waves accurately [46]. The use of default settings has also been suggested in numerous studies like Zaidi et al. (2017) [47] and Khong et al. (2019) [48]. The tool subsequently uses a threshold adjustment factor for the identification of the R peaks. In other words, a threshold value is used to detect the peak of the R-wave. The default threshold adjustment factor of 0.1 was used in our study. Furthermore, the “remove noise from raw signal” box was ticked to obtain a noise-free measurement, as recommended by Khong et al. (2019) [48]. The HRV signals were resampled at 4 Hz before subjecting them to decomposition using the EMD, DWT, and WPD methods [49].

4.2. Decomposition of the HRV Signals

4.2.1. EMD

The decomposition of the signals using EMD is a relatively new nonlinear signal processing method. It is employed for the processing of nonlinear and non-stationary signals [11]. Herein, the basis functions for decomposition are derived from the signal itself, unlike the Fourier or wavelet transforms where the basis signal is pre-fixed. The EMD method decomposes a given signal into several intrinsic mode functions (IMFs) and a residue (Equation (1)) using the process regarded as sifting [50]. The IMFs are a set of amplitude and frequency (AM–FM) modulated signal components. They satisfy two criteria: (i) the number of maxima and minima should be either the same or vary only by one to the number of zero crossings, and (ii) the average value of the envelopes formed by connecting local maxima and minima of the signal is zero [8]. As the HRV signals are nonlinear and non-stationary [38], the decomposition of the HRV signals was carried out by EMD. The implementation of the decomposition process was carried out in MATLAB software (2015a, MathWorks Inc., Natick, MA, USA).

$$x(t)={\displaystyle \sum _{k=1}^M{f}_k(t)+r_M(t)}$$

(1)

where M represents the number of IMFs, f_k(t) indicates the kth IMF, and r_M corresponds to the residue.

4.2.2. DWT

The DWT is a widely used joint time-frequency analysis method [16]. Herein, the term wavelet refers to irregular, non-symmetric, and short-duration waveforms having finite energy, zero mean, and a real value of Fourier transform [19]. Wavelets have been used to analyze typical events that are embedded within a signal. Researchers have used DWT as an efficient tool for the processing of non-stationary signals. In DWT, the signals are decomposed into the detail and the approximation coefficients at each level by passing them through a high-pass and a low-pass filter, respectively. The detail coefficient is kept undivided, but the approximation coefficient is subjected to decomposition again in the next step, which results in the formation of a new set of detail and approximation coefficients. The decomposition process continues till the desired level of decomposition has arrived. Hence, a signal x(t) can be expressed as the sum of its approximation coefficient at a specific scale m₀ (i.e., x_m0(t)) and the detail coefficients with scales ranging from −$\infty$ to m₀ as shown in Equation (2) [51]. The decomposition of the HRV signals using DWT was carried out in this study with the help of MATLAB software (2015a, MathWorks Inc., Natick, MA, USA).

$$x(t)=x_{m_0}(t)+{\displaystyle \sum _{m=-\infty }^{m_0}{d}_m(t)}$$

(2)

where, x_m0(t) = approximation coefficient at scale m₀ and d_m(t) = detail coefficient at scale m.

4.2.3. WPD

The WPD method is an extension of the DWT method with the advantage of providing a more precise decomposition of the high-frequency components of the given signal [52]. It differs from the DWT method in the sense that the decomposition of both the approximation and the detail coefficients takes place at each level of WPD, which contrasts with the DWT method where only the approximation coefficient is decomposed. The decomposition process in WPD segregates the time-frequency plane into rectangles having a constant aspect ratio [19]. In other words, as the level of decomposition is increased, the side of the rectangle representing the time axis becomes broader, and the side representing the frequency axis becomes narrower. In this study, the decomposition of the HRV signals using WPD was performed with the help of MATLAB software (2015a, MathWorks Inc., Natick, MA, USA).

4.3. Parameter Extraction

In this study, 11 entropy-based parameters were extracted from each of the decomposed (EMD, DWT, and WPD) signals using Python (Version 3.7, Python Software Foundation, Wilmington, DE, USA). The extracted parameters include: Approximate entropy (ApE), Sample Entropy (SaE), Shannon Entropy (ShE), Spectral Entropy (SpE), SVD Entropy (SVDE), Permutation Entropy (PE), Fisher Information (FI), Signal Activity (SiA), Hjorth Mobility (HjM), Hjorth Complexity (HjC), and Petrosian Fractal Dimension (PFD). A brief description of these parameters has been given below.

4.3.1. Approximate Entropy (ApE)

The ApE parameter can be regarded as the entropy that estimates the variation and instability in a signal [8]. It is calculated as given in Equation (3) [53]. The value of ApE quantifies the regularity in the signal.

$$\mathrm{ApE}=\ln \left(\frac{S_l(k)}{C_{l+1}(k)}\right)$$

(3)

where k represents the coefficient of similarity and $S_l(k)$ and $C_{l+1}(k)$ represent patterns with a mean length of l and l + 1, respectively. The parameter l was set to 2 for the calculation of ApE in our study.

4.3.2. Sample Entropy (SaE)

The SaE parameter represents a type of entropy that tries to determine the regularity inherent in a signal irrespective of the signal length. Its value can be computed as given in Equation (4) [54]. A high value of SaE corresponds to a significantly unpredictable signal and vice versa.

$$\mathrm{SaE}=-\log \left(\frac{M}{N}\right)$$

(4)

where M and N indicate the vector pair having lengths of a + 1 and a, respectively. The vector length a was set to 2 during the calculation of SaE in our study.

4.3.3. Shannon Entropy (ShE)

The ShE parameter divulges information regarding the extent to which the probability of a signal is spread out over all the possible magnitudes of the signal. It is often considered a measure of uncertainty. ShE is calculated from the signal amplitude using Equation (5).

$$\mathrm{ShE}=-{\displaystyle \sum _{t=1}^{n}p(x_t)}\cdot \ln (p(x_t))$$

(5)

where x_t represents the possible amplitude values of the signal.

4.3.4. Spectral Entropy (SpE)

The SpE parameter is a special case of ShE wherein the calculation of the entropy is done using the distribution of the normalized power spectrum of the signal. Mathematically, it is represented by Equation (6).

$$\mathrm{SpE}=-{\displaystyle \sum _{t=1}^{n}p(Y_t)}\cdot \ln (p(Y_t))$$

(6)

where Y_t represents the possible amplitude values in each frequency band.

4.3.5. Singular Value Decomposition Entropy (SVDE)

The SVDE is a complexity measure based on the singular value decomposition of the data matrix (signal). The value of SVDE corresponds to the orderliness or disorderliness of a signal, which is elucidated by a single eigenvector. Mathematically, SVDE is defined using Equation (7) [55]. The complexity of a signal is a function of its attributes. A higher value of the SVDE of a signal suggests that there is more complexity and the involvement of more attributes [56].

$$\mathrm{SVDE}=-{\displaystyle \sum _{i=1}^M\overline{{\sigma }_i}}\cdot {\log }_2(\overline{{\sigma }_i})$$

(7)

where M represents the number of values and $\overline{{\sigma }_i}$ represents the normalized singular value.

4.3.6. Permutation Entropy (PeE)

The PeE is a measure of complexity for time series similar to Lyapunov exponents [57]. However, it provides meaningful results even in the presence of noise. Its value is calculated using Equation (8) [58]. A high value of PeE is indicative of the asymmetry in the given signal [8]. For the calculation of PeE in our study, the decomposed signals were converted into a time series of time delay = 1 and an embedding dimension = 3 for representation in the state space.

$$\mathrm{PeE}=-{\displaystyle \sum p(\pi )}{\log }_2(p(\pi ))$$

(8)

where $p(\pi )$ represents the probability of occurrence of each permutation π of order n.

4.3.7. Fisher Information (FI)

The FI parameter represents the amount of information conveyed by a random variable X for a parameter of interest θ (Equation (9)) [59]. This concept has a relation with the law of entropy because both of them offer ways to measure the disorderliness in a system [60]. Similar to the PE calculation, the decomposed signals were converted into a time series of time delay = 1 and an embedding dimension = 3 for the calculation of PeE in our study.

$$I_X(\theta )=\{\begin{array}{l}{{\displaystyle {\sum }_{x\in X}(\frac{d}{d\theta }\log f(x|\theta ))}}^2{p}_{\theta }(x)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}if\hspace{0.17em}X\hspace{0.17em}is\hspace{0.17em}discrete\\ {{\displaystyle {\int }_X(\frac{d}{d\theta }\log f(x|\theta ))}}^2{p}_{\theta }(x)dx\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}if\hspace{0.17em}X\hspace{0.17em}is\hspace{0.17em}continuous\end{array}$$

(9)

where the derivative $\frac{d}{d\theta }\log f(x|\theta )$ is called the score function and describes the sensitivity of the model (i.e., the function f) for the changes in θ.

4.3.8. Hjorth Descriptors

A Hjorth descriptor represents a digital signal processing method that offers the statistical parameter values in the time domain [61].

Signal Activity (SiA)

The SiA is the first Hjorth descriptor and can be defined as a measure of the squared standard deviation of the amplitude or the variance of a signal (Equation (10)) [62].

$$\mathrm{SiA}={\displaystyle \sum _{i=1}^N\frac{x_i-\mu }{N}}$$

(10)

where x_i and µ represent the amplitude value of the signal and the mean of the signal, respectively. N represents the number of samples of the signal.

Hjorth Mobility (HjM)

The HjM represents the second Hjorth descriptor that provides information about the mean frequency of the signal. It can be expressed using Equation (11) [63].

$$\mathrm{HjC}=\frac{{\sigma }_x^{\prime }}{{\sigma }_x}$$

(11)

where σ_x represents the variance of the signal and ${\sigma }_x^{\prime }$ represents the 1st derivative of the variance, respectively.

Hjorth Complexity (HjC)

The HjC is the third Hjorth descriptor, which provides an estimation of the bandwidth of a signal. Here, the bandwidth is represented by the ratio of peak value to the harmonic content of the signal. Mathematically, it is given by Equation (12) [62].

$$\mathrm{HjC}=\frac{\raisebox{1ex}{${\sigma }_x^{″}$}\!\left/ \!\raisebox{-1ex}{${\sigma }_x^{\prime }$}\right.}{\raisebox{1ex}{${\sigma }_x^{\prime }$}\!\left/ \!\raisebox{-1ex}{${\sigma }_x$}\right.}$$

(12)

where σ_x represents the variance of the signal, and ${\sigma }_x^{\prime }$ and ${\sigma }_x^{″}$ represent the 1st and the 2nd derivative of the variance, respectively.

4.3.9. Petrosian Fractal Dimension (PFD)

The fractal dimension of a signal calculated using Petrosian’s algorithm is regarded as PFD. The fractal dimension helps to detect the occurrence of transients in the signal. The calculation of the PFD takes place very fast because the computation is carried out directly in the time domain. If a signal is an analog, then Petrosian’s algorithm derives a digital sequence from it by subtracting the consecutive samples of the signal and assigning either a + 1 or a − 1 to the subtraction result based on whether it is positive or negative. Mathematically, PFD is given by Equation (13).

$$\mathrm{PFD}=\frac{{\log }_{10}n}{{\log }_{10}n+{\log }_{10}(\raisebox{1ex}{$n$}\!\left/ \!\raisebox{-1ex}{$n+0.4N△$}\right.)}$$

(13)

where n represents the length of the sequence and $N△$ refers to the number of sign changes in the sequence.

4.4. Statistical Analysis

The Shapiro–Wilk test was used to determine the nature of the distribution of the parameters extracted using all the decomposition methods, namely, EMD, DWT, and WPD. The parameters having a p-value of ≤0.05 were confirmed to have non-Gaussian distribution. On the other hand, the parameters having a p-value of ≥0.05 were considered to follow the Gaussian distribution. The parameters having non-Gaussian distribution were tested for their significance using the Mann–Whitney U test, also regarded as the Wilcoxon rank-sum test, using IBM SPSS Statistics software (ver. 24, IBM Corporation, Armonk, NY, USA) [64]. This test does not require the normal distribution of the parameters due to its nonparametric nature [65]. For parameters with Gaussian distribution, the t-test was used for statistical analysis. The Mann–Whitney U test/t-test was performed on the parameters of the different groups in the population under investigation, namely Category-B and Category-C. Here, Category-B refers to the bhang-consuming population and Category-C indicates the control group. There were 100 samples in each of the groups; therefore, each of the groups had 100 samples in the Mann–Whitney U test/t-test.

4.5. Development of Machine Learning-Based Models

In recent years, many studies have reported the use of machine-learning model-based automated diagnosis/identification of stimulants or diseases [66]. This helps the clinicians to accelerate the treatment process [39,67]. Hence, machine learning models have been developed in our study (using RapidMiner software, Educational Version 9.3, RapidMiner Inc., Troy, MI, USA), which can automatically recognize the cannabis-consuming population using the extracted entropy-based parameters of the decomposed HRV signals [68].

4.5.1. Selection of Input Parameters

The selection of suitable input parameters is important for the proper performance of the machine learning models [69]. In this study, the choice of the parameters was performed using the parameter ranking methods of (Information Gain (IG), Information Gain Ratio (IGR), Uncertainty, Gini Index (GI), Chi-Squared Statistic (CSS), Correlation, Deviation, Relief, Rule, Tree Importance (TI), Support Vector Machine (SVM), and Component Model (CM)), and the dimensionality reduction methods of (Principal Component Analysis (PCA), Kernel PCA, Independent Component Analysis (ICA), Singular Value Decomposition (SVD), and Self-Organizing Map (SOM)) [40]. A short description of the parameter selection methods and their Rapidminer implementation details are provided in

Table 8. Description of the parameter selection methods.

Method	Description		Rapidminer Implementation	Ref.
IG	IG is a weight-based parameter selection method that describes the dependency between a parameter X with a class variable Y by divulging information about the reduction in entropy. IG is defined by Equation (14) [70].		The IG method is implemented using the “Weight by Information Gain” operator. It finds out the relevance of the parameters through information gain and allocates weights to them. It has three critical attributes, namely, normalize weights, sort weights, and sort direction. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending	[70]
	$IG=H(Y)-H(Y\backslash X)=H(X)-H(X\backslash Y)$	(14)
	where H(Y) represents the entropy of Y and H(Y|X) corresponds to the entropy of Y given X.
IGR	IGR is a parameter selection method that is derived from IG by dividing it with the entropy of the parameter (Equation (15)). IGR helps to expiate the bias introduced by the IG method.		The IGR method is implemented using the “Weight by Information Gain Ratio” operator. It detects the relevance of the parameters through the information gain ratio and allocates weights to them. It has three critical attributes, namely, normalize weights, sort weights, and sort direction. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending	[71]
	$IGR=\frac{IG}{H(X)}$	(15)
	where H(X) represents the entropy of parameter X.
Uncertainty	Uncertainty is another parameter selection method that focuses on eliminating the inherent bias introduced by the IG method. It is computed as the ratio of twice the IG to the sum of the entropies of the parameter X and the class variable Y (Equation (16)).		The uncertainty method is implemented using the “Weight by Uncertainty” operator. The uncertainty method measures the symmetrical uncertainty to identify the importance of the parameters. It has four critical attributes, namely, normalize weights, sort weights, sort direction, and number of bins. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending number of bins = 10	[71]
	$U=\frac{2 \times IG}{H(X) + H(Y)}$	(16)
	where U indicates the uncertainty of Y.
GI	GI is an impurity-based parameter selection method. It describes the likelihood of the wrong classification of a randomly selected variable. For a given data set S (i.e., s1, s2, s3…sn) and a class variable Ci (1 ≤ i ≤ k), GI is computed using Equation (17). The value of GI lies between 0 and 1, where 0 means the variable is most useful for classification and vice-versa.		The GI method is implemented using the “Weight by Gini Index” operator. It computes the relevance of the parameters through the impurity index. It has three critical attributes, namely, normalize weights, sort weights, and sort direction. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending	[72]
	$GI(S)=1-{\displaystyle \sum _{i=1}^k}{P}_i^2$	(17)
	where Pi refers to the probability of any sample of Ci
CSS	CSS is a popular nonparametric method of parameter selection. It determines the importance of a parameter using the value of the chi-squared statistic (χ2) that is calculated using a class as the reference (Equation (18)). A higher value of χ2 refers to the higher importance of the parameter.		The CSS method is implemented using the “Weight by Chi-Squared Statistic” operator. It quantifies the relevance of the parameters through the computation of CSS. It has four critical attributes, namely, normalize weights, sort weights, sort direction, and the number of bins. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending number of bins = 10	[73]
	${\chi }^2={\displaystyle \sum _{i=1}^r{\displaystyle \sum _{j=1}^c\frac{{(O_{ij}-E_{ij})}^2}{E_{ij}}}}$	(18)
	where Oij refers to the perceived frequency, and Eij refers to the expected frequency.
Correlation	Correlation can be regarded as a parameter selection method that is based on the extent of similarity among the parameters. The degree of similarity between any two parameters X and Y is represented with the help of correlation coefficient r (Equation (19)). The value of the correlation coefficient ranges from −1 to 1, where the sign represents the kind of association, i.e., negative or positive, respectively. Its value becomes 0 when the parameters are uncorrelated.		The “Weight by Correlation” operator is used for the implementation of the Correlation method. It quantifies the relevance of the parameters through the computation of the absolute or squared value of correlation. It has four critical attributes, namely, normalize weights, sort weights, sort direction, and squared correlation. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending squared correlation = false	[74,75]
	$r=\frac{{\displaystyle \sum _{i=1}^n({\mathrm{X}}_i- \overline{\mathrm{X}} ){.(\mathrm{Y}}_i- \overline{\mathrm{Y}} )}}{(n-1).\sqrt{\frac{{\displaystyle \sum _{i=1}^n{{(\mathrm{X}}_i- \overline{\mathrm{X}} )}^2}}{n-1}}.\sqrt{\frac{{\displaystyle \sum _{i=1}^n{{(\mathrm{Y}}_i- \overline{\mathrm{Y}} )}^2}}{n-1}}}$	(19)
	where i indicates the increment variable and n refers to the number of samples of the parameters X and Y.
Deviation	Deviation refers to the normalized standard deviation of the parameters. For a parameter X, the standard deviation is calculated using Equation (20) and its normalization can be carried out using the maximum or minimum value of the parameter.		The “Weight by Deviation” operator is used for the implementation of the Deviation method. It has four critical attributes, namely, normalize weights, sort weights, sort direction, and normalize. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending normalize = none	[75]
	$SD=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{{(\mathrm{X}}_i- \overline{\mathrm{X}} )}^2}}{n-1}}$	(20)
	where i indicates the increment variable and n refers to the number of samples of the parameters X and Y.
Relief	Relief is a supervised parameter selection method generally used in classification problems. In this method, the samples are chosen arbitrarily from the given data set. Then, their nearest samples belonging to the same class (i.e., near-Hit) and their nearest samples belonging to the other class (i.e., near-Miss) is determined. A score (St) is assigned to the parameter under consideration using Equation (21). The S scores of all the parameters are compared, and the top K parameters are finally considered as the relevant parameters.		The relief method is implemented using the “Weight by Relief” operator. It has six critical attributes, namely, normalize weights, sort weights, sort direction, and the number of bins. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending number of neighbors = 10 sample ratio = 1.0 use local random seed = false	[76]
	$\begin{array}{l}{S}_t(i)=S_{t-1}(i)-\frac{d(x_t-nearHi{t}_t)}{n}\\ +\frac{d(x_t-nearMis{s}_t)}{n}\end{array}$	(21)
	where xt indicates the arbitrarily chosen sample of the given data set at iteration number t, n represents the total number of samples of the given data set, and d(.) corresponds to Euclidean distance.
Rule	The Rule represents a parameter selection method that creates a rule for each of the parameters and calculates the error for them. Each parameter is assigned with a weight based on the error associated with it. The relevance of the parameters is decided based on the value of the weights assigned to them.		The rule method is implemented using the “Weight by Rule” operator. It has three critical attributes, namely, normalize weights, sort weights, and sort direction. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending	[75]
TI	TI represents the parameter selection method that uses a random forest for determining the importance of the parameters. The random forest is an ensemble learning method containing many decision trees. These decision trees are produced using the parameters extracted from the given dataset. The reduction in impurity caused by each node of all the decision trees is computed. The average value of impurity reduction caused by a parameter over all the trees determines the importance of that parameter.		The TI method is implemented using the “Weight by Tree Importance” operator. It has three critical attributes, namely criterion gain_ratio and normalize weights. In our study, the following values of the attributes were chosen: criterion = gain_ratio normalize weight = false	[77]
SVM	SVM is a widely used machine learning method that employs hyperplanes (i.e., normal vectors) for classifying the samples of a signal into several classes. The coefficients associated with the hyperplanes are used to assign weights to the parameters and to rank them. Nevertheless, SVM can act as a parameter selection method only when the parameters have numeric values.		The SVM method is implemented using the “Weight by SVM” operator. It has four critical attributes, namely, normalize weights, sort weights, sort direction, and complexity weighting factor (C). In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending C = 0.0	[78]
CM	The CM method is also a weight-based parameter selection method. However, the peculiarity of this method lies in the fact that it assigns weights to the parameters based on a component generated using the techniques like PCA, ICA, etc. The weights are usually normalized to retain them in the span of 0 to 1.		The CM method is implemented using the “Weight by Component Model” operator. It has four critical attributes, namely, normalize weights, sort weights, sort direction, and component number. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending component number = 1	[75]
PCA	PCA is a popular statistical method that uses an orthogonal transformation to convert a number of correlated parameters to a set of uncorrelated parameters known as principal components. The orthogonal transformation is carried out using the eigenvalue analysis of the covariance matrix (S), generated from the parameters of the given signal. The elements of the covariance matrix are defined using Equation (22). The well-defined patterns that are stronger than the noise can be detected in the signal using PCA. Therefore PCA-based dimension reduction also finds application in noise removal. The importance of PCA in parameter selection lies in the fact that it employs the variance of the signal and transforms the signal to new dimensions having fewer parameters, but still preserving maximum variance.		The PCA method is implemented using the “Weight by PCA” operator. It has four critical attributes, namely, normalize weights, sort weights, sort direction, and component number. In our study, the following values of the attributes were chosen: normalize weight = false sort weight = true sort direction = ascending component number = 1	[79,80]
	$s_{ij}=\mathrm{cov}ariance(d_{*i},\hspace{0.17em}{d}_{*j})$	(22)
	where sij indicates the covariance of the ith and jth parameters of the given signal.
Kernel PCA	Kernel PCA refers to the generalization of the PCA method using kernels (such as linear, polynomial, or Gaussian) for application to nonlinear data. In this method, the input signal is transformed into a new parameter space using a nonlinear transformation. A kernel matrix K is formed through the dot product of the newly generated parameters in the transformed space, which act as the covariance matrix. In the end, PCA is performed on the kernel matrix K and is called the kernel PCA method.		The Kernel PCA method is implemented using the “Weight by PCA (Kernel)” operator. It has two critical attributes, namely kernel type and kernel gamma. In our study, the following values of the attributes were chosen: kernel type = false kernel gamma = 1.0	[81]
ICA	ICA can be regarded as a statistical method that decomposes a complex signal into independent components. ICA is a generalization of the PCA method. Nevertheless, ICA optimizes the higher-order statistics (e.g., kurtosis), unlike PCA, which optimizes the 2nd order statistics of the given signal. Therefore ICA produces independent components, whereas PCA generates uncorrelated components.		The ICA method is implemented using an “Independent Component Analysis” operator. The critical attributes of this operator and their values in our implementation are listed below: dimensionality reduction = none algorithm type = deflation function = logcosh alpha = 1.0 row norm = false max iteration = 200 tolerance = 10−4 use local random seed = false	[82,83]
SVD	SVD is also an extension of the PCA method where the highly correlated parameters are eliminated to reduce redundancy. It results in fewer components as compared to PCA, but retains most of the variance of the extracted signal parameters.		The SVD method is implemented using the “Singular Value Decomposition” operator. It has two critical attributes, namely, dimension reduction and dimensions. In our study, the following values of the attributes were chosen: dimension reduction = fixed number dimensions = 1	[84]
SOM	SOM corresponds to a neural network that helps in dimension reduction-based parameter selection. It is also called the Kohonen map, where the map denotes the low-dimensional representation of the parameters of the given signal. It is distinct from the other artificial neural networks in terms of the implementation of the neighborhood function. This further facilitates the preservation of the topological characteristics of the input parameters and the low-dimensional representation of the high-dimensional signals.		The SOM method is implemented using “Self-Organizing Map” operator. The critical attributes of this operator and their values in our implementation are listed below: return preprocessing model = false number of dimensions = 2 net size = 10 training rounds = 30 learning rate start = 0.8 learning rate end = 0.01 adaption radius start = 10.0 adaption radius end = 1.0	[85]

.

4.5.2. Machine Learning Techniques

The ML methods, namely, Naïve Bayes (NB), Generalized Linear Model (GLM), Linear Regression (LR), First Large Margin (FLM), Deep Learning (DL), Decision Tree (DT), Random Forest (RF), Gradient Boosted Tree (GBT), and Support Vector Machine (SVM) were implemented in our study using the Rapidminer software [68]. The selection of the nine ML models was made as per the recommendation of the Auto Model feature of the Rapidminer software [86]. Evaluation of the performance of the developed models using validation techniques plays an important role in establishing their generalizability. Cross-validation provides an efficient way of evaluating the performance of ML models with a limited data set. The efficacy of the developed models was examined through a 10-fold cross-validation technique. The partition of the data set into ten equal subsets was performed using a stratified sampling method to implement the 10-fold cross-validation method [75]. In this process, the total data set was divided into training and validation data sub-sets in a 9:1 ratio, randomly 10 times. Finally, the performance of the 10-fold cross-validated ML models was highlighted using the following metrics: accuracy, area under the receiver operating characteristics curve (AUC), precision, sensitivity, F-Measure, and specificity (

Table 9. Performance measures of classification models.

Performance Measures	Description		Ref.
Accuracy	Accuracy represents one of the most popular performance evaluation tools. It can be obtained by dividing the number of accurately classified observations by the total number of observations done by the classification model. Mathematically, accuracy is given by Equation (23).		[87]
	$\mathrm{Accuracy}\hspace{0.17em}=\frac{TP+TN}{TP+FP+TN+FN}$	(23)
	where TP, TN, FP, and FN refer to the true positive value, the true negative value, the false positive value, and the false-negative value, respectively. A true positive is an outcome when the model accurately predicts the positive class. A true negative is a result for which the model provides an accurate prediction of the negative class. If the model mistakenly predicts a positive class, this is called a false positive. When the model erroneously forecasts the negative class, this is known as a false negative.
AUC	AUC refers to the total area under the receiver operating characteristics (ROC) curve. The ROC curve represents a probability curve that indicates the performance of an ML model in differentiating between the classes at all classification thresholds. The value of AUC describes the degree of separability of the classification model.		[38]
Precision	Precision represents the ratio of accurately classified positive observations to the number of observations classified as positive (Equation (24)). It is also regarded as the positive predictive value.		[87]
	$\mathrm{Precision}\hspace{0.17em}=\frac{TP}{TP+FP}$	(24)
	where TP and FP refer to the true positive value and the false positive value, respectively.
Sensitivity	Sensitivity refers to the ratio of accurately classified positive observations to the total number of positive observations (Equation (25)). It is also called true positive rate (TPR) and recall.		[87]
	$\mathrm{Sensitivity}=\frac{TP}{TP+FN}$	(25)
	where TP and FN refer to the true positive value and the false negative value, respectively.
F-measure	F-measure represents the harmonic mean of precision and sensitivity (Equation (26)). Its value can vary from 0 to 1 and is nearly the same as accuracy (in %).		[17]
	$\mathrm{F}-\mathrm{measure}=2 \times \frac{\mathrm{Pr}ecision \times Sensitivity}{\mathrm{Pr}ecision+Sensitivity}=\frac{2 \times TP}{2 \times TP+FP+FN}$	(26)
	where TP, FP, and FN refer to the true positive value, the false positive value, and the false-negative value, respectively.
Specificity	Specificity corresponds to the ratio of accurately classified negative observations to the total number of negative observations (Equation (27)).		[17]
	$\mathrm{Specificity}\hspace{0.17em}=\frac{TN}{TN+FP}$	(27)
	where TN and FP refer to the true negative value and the false positive value, respectively.

).

4.5.3. Final Model Generation

The performance of all the models was examined from their performance metrics mentioned above. Based on the result of the performance comparison of all the developed ML models, the best model was selected to automatically recognize the cannabis-consuming population.

5. Conclusions

The occurrence of cardiovascular diseases in cannabis users is increasing day by day. This demands that the alteration in the physiology of the CAR (the primary regulator of heart activity) is recognized and that automated cannabis user identification tools are developed. The current study attempted to detect the alteration in the CAR activity due to regular cannabis intake. The HRV signals obtained from 200 Indian male paddy-field workers were subjected to three popular decomposition methods, namely, EMD, DWT, and WPD. The extraction of entropy-based parameters was carried out from the IMFs and the wavelet coefficients. The statistical analysis of the entropy parameters using the Mann–Whitney test suggested a significant variation of the entropy parameters between the control and the bhang-consuming group. This fact suggested a change in CAR activity caused by cannabis intake. The present study also attempted to propose an ML model for the automated recognition of the bhang consuming population. The suitable input parameter set for the ML models was chosen using a weight-based parameter ranking and dimension reduction methods. For each set of input parameters, nine ML models were developed. The performance indices of the ML models developed from EMD, DWT, and WPD-based processing of the HRV signals were scrutinized to select the best model. The results suggest that an NB model developed from WPD-based decomposition (level 8, db02 mother wavelet) of the HRV signal is the most efficient model for automated identification of cannabis users. The model used the top 10 parameters suggested by the weight-based parameter ranking method, i.e., SVM, as the input parameters. The weight-based feature ranking methods are used to identify the most relevant features in a data set. This helps to improve the speed of computation and enhances the accuracy of classifiers. Many recent studies like Chang et al. (2017) [88], Wang et al. (2018) [89], and Maguire et al. (2022) [90] have recommended the use of the top-10 features obtained in feature ranking methods for the development of machine learning (ML) models. Hence, the top-10 features were used for classification purposes in our study. In summary, a variation in the CAR activity was detected due to regular cannabis intake, and the WPD method was found to be a superior parameter extraction method as compared to the other decomposition methods, namely EMD and DWT. However, one limitation of the current research lies in the fact that the increase in the family-wise error rate in the statistical analyses performed in our study was not controlled [91]. As multiple statistical tests were used in our study, it was planned to apply the multiple testing correction method called the sequential Bonferroni correction technique. This technique keeps the p-values at a constant value of 0.05. However, several researchers have argued against its use for testing correction, due to its mathematical and logical flaws. Hence, it was not performed [91]. Overall, we consider this research relatively preliminary and encourage future replication of this study.