Wavelet based Machine Learning Approaches towards Precision

Medicine in Diabetes Mellitus

Adeethyia Shankar

, Stephanie Chang

, Xiaodi Wang

and Yongzhong Zhao

Department of Mathematics, Western Connecticut State University, 181 White Street, Danbury, U.S.A.

Department of Cellular and Molecular Medicine, Cleveland Clinic, Cleveland, U.S.A.

Keywords: Diabetes Mellitus, Discrete M-band Wavelet Transform, Machine Learning, Precision Medicine, Data

Visualization, t-SNE, UMAP.

Abstract: It is estimated that 422 million people around the world have diabetes mellitus (DM)—a devastating, complex,

and highly heterogeneous disease—requesting better interventions based on disease subtyping. In this

research, we utilize the discrete wavelet transform (DWT) to decompose and denoise DM data. Using DWT,

we enhance heart rate variability (HRV) based DM diagnosis, data visualization of the disparities in Human

Microbiome Project (HMP) data (gut bacteria, metabolomics, proteomics, RNA sequencing, targeted

proteomics, and transcriptomics data) using demographic features, and insulin resistance prediction. We also

attempt to forecast continuous glucose monitoring (CGM) ahead by 90 minutes because CGM is unable to

provide real-time blood glucose measurements. We achieve 91.9% diagnosis accuracy for Type 1 DM using

Random Forest on data transformed with DWT, holding the potential for usage in clinics. In addition, our

DWT-based t-SNE and UMAP explorative analysis of HMP data support subtypes of prediabetic patients

stratified by sex, race, and age. Moreover, DWT-based transformations provide multi-view clustering that

any other methods would not provide on metabolomics, proteomics, RNA sequencing, targeted proteomics,

and transcriptomics data and outperform those without DWT. Taken together, DWT-based machine learning

approaches enable a fine resolution of subtyping DM towards precision medicine.

1 INTRODUCTION

Diabetes Mellitus (DM)—a group of metabolic

diseases that manifest themselves with chronic

hyperglycemia resulting from issues with insulin

absorption or production—is estimated to have a

prevalence of 422 million people around the world.

DM is a devastating, complex, and highly

heterogeneous disease, requesting better

interventions based on disease subtyping (Kharroubi

& Darwish, 2015).

Hypoglycemia is a condition where blood sugar

drops below normal levels. It is a relatively common

condition in diabetic patients, although it occurs more

frequently in individuals affected by type 1 DM

(T1D). While hypoglycemia is usually harmless,

prolonged hypoglycemia without action can lead to

seizure, brain damage, or even death. Conversely,

hyperglycemia is a condition where blood sugar rises

above normal levels and this condition is more

https://orcid.org/0000-0003-4298-2797

common with individuals affected by T1D. However,

untreated hyperglycemia can result in damage to

various tissues, comatose, or even death.

Because of these conditions, monitoring blood

glucose levels is vital. While accurate blood glucose

can be given in near real-time, predicting blood

glucose levels into the near future would be a useful

tool in preventing abnormal levels of glucose. By

using machine learning methods, we sought to

provide accurate predictions for blood glucose levels

in individuals with T1D or type 2 DM (T2D).

At the same time, diagnosing DM is essential for

the long-term health of patients. Nevertheless, many

of these tests are either inaccurate or very

inconvenient. For example, the A1C test is affected

by many factors, including anemia, smoking,

pregnancy, and certain infections (Bonora &

Tuomilehto, 2011). Other tests, like the glucose

tolerance test, take too much running time for many

individuals. By using machine learning methods, we

290

Shankar, A., Chang, S., Wang, X. and Zhao, Y.

Wavelet based Machine Learning Approaches towards Precision Medicine in Diabetes Mellitus.

DOI: 10.5220/0010993100003123

In Proceedings of the 15th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2022) - Volume 4: BIOSIGNALS, pages 290-297

ISBN: 978-989-758-552-4; ISSN: 2184-4305

sought to classify individuals as healthy or T1D by

using heart rate variability (HRV).

In this research, we utilize the discrete wavelet

transform (DWT) to decompose and denoise DM

data, and to create multi-view clustering viewing

window as well.

To address many aspects of the DM illnesses and

their treatments, we base our study on CGM forecast,

HRV-based diagnosis, and DM subtyping. Across

these topics, we identify prediabetes (i.e., subtyping

by demographics, prediction of insulin resistance), as

well as type 1 (i.e., diagnosis, managing blood

glucose) and type 2 DM (i.e., managing blood

glucose). Combining all of these topics shines light

on DWT-based machine learning approaches towards

precision medicine. In addition, our DWT-based t-

SNE and UMAP explorative analysis of HMP data

support subtypes of prediabetic patients stratified by

sex, race, age, insulin resistance(IR)/insulin

sensitivity(IS) based on DWT of proteomics, targeted

proteomics, and transcriptomics data.

1.1 CGM Forecast

The introduction of continuous glucose monitoring

(CGM) enables non-invasive and more

comprehensive monitoring. CGM sensors can deliver

interstitial glucose levels every 1 to 5 minutes, in

contrast with previous glucose monitoring methods.

This provides a significantly more detailed time series

on glucose levels that can be automatically sent to

smart devices. However, CGM devices are unable to

accurately find blood glucose levels; rather, CGM

lags behind the trend of blood glucose levels. As a

result, it is necessary to be able to forecast glucose

levels by using CGM measurements to provide real-

time glucose updates for diabetic patients (Lobo et al.,

2021).

Using a modified Artificial Neural Network

(ANN), a model that replicates the interconnected

neurons of the brain, Bertachi et al. predicted blood

glucose 15, 30, 45, and 60 minutes ahead and

achieved RMSEs of 6.43, 7.45, 8.13, and 9.03,

respectively (Bertachi et al., 2018). In 2017, Fiorini et

al. trained 4 different models namely Long Short

Term Memory (LSTM), Auto Regressive Integrated

Moving Average (ARIMA), Kalman Filter, and

Kernel Ridge Regression (KRR) with a dataset of 148

patients (Fiorini et al., 2017). KRR was the most

accurate for 30, 60, and 90 minutes, successively.

However, each model was trained to fit separate

individuals, rather than fitting all of the patients.

These methods differed from previous ones with the

introduction

of methods that are not based on neural

networks, such as KRR.

In this research, we propose a method to

accurately predict glucose levels using a novel

technique developed by Facebook called Prophet. We

also use traditional methods ARIMA and KRR as

benchmarks (Taylor & Letham, 2017).

1.2 Diabetes Prediction using HRV

Heart rate variability (HRV) refers to the variability

in RR intervals, which are the time between

consecutive heartbeats. As DM has a harmful impact

on the heart, HRV in diabetic patients is reduced

(Kardelen et al., 2006). As a result, HRV has been

used to detect DM. Seyd et al. used an ANN, to

classify HRV signals from 65 healthy people and 65

diabetic patients. Using the ANN, they achieved an

accuracy of 93.08%, a precision of 96.67%, and a

recall of 89.23% (P.t. et al., 2011). Similar to Seyd et

al., Swapna used a Convolutional Neural Network

(CNN), but combined with LSTM and support vector

machine (SVM) for the classification of

echocardiogram (ECG) signals of 20 diabetic patients

and 20 healthy individuals. Swapna et al. attained a

high accuracy of 95.7% with the combination model

(Swapna et al., 2018).

On the other hand, machine learning (ML)

algorithms have also been used to classify HRV data

with comparably high metrics. Acharya et al.,

recording ECG signals and obtaining HRV signals

from 15 healthy and 15 diabetic patients, achieved an

accuracy of 90.0%, precision of 88.9%, and recall of

92.5% with the AdaBoost classifier with the least

squares method (Rajendra acharya et al., 2013).

Furthermore, in a later work, Acharya et al. carried

out the Decision Tree algorithm on the same HRV

signals transformed using Wavelet decomposition up

to 5 levels, resulting in an accuracy of 92.64%,

precision of 92.59%, and a recall of 92.68%

(Rajendra acharya et al., 2015).

To predict DM using HRV signals, we examined

the SVM, XGBoost, and Random Forest (RF) on

HRV signals transformed in a variety of methods via

DWT. While RF has been used to diagnose DM

(Samant & Agarwal, 2018; Benbelkacem, 2019),

XGBoost and RF have not been used prior to classify

HRV signals transformed using DWT, and our

remarkable experimental results strongly support our

algorithm.

1.3 Wavelet based t-SNE and UMAP

t-SNE (t-Distributed Stochastic Neighbor

Embedding) visualization in biomedical fields has

Wavelet based Machine Learning Approaches towards Precision Medicine in Diabetes Mellitus

291

been recently growing in popularity, particularly for

high-dimension single-cell sequencing data.

However, its application in the detection of DM still

remains rare and limited. UMAP (Uniform Manifold

Approximation and Projection) is widely applied in

data visualization and dimension reduction (McInnes

et al., 2018).

Using t-SNE visualization, Gupta et al.

successfully distinguished patients diagnosed with

T2DM from the non-diabetic, healthy samples based

on a dataset of 9,948 samples (Gupta et al., 2015).

However, the visualization was unable to cluster the

healthy and diagnosed individuals into individual

clusters.

Bej et al. analyzed a dataset of 10,125 T2DM

patients from the National Family Health Survey-4,

involving many features such as medical history,

dietary habits, addictions, and socioeconomic status.

They found that the conventional application of

UMAP was ineffective and uninformative. However,

applying a feature type-wise clustering method, Bej

et al. enabled visualizing the patients by clusters

corresponding to different features. Their findings

indicated that age and body mass index (BMI) are the

most important factors for T2DM (Bej et al., 2020).

For data visualization, we first denoised the data

by applying DWT on the HMP Stanford datasets

(iHMP Research Network Consortium, 2014) into

multi-view wavelet domain followed by applying t-

SNE and UMAP to the transformed data. Our newly

derived DWT-based t-SNE and UMAP methods on

metabolomics, proteomics, RNA sequencing,

targeted proteomics, and transcriptomics data enable

better clustering than do those without DWT.

2 RESULTS

2.1 Data Pre-processing

We used CGM and ECG data from the D1NAMO

dataset, a collection of data from 20 healthy

individuals and 9 patients with type 1 DM. The data

contain 4 day and collected ECG, CGM, food, and

breathing variables. CGM data were measured in

five-minute intervals before each meal and two hours

afterwards, for a total of 6 times a day. We

transformed the CGM unit from mmol/L to mg/dL.

Alongside breathing data and the CGM data, the ECG

data were collected at a rate of 250 Hz (Dubosson et

al., 2018). The HRV data recorded many RR intervals

in succession. We excluded a misclassified healthy

control with type 1 DM.

The Human Microbiome Project (HMP) began in

2008 to investigate how microbiomes affect their

hosts. Split up into two phases, HMP and Integrative

HMP (iHMP or HMP2), HMP has collected over

10000 samples from 300 subjects. HMP took

microbiomes from both healthy adults and diseased

individuals. iHMP explored how microbiomes

interacted with their hosts. Metabolism, immunity,

and molecular activity were all investigated, along

with how microbiomes might inform us about the

onset of type 2 DM. We downloaded the data from

the iPOP Project Data Portal from each of the

abundance entries (Snyder Lab, n.d.). We describe

results from amounts of certain types of bacteria in

the gut, amounts of certain products of metabolism,

untargeted profile of the amounts of certain proteins,

RNA transcripts, targeted profile of the amounts of

certain proteins, and also RNA transcripts.

For the glucose data from the DM patients in the

D1NAMO dataset, we removed the manual glucose

measurements so that the glucose data would solely

consist of CGM data. We then used the glucose

column, where each index represents five minutes. To

preprocess the HRV data, we first had to find

intervals of data without any outliers (which we

defined as any HRV measurement of under 500

milliseconds or above 2000 milliseconds). We chose

to use intervals of length 512 to be able to use DWT

to denoise the data and generate TS data. We also

decided to treat each interval as an independent

sample, which gave us 3003 healthy HRV samples

and 769 diabetic HRV samples. To fix this data

imbalance, we used SMOTE Tomek resampling,

which resulted in about equal numbers of healthy and

diabetic HRV samples.

To preprocess the abundance matrices from the

HMP dataset, we matched each subject’s VisitID to

their IR/IS classification (either IR or IS; we removed

subjects with Unknown). Subsequently, we removed

subjects for whom there were missing values. In

addition, we normalized the data by adding 0.1 and

taking the log base 2. We then performed DWT on

the normalized data. Figure 1 illustrates the workflow

we followed.

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Figure 1: The workflow of forecasting CGM, predicting

DM using HRV, data visualization using t-SNE and

UMAP, and predicting IR in prediabetes.

2.2 CGM Forecast

In our research we used 3 different methods to predict

blood glucose levels. Table 1 bolds the best RMSE

and MAE for 30, 60, and 90 minutes, which are

shared by KRR and ARIMA. In figure 2, KRR even

correctly anticipates a drop in CGM for patient 3.

These results support KRR and ARIMA as good

forecasters of CGM, whereas Prophet did not yield

good forecasts.

Table 1: Each metric is represented in the form mean

(standard deviation) based on the results of each patient.

30 min 60 min 90 min

RMSE MAE RMSE MAE RMSE MAE

KRR 24.27 26.99 43.05 42.88 59.60 56.38

(25.37) (29.09) (44.74) (43.95) (63.01) (60.02)

ARIMA 25.92 17.50 54.41 37.09 72.359 51.14

(7.22) (4.23) (16.95) (8.83) (25.65) (17.05)

Prophet 60.43 45.79 67.17 50.85 73.29 55.68

(26.27) (21.69) (28.17) (23.08) (30.09) (24.58)

The best metrics for each category are bolded.

Figure 2: A 90-minute forecast by KRR for patient 3.

Of the four, KRR had the lowest RMSE for each

prediction horizon while ARIMA had a lower MAE.

Because of this, KRR may not be a reliable model to

use when forecasting blood glucose. KRR had

difficulty predicting when blood glucose would

suddenly rise or drop. ARIMA had the lowest

standard deviations of any group. This is represented

in its MAE, where it consistently has the lowest value.

Prophet performed poorly. Its RMSE and STD were

both relatively high.

A limitation in our work was the limited datasets

that were available to us. The small training size that

we had, nine diabetic patients, causes our models

difficult to generalize. The accuracy of our models

was most likely negatively affected by the shorter

time series data. For future research, a larger dataset

of patients would be desirable.

2.3 Diabetes Prediction using HRV

In this section, we assess machine learning algorithms

on data transformed in a variety of ways using DWT

(Table 2). RF algorithm on HRV signals transformed

to the Wavelet Domain (TS) and resampled using the

SMOTE Tomek method; the algorithm yielded an

accuracy of 91.9%, precision of 95.5%, and recall of

87.9%. These results, while the accuracy and recall

are lower and the precision is higher, are comparable

to those of Acharya. Moreover, Acharya used 1000

HRV samples at a time while we only used 512; as a

consequence, our model classifies HRV signals with

nearly as much accuracy while taking about half as

much time to record a patient’s HRV.

Table 2: Best overall results out of all data transformations

tested.

Accu-

racy

Balanced

Accuracy

Preci-

sion

Recall ROC

AUC

Score

RF 0.919 0.919 0.955 0.880 0.968 0.916

XGBoost 0.788 0.788 0.788 0.789 0.871 0.788

SVM 0.775 0.775 0.771 0.783 0.853 0.777

RF: Random Forest. The best metrics for each category are bolded.

As shown in Figure 3, it appears that the best

recall of 88.4% occurred with RF for classifying HRV

signals. For RF, all data were classified with

comparable ROC AUC and average precision (Figure

4 & 5). Nevertheless, (TS)* data performed best in

diagnosing diabetes.

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Figure 3: The four best confusion matrices for Random

Forest are (TS)*, a

, TS, and No DWT, in that order. Each

entry is of the form mean ± standard deviation.

Figure 4: The four best ROC curves for Random Forest are

(TS)*, a

, TS, and No DWT with mean AUC of 0.97, 0.96,

0.96, and 0.96 respectively. Each ROC curve displays 10

folds as well as a mean curve (mean ± standard deviation).

Previously, Acharya et al., using the Decision

Tree algorithm on the same HRV signals transformed

using DWT decomposition up to 5 levels, obtained an

accuracy of 92.64%, precision of 92.59%, and recall

of 92.68% (Acharya et al., 2015).

However, compared to the neural networks of

other papers, RF on HRV data transformed to the

Wavelet

Domain performed poor. Seyd P.T.’s ANN

Figure 5: The four best Precision v. recall curves for

Random Forest are (TS)*, a

, TS, and No DWT with mean

average precision of 0.97, 0.96, 0.97, and 0.97 respectively.

Displayed are the results from each of the 10 folds.

Performed with an accuracy of 93.08%, precision of

96.67%, and recall of 89.23%. Of note, RF is a

simpler model than a neural network, so our model is

promising for relatively fast and accurate DM

diagnosis for use by clinicians.

However, a limitation of our classification work

with HRV is that we resample the HRV signals to

correct the data imbalance between healthy and DM.

This means that some of the samples may not be

accurate representations of HRV. Also, given that we

do not know how long the DM patients in the

D1NAMO dataset have had DM, and as DM worsens

cardiac health over time, it is most likely that people

with DM who have not had DM for very long may be

classified with lower accuracy. Thus, for future

research, we recommend using RF and transforming

the HRV signals to the DWT domain using DWT on

HRV signals from DM patients who have not had the

condition for more than a few years.

2.4 t-SNE and UMAP

Given the high complexity of the HMP Stanford

datasets, t-SNE and UMAP figures reflect the

heterogeneity and homogeneity in different datasets.

Both t-SNE and UMAP enable successfully

distinguishing several qualities within prediabetes

patients. We first applied 6 different treatments for

the dataset, namely: Preprocessed, Preprocessed with

Wavelet Denoise, Preprocessed in Wavelet Domain,

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Normalized, Normalized with Wavelet Denoise, and

Normalized in Wavelet Domain. In addition, t-SNE

and UMAP were each used to test the separability of

5 different bases for separation, which include:

Gender, Race, Insulin Resistance (IR)/Insulin

Sensitivity (IS) Classification, Age Group, and BMI

Group.

We were able to utilize UMAP to obtain well-

defined clusters, particularly in gender classification

(Figure 6) to the Targeted Proteomics dataset.

Figure 6: UMAP on the Targeted Proteomics dataset.

The ‘Preprocessed’ data presents two clusters,

largely separating males and females. On the other

hand, the ‘Normalized’ data presents a scatter of

points, with the males and females largely mixed

together. The ‘Preprocessed WT Domain’ figure

displays two compact clusters, comparatively cleaner

than both the ‘Wavelet Denoised’ and preprocessed

figures.

Of the Lipidomics dataset figures, the t-SNE

results contain noticeable clusters for Black and

Hispanic, particularly in the ‘Preprocessed’,

“Denoised”, and ‘WT Domain’ with figure presenting

a more compact result (Figure 7).

Figure 7: t-SNE on the Lipidomics dataset.

We analyzed the Cytokine dataset, resulting in

distinct BMI-based clusters observed with both the t-

SNE and UMAP. In t-SNE, the Figure 8 shows that

‘Denoised’ and ‘Normalized Denoised’ pretreated

datasets present more compact clusters and points.

The other classification subjects also aggregate into

tight, compact clusters. It appears that certain

prediabetic subjects share different characteristics,

possibly presenting a stratification of these patients in

each cluster (Figure 8).

Figure 8: t-SNE on Cytokine abundance dataset.

Figure 9: UMAP on the Transcriptomics dataset.

Of the Transcriptomics dataset figures, the UMAP

results contain well-defined clusters, particularly in

gender classification (Figure 9). In all gender

classification figures for Transcriptomics, we

observed a gender-based cluster pattern. Thus, it has

implications in gender-based stratification of patients

in precision medicine for prediabetic patients.

The application of UMAP on the Gut 16

Microbiome dataset resulted in clear separation based

on IR/IS classification (Figure 10). These results

allow us to observe the patterns in clusters in the set

of prediabetic subjects, based on gut microbiomes.

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Figure 10: UMAP on the Gut 16 Microbiome dataset.

2.5 Prediabetes Insulin Resistance

Prediction

For SVM on the metabolomics data, both the

normalized and (TS)* normalized data obtained the

best results, with 77.7% accuracy, 75.0% balanced

accuracy, 100% precision, 50% recall, AUC of 1.000,

and F1 of 0.661. Similarly, the best results for SVM

on the proteomics data were from the normalized and

TS normalized data, bolded in Table 3, with 91.6%

accuracy, 90.5% balanced accuracy, 100% precision,

81.1% recall, AUC of 1.000, and F1 of 0.892. We

observed a similar propensity for SVM on the

Targ.proteomics data and the Transcriptomics data.

The normalized and TS normalized data enable

perfect accuracy, balanced accuracy, precision, recall,

AUC, and F1. For SVM on the Transcriptomics data,

denoised normalized data also got perfect metrics.

Table 3: Results of classifying SVM model data as IR or IS

on Proteomics.

Data

Type

Accu-

racy

Balanced

Accuracy

Preci-

sion

Recall ROC

AUC

Score

o DWT 0.558 0.500 0.000 0.000 0.500 0.000

(TS)* 0.558 0.500 0.000 0.000 0.500 0.000

Denoised 0.558 0.500 0.000 0.000 0.500 0.000

0.916 0.905 1.000 0.811 1.000 0.892

(TS)* N 0.916 0.905 1.000 0.811 1.000 0.892

Denoised

0.558 0.500 0.000 0.000 0.500 0.000

N means Normalized. The best metrics for each model are bolded.

On the other hand, the TS data yielded the best

overall results for Random Forest on the

RNAseq_abundance data (72.1% accuracy, 58.9%

balanced accuracy, 19.0% recall, 0.309 F1), though

all the data types performed mostly the same for SVM

on the RNAseq_abundance data (67.2% accuracy,

51.0% balanced accuracy, 30.0% precision, 2.0%

recall, F1 of 0.037; denoised got an AUC of 0.988).

The TS data also did best overall for Random Forest

on the Transcriptomics data, with 92.2% accuracy,

91.2% balanced accuracy, 84.5% recall, AUC of

0.990, and F1 of 0.890, though the results for the

denoised data are comparable (had highest precision

of 98.0%). Thus, across all HMP data, DWT

transformed data yielded better performance in

predicting IR or IS in prediabetes.

Our application of the DWT based two

experimental visualization techniques to the HMP

Stanford dataset hold promising potential in allowing

biomedical specialists to interpret the data by

studying different visualizations of the dataset. We

envision that our approach has the potential to

uncover correlations between certain microbiomes

and attributes in prediabetes patients, holding a

promise for earlier detection and investigation of

diabetic behavior in patients.

3 CONCLUSIONS

With our decomposed and denoised DM data, we

enhance HRV based DM diagnosis, data visualization

of the disparities in HMP data demographic features,

and insulin resistance prediction. We forecast

continuous glucose monitoring (CGM) 90 minutes in

the future because CGM is unable to provide real-

time blood glucose measurements. Moreover, we

achieved 91.9% T1D diagnosis accuracy using

Random Forest on data transformed with DWT,

holding the potential for usage in clinics.

Furthermore, our DWT-based t-SNE and UMAP

explorative analysis of HMP data supports subtypes

of prediabetic patients stratified by sex, race, and age.

Thus, DWT-based transformations on metabolomics,

proteomics, RNA sequencing, targeted proteomics,

and Transcriptomics data yield better separation and

clearer clusters than those without DWT.

Our results have implications in precision

medicine. Precision medicine is based on

stratification of patients, taking into account personal

lifestyle, genetic information, and biomarkers. Our

research involves two datasets, the HMP Stanford

dataset along with the D1NAMO dataset, both of

which contain extremely detailed information upon

microbiomes, protein structure, CGM, ECG, food

consumption, and other vital data, suitable for

exemplification of machine learning modeling in

precision medicine. Taken together, DWT-based

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machine learning approaches enable a fine resolution

of subtyping DM towards precision medicine.

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