A Novel Model for Noninvasive Haemoglobin Detection Based on Visibility Network and Clustering Network for Multi-Wavelength PPG Signals

Abstract

Non-invasive haemoglobin (Hb) testing devices enable large-scale haemoglobin screening, but their accuracy is not comparable to traditional blood tests. To this end, this paper aims to design a non-invasive haemoglobin testing device and propose a classification-regression prediction framework for non-invasive testing of haemoglobin using visibility graphs (VG) with network clustering of multi-sample pulse-wave-weighted undirected graphs as the features to optimize the detection accuracy of non-invasive haemoglobin measurements. Different prediction methods were compared by analyzing 608 segments of multiwavelength fingertip PPG signal data from 152 volunteers and analyzing and comparing the data and methods. The results showed that the classification using NVG with complex network clustering as features in the interval classification model was the best, with its classification accuracy (acc) of 93.35% and model accuracy of 88.28%. Among the regression models, the classification regression stack: SVM-Light Gradient Boosting Machine (LGBM) was the most effective, with a Mean Absolute Error (MAE) of 6.67 g/L, a Root Mean Square Error (RMSE) of 8.21 g/L, and an R-Square (R2) of 0.64. The results of this study indicate that the use of complex network technology in non-invasive haemoglobin detection can effectively improve its accuracy, and the detector designed in this study is promising to carry out a more accurate large-scale haemoglobin screening.

1. Introduction

Haemoglobin (Hb) is an important protein that transports oxygen and carbon dioxide around the body and is found in human red blood cells [1]. Abnormalities in its physiological indicators can lead to polycythemia and anemia [2]. The mainstream non-invasive Hb testing techniques include body part imaging, spectroscopy, and Photoplethysmography (PPG) [3]. In this case, body part image detection uses images of the eyelid or palm area of the tested person to complete the classification of anemia or regression prediction of specific haemoglobin levels through techniques such as deep learning. The detection method is relatively new and the signal input is easy to obtain, but the image quality varies when applied, so it exists more in theoretical models. Appiahen et al. used 527 images of test subjects’ palms to screen for anemia in 2023 and achieved classification results with 99.26% accuracy using a Bayesian classifier [4]. In 2024, Linquan Xu, Yuwen Chen et al. used eyelid images to predict hemoglobin concentration and proposed two networks, Actor Predictor and Hemoglobin Predictor, for predicting hemoglobin concentration. The results show that the prediction framework can achieve an MAE of 1.19 g/dL, representing a successful attempt for medical images to be used for haemoglobin regression prediction [5]. Among the non-invasive detection methods, spectral detection has also interested researchers [6]. Compared with image detection, this method has more interpretability for Hb, but its signal is more difficult to obtain. In recent studies, Yun Yi Wang, Gang Li, et al. used spectroscopic assay for erythrocyte and Hb detection, which developed a multi-wavelength spectroscopic acquisition device and used spectral data from 272 subjects. Its resultant accuracy in the RMSE of haemoglobin was reduced by 0.85 g/L compared to the classical spectral data, which was better [7]. Ilia Bardadin made a more novel attempt to analyze multispectral signals using Monte Carlo analysis. A relative error of 15 g/L was obtained using a tissue model for Hb detection [8]. PPG is one of the non-invasive methods for Hb detection [9]. Hb non-invasive detectors, developed using PPG technology, can be integrated into wearable devices [10], achieving risk-free detection, convenient result acquisition, and easy operation [11], enabling the measurement of multiple valuable physiological parameters [12]. The detection principle is based on the Beer–Lambert law. Due to the different absorbance of different substances in the blood, the information in the PPG signal obtained is not the same. Some relevant studies have shown that deoxyHb and oxyhaemoglobin in the blood are very sensitive to the light intensity of 600 nm–1000 nm. Therefore, PPG signals for non-invasive detection of Hb feature detection methods using different wavelengths of light [13]. In 2015, Resit Kavsaoglu et al. extracted 40 features related to PPG signaling from dual-wavelengths (660 nm, 905 nm). They used machine learning with neural network models to predict Hb levels after feature selection. The study used data from 20 individuals and obtained a small range of excellent results, with MSE = 0.0027 [14]. In 2020, Soumyadipta Acharya et al. proposed a multi-model stacking framework for Hb prediction using PPG signals at four wavelengths (590 nm, 660 nm, 810 nm, and 940 nm), achieving a good RMSE = 1.353 g/dL [15]. In the same year, Hongyun Liu et al. distinguished anemia ranges using eight-wavelength PPG signals (610–940 nm) and obtained favorable outcomes [16]. In 2023, Vladislav V. Lychagov et al. used six wavelengths (655 nm, 765 nm, 805 nm, 850 nm, 940 nm, 975 nm) of reflective PPG signals for noninvasive haemoglobin detection, predicted them using machine learning and deep learning models, and compared the results. Among them, the best result was MAE = 12.66 g/L, R = 0.66, which is a more optimistic result [17]. By 2024, Ranjith R et al. had collected clinical dual-wavelength (630 nm,940 nm) PPG signals from subjects to fit a non-invasive Hb detection model, achieving satisfactory effects [18].

A complex network is a network structure formed by connecting nodes and edges according to certain predefined rules. Many complex problems in nature can be better understood through complex network theory [19]. Connections in a complex network can be directed or undirected, and they can be either weighted or binary, depending on the specific needs [20]. Several kinds of literature are proving that the use of complex network techniques in physiological state detection can be attempted. In 2018, Diykh M, Li Y, et al. used complex network techniques applied in deep anesthesia assessment with more optimistic results [21]. Subsequently, in 2022, Wang W, Mohseni P, et al. trained and validated a deep learning model for continuous blood pressure prediction using visibility graph (VG) complex network transformations on PPG signals and used its adjacency matrix thermal pictures to achieve accurate predictions [22]. In 2024, Raj K D, Lal G J, et al. extracted complex network features and performed classification model training for Parkinson’s disease severity after biomarkers of Parkinson’s disease were transformed using a visibility complex network and achieved high accuracy [23]. In a previous study, HuiShan Qin et al. [24] used a four-wavelength PPG signal for non-invasive detection of Hb. This study shows that the use of MW-PPG signals is superior to single-wavelength PPG signals for Hb detection and confirms that MW-PPG features correlate with Hb and that the machine learning model XGBoost gives the best fitting results and better model performance.

In this study, the application of complex network technology in non-invasive detection technology of Hb is mainly explored in depth, and the MW-PPG signals were transformed into natural visibility graph (NVG) and horizontal visibility graph (HVG) complex networks, respectively [25]. Multi-sample complex networks were generated according to the morphological features of PPG signals. Among them, natural visibility graph (NVG) is a method to map time series into complex networks. It can reveal some important laws and information hidden in the time series. HVG, on the other hand, is a new visibility graph algorithm proposed by Luque et al. [26], which shortens the change time of NVG and simplifies it. Considering that this study aims to explore the relationship between different wavelengths, different samples, and Hb indexes, the weighted undirected graph is chosen to generate the complex network [27]. This complex network contains more information than the binary network and can better explain the implicit relationship between different samples in complex systems. In the signal acquisition device, PPG signals of 660 nm, 730 nm, 850 nm, and 940 nm wavelengths were still selected for acquisition, and, considering the influence of contact pressure on the morphological characteristics of fingertip PPG signals [28], a mechanical structure was designed under the signal receiving end of the acquisition device to control the subjects to maintain the appropriate contact pressure to minimize the influence on the quality of PPG signals. Subsequently, multi-wavelength fingertip PPG signals with invasive test results were collected from 152 volunteers in a hospital. The PPG was generated into natural visibility graph (NVG) and horizontal visibility graph (HVG) complex networks according to the period, and its related features were extracted. Meanwhile, all the samples were generated into a multi-sample weighted undirected graph complex network, its network clustering was obtained, and the related information features of each point in the multi-sample complex network were extracted. Finally, reliefF feature filtering was used to select the most relevant features, and the filtered features were used for classification and regression model training. We then derived a classification-regression prediction framework using visibility graphs (VGs) and network clustering of multi-sample PPG signal as feature inputs. Finally, we compared and analyzed it with other classical prediction models.

2. Materials and Methods

2.1. MW-PPG Signal Collection and Hb Prediction System

The PPG signal acquisition device consists of DCM08, FSR400, a capacitive touch screen, a microcontroller, and a power supply circuit. The DCM08 is the MW-PPG acquisition sensor, which ensures long-term operational stability, and the FSR400 is the contact pressure sensor in this study, which can capture the pressure changes in the strain gauge and transmit the pressure signal to the main control MCU for subsequent processing. To capture the contact pressure at the time of signal acquisition more accurately, a contact pressure transfer structure is designed in this study. The structure is divided into three layers: the subject contact module, the pressure transfer module, and the sensor base. Among them, the center of the subject contact module adopts a recessed design to enable precise finger placement and pressure application, and the light-emitting source is extended in the center of the recess. The multi-wavelength sensor DCM08 signal receiving end is fixed and placed in the pressure transfer module, and an FPC flexible circuit board is used to transmit the multi-wavelength PPG signal and the contact pressure signal to the circuit board where the main control chip is located. The sensor is stabilized on the sensor base, and a convex structure is used underneath to transmit the pressure applied by the subject to the sensor to the FSR400 for real-time pressure detection. The framework diagram of the MW-PPG acquisition and Hb prediction system is shown in Figure 1, and the exterior of the MW-PPG signal acquisition device and the internal structure of the sensor are shown in Figure 2.

To facilitate the preservation and management of MW-PPG data, this study used the Qt creator companion to design and develop an MW-PPG signal storage platform. The application can communicate with the MW-PPG acquisition device described in the previous section via serial port or Wi-Fi and transfer the obtained MW-PPG signals and contact pressure signals to the computer to be saved in a local database (SQLite). During the data acquisition process, the application needs to first fill in the subject’s personal physiological information with the application’s personal information fill-in field and notify the subject to sit still and prepare for the acquisition. After ticking the checkboxes in the Acquisition Mode column according to the time of the signal to be extracted, the Start button is clicked and the pulse wave signal of the subject is acquired. Once the acquisition is complete, it is also possible to check the quality of the PPG signal by plotting the waveform of the acquired PPG signal. The application also has the function to export the personal information and pulse wave signals in the database one by one according to their IDs to a CSV file in a fixed folder in order to facilitate the subsequent processing of data and other operations.

Throughout the MW-PPG signal acquisition and Hb prediction system, to apply the prediction model in this study, our research team simultaneously developed another application program (App) to be used to call the model and predict the real-time physiological metrics of the test subject. In this application, users can create an account to save and manage their physiological and health information and predict heart rate, oxygen saturation, and Hb in real-time. The app consists of a login screen, a waveform display, a measurement screen, and a test record query screen. After the subject selects the 1-min static indicator and clicks the Start Measurement button, the app will prompt the user to start the measurement after three seconds. During the measurement process, the app will collect the subject’s fingertip pressure signal in real-time during the acquisition and display it in the status bar; if the contact pressure is too large or too small, the app will remind the subject to adjust the pressing force through a real-time pop-up window. Heart rate and blood oxygen will be calculated every five seconds and displayed in the detection column. The time box will start counting to 60 s and end the measurement when the countdown is over. Then the measurement results will be displayed, showing the one-minute physiological indexes such as the heart rate, blood oxygen, Hb, and so on, calculated from the signal. After obtaining the values of each index, the app will save the results of each measurement in the database of the personal account and visualize them in the physiological index query column, so that the tester can check the physiological indexes obtained from each test after logging into his/her account. The detailed flowchart and interface diagrams of the MW-PPG data acquisition application and the Hb prediction application are shown in Figure 3.

2.2. Dataset

The data used in this study are a clinical dataset. The dataset consists of 608 signal samples of multi-wavelength pulse waves (MW-PPG) obtained from 152 volunteers (80 females and 72 males) using this PPG signal acquisition instrument. The data were obtained from the hospital and were reviewed for medical ethics; all the volunteers noted the collection procedure and signed a consent form. Volunteers underwent a blood test before collection, and the Hb value, measured by cobas b 123 blood analyzer, was used as the reference data for the sample results. The volunteers were asked to sit still during the collection, and the collection of MW-PPG signals of the volunteers was carried out by using the MW-PPG collection device developed in this study.

The data consisted of a 1-min MW-PPG signal with a signal sampling rate of 200 Hz. The age, height, weight, gender, and Hb values of the volunteers were also recorded. The age distribution of the dataset along with the distribution of the Hb values and the box plot of the dataset are shown in Figure 4:

2.3. VG Feature Extraction

Feature extraction is a crucial preparatory step in machine learning, as it directly impacts model performance, accuracy, and other key metrics. In typical research, the analysis of complex networks often involves feature engineering to study the structure and properties of the network [29]. In this study, after cutting the PPG signal into individual waveforms, the viewable view is transformed and the features are extracted; the extraction flowchart is shown in Figure 5. A total of six complex network features are extracted in each wavelength viewable view in this study in order to prepare for the subsequent processing, classification, and regression tasks.

2.3.1. Transitivity in Complex Networks

In graph theory, transitivity is an essential concept in network analysis. It is commonly used to describe the relationships between nodes in a network and the structural characteristics of these relationships [30]. The transitivity ratio is calculated using the formula:

$$T={\displaystyle \frac{Tri}{Tr}}$$

(1)

where Tri represents the number of triangles in the network and Tr represents the number of triplets in the network. The transitivity ratio ranges from 0 to 1, with higher values indicating closer connections and stronger transitivity among nodes in the network.

2.3.2. Average Node Degree in Complex Networks

The average node degree in complex networks describes the density of connections among nodes. The degree (Degree) of a node refers to the number of edges directly connecting it to other nodes. The average node degree reflects the overall connectivity characteristics of the complex network. In a network with N nodes, the average degree $⟨k⟩$ can be calculated using the formula:

$$⟨k⟩={\displaystyle \frac{1}{N}}\sum _{i=1}^{N}Ki$$

(2)

This feature allows for a more intuitive description of the denseness of the viewable complex network connections, thus quantifying the rough structure of the complex network, which in turn makes it easier to find connections between different complex network structures and physiological indicators.

2.3.3. Average Density

In complex networks, this metric reflects the ratio of actual edges present in the network to the potential maximum number of edges. The formula for calculating average density is as follows:

$$D={\displaystyle \frac{2E}{N\left(N-1\right)}}$$

(3)

This metric indicates the connectivity within the network. A higher average density implies closer connections among nodes and efficient information propagation; conversely, a lower average density signifies sparse connections among nodes and inefficient information propagation.

2.3.4. Global Efficiency

Global efficiency is a metric that quantifies the efficiency of information propagation in a network. It represents the average information communication capability between any two nodes in the network, and its definition is given by the following formula:

$$EG={\displaystyle \frac{1}{N\left(N-1\right)}}{\sum }_{i=j}{\displaystyle \frac{1}{dij}}$$

(4)

where dij represents the length of the shortest path between node i and node j, N is the number of nodes, and EG is the global efficiency. Global efficiency reflects the ability of information to propagate from one node to another in the network. A higher value indicates faster information propagation efficiency. Additionally, this metric can also signify information about network properties such as connectivity.

2.3.5. Average Betweenness Centrality

Betweenness centrality is commonly used to measure a node’s capability as an intermediary for information propagation in a network, reflecting the “bridge” role played by a node. Specifically, for a node V, its betweenness centrality CB (V) is defined as:

$$CB\left(V\right)=\sum _{s=v=t}{\displaystyle \frac{\sigma st\left(V\right)}{\sigma st}}$$

(5)

where σst is the number of shortest paths between nodes s and t and σst(V) is the number of those paths that pass-through node v [31]. A higher value of this feature indicates that the node plays a more crucial role as an information mediator in the network. Consequently, a higher average betweenness centrality for the entire network suggests a denser network with higher information propagation efficiency.

2.3.6. Assortativity Coefficient

The assortativity coefficient reflects the tendency of nodes in a network to connect with similar nodes, particularly the feature of whether adjacent nodes are interconnected. Specifically, it is the ratio of the actual number of connections among a node’s neighbors to the potential maximum number of connections. Ci for a node i is defined as follows:

$$Ci={\displaystyle \frac{2Ei}{Ki\left(Ki-1\right)}}$$

(6)

where Ei is the actual number of edges between the neighbors of node i, and Ki is the degree of node i. The average assortativity coefficient indicates the overall trend of node clustering in the network, reflecting its density and network property analysis.

2.4. Preprocessing PPG Signal and Generation of Complex Networks

This study initially performed preprocessing operations on the MW-PPG signals. During preprocessing, the obtained one-minute segments of MW-PPG signals were screened and cleaned. A second-order Butterworth bandpass filter was applied to filter the MW-PPG signals [32]. Considering that the primary frequency band of PPG signals lies within 0.1–10 Hz, and the major noise component in the captured signals is concentrated around 9 Hz, the filter’s bandwidth was selected to be between 0.5–8 Hz. The signals before and after filtering are illustrated in Figure 6A.

When generating multi-sample complex networks, this study selected 26 PPG features that could describe the morphology and shape of the PPG signal as comprehensively as possible. These features include the height of the peak point (Iso), the height of the dicrotic peak (Ido), the height of the dicrotic notch (Ino), the total conduction time of the PPG signal (To2o), the time from the start of the PPG signal to its peak (Tso), and so on. A detailed list of all extracted features is presented in

Table 1. Schematic Representation of Extracted PPG Signal Features.

Feature Type	Abbreviations for Features	Feature Description
Height of PPG	Iso	Height of the peak of the PPG signal
	Info	Height of the dicrotic notch in the PPG signal
	Ido	Height of the dicrotic peak in the PPG signal
Conduction time of the PPG	To2o	Total conduction time of the PPG signal
	Tso	Conduction time from the start of the PPG signal to its peak
	Tno	Conduction time from the start of the PPG signal to the dicrotic notch
	Tdo	Conduction time from the start of the PPG signal to the dicrotic peak
	Tsd	Conduction time from the peak of the PPG signal to the dicrotic peak.
	Tnn’	The period from N’ to N in the PPG signal
Different equipment of PPG	R25	Widths at 3/4, 1/2, and 1/4 points between the rising contour and the peak of the PPG signal
	R50
	R75
	D25	Widths at 3/4, 1/2, and 1/4 points between the falling contour and the peak of the PPG signal
	D50
	D75
Different areas of PPG	V1	Area of different regions in the PPG signal
	V2
	A1
	A2
Different slopes of PPG	S1	Total slope of the rising branch of the PPG signal
	S2	Total slope of the falling branch of the PPG signal
	S3	The slope from the dicrotic peak to the end of the PPG signal
	S4	The rising slope before the w-point of the PPG signal
	S5	The rising slope after the w-point on the rising branch of the PPG signal

, and their schematic representation is shown in Figure 6B.

After extracting the features from one-minute PPG signals, the multiple PPG signal features within the same sample were averaged to obtain a 1 × 26 feature vector for each of the four samples. Subsequently, each 1 × 26 feature vector, representing a wavelength within each sample, was treated as a node, and the Euclidean distance [33] between these feature vectors was calculated. Euclidean distance, a common method for defining the distance between two distinct points, is defined as follows: For two points A = (a1, a2, …, an) and B = (b1, b2, …, bn) in an n-dimensional space, their Euclidean distance d is given by:

$$d\left(\mathrm{A},\mathrm{B}\right)=\sqrt{{\sum }_{i=1}^n\left(ai-bi\right)}$$

(7)

To explore the similarity among different samples, this study weighted the complex network with 1/d, where a larger value indicates greater similarity between two nodes and a smaller value represents lesser similarity. Subsequently, a multi-sample weighted undirected graph network was constructed with feature vectors as nodes and 1/d as the weights between nodes. The generation process of this network is illustrated in Figure 7 and the next step after obtaining this network is to calculate and analyze the clustering of this network.

2.5. Model Prediction

In this study, the predictive framework of categorical regression stacking was used for Hb prediction and compared the direct regressions, such as SVM [9], XGBoost [34], and Random forest [35]. A schematic of the prediction framework for categorical regression stacking in this study is shown in Figure 8.

The specific process of this prediction framework is as follows: in the first step, the MW-PPG signals were extracted from their relevant morphological features while VG changes were performed, and then multi-sample weighted undirected graph complex networks were generated according to the method in the previous section. In the second step, the VG-related features were extracted separately; the clustering results of the multi-sample complex network were extracted as features after clustering computation. In the third step, the VG features were subjected to feature screening, and the screened features and the clustering results were input into a classifier to perform interval classification of Hb. In the final step, the VG features and PPG morphological features were assessed for their suitability as regression features. These features were then combined with the intervals derived from the previous classifier for model training. The type of regressor employed was selected based on the interval results from the earlier classifier during the prediction phase. Regression predictions were performed by incorporating the chosen VG and PPG morphological features for the sample, ultimately leading to the determination of the specific content of Hb.

3. Result

In this study, to investigate the relationship between different wavelengths and different samples and Hb indexes, a multi-sample weighted undirected graph complex network was generated to correlate them. A classification-regression stacking model was devised to use the clustering results of this complex network as features to classify Hb intervals, followed by regression prediction of specific Hb concentrations based on the interval classification results. Machine learning regression models such as LGBM, XGBoost, and Random Forests were also compared in this study.

3.1. Complex Network Clustering Results

In this study, multi-sample weighted undirected networks were clustered and analyzed. The Louvain algorithm was used for clustering analysis to identify communities within the weighted undirected graph. The Louvain community detection algorithm, a popular method for network structure analysis, identifies community structures in networks by optimizing modularity. Widely applied in the clustering detection of complex networks, the Louvain algorithm aids researchers in identifying and understanding clustering structures within networks.

To validate the degree of network modularity, the Louvain algorithm was executed 10 times with modularity parameters ranging from 0.1 (extensive detection) to 1.0 (classical cluster size detection). The resulting modularity indices are shown in

Table 2. Clustering metrics table.

Modular Parameter	Cluster Index
0.1	0.9
0.2	0.8
0.3	0.7001
0.4	0.6001
0.5	0.5073
0.6	0.420
0.7	0.352
0.8	0.315
0.9	0.283
1.0	0.259

.

According to Table 2, when the modularity detection parameter in the Louvain algorithm is set to 0.1, that is, when extensive clustering is detected, the network modularity index reaches a significant peak of more than 0.6. Then, the modularity detection parameter gradually increases, the network modularity index is gradually narrowed, and is finally stabilized in the range of 0.2 to 0.4, which is the result of an index with a more significant modularity. This also indicates that, at first, the Louvain algorithm integrates all sample points into one cluster when performing extensive modularity detection. However, as the detection parameters gradually increase, this detection structure evolves into smaller, more defined clusters. This pattern suggests that the network displays distinct clustering properties and maintains a relatively cohesive cluster structure.

Following this result, the study conducted clustering validation on multiple clustering partitions, yielding a modularity index of 0.351 and dividing the complex network into four clusters. Through comparative analysis, Cluster 1 was designated as high Hb, Clusters 2 and 3 as normal Hb, and Cluster 4 as low Hb. This result underscores the capability of the clustering approach in delineating distinct ranges of Hb levels. The statistical histogram illustrating the clustering outcomes is presented in Figure 9.

3.2. Comparison of Complex Network Features

In this study, we tried two different methods of visibility change, Natural Visibility Graph (NVG) and Horizontal Visibility Graph (HVG), and extracted the same features from different networks as inputs to the model. During the change process, we found that the change time of HVG is significantly faster than NVG, and that the network obtained by NVG has more connected edges and the network is more complex compared to HVG. The heat map comparison between NVG and HVG is shown in Figure 10. Subsequently, we compared the relevant positional features and clustering features of the weighted undirected graph complex network and compared them according to different feature inputs and feature filtering, obtaining different classification results. The comparison of their results is shown in

Table 3. Comparison of Classification Model Performance.

Feature Input	Feature Selection Method	Classifier	Number of Features	Accuracy	Precision
NVG—Clustering Features	reliefF	SVM	10	90.71%	75.00%
			15	93.35%	88.28%
			20	91.00%	76.08%
NVG	reliefF	SVM	10	87.98%	75.66%
			15	87.62%	73.34%
			20	85.97%	74.64%
HVG—Clustering Features	reliefF	SVM	10	68.00%	65.37%
			15	75.29%	68.26%
			20	63.14%	62.7%
HVG	reliefF	SVM	10	53.13%	58.12%
			15	62.76%	60.15%
			20	52.27%	51.70%

and Figure 11A, and the confusion matrix of the best results of the model is shown in Figure 11B.

3.3. Comparison of Predictive Model Performance

This study compares the direct regression performance of fundamental machine learning models, including Random Forest (RF), Support Vector Machine (SVM), XGBoost (XGB), and Light Gradient Boosting Machine (LGBM). Additionally, it contrasts the efficacy of the proposed classification-regression stacking approach with direct regression models. The comparative results of model performance, along with the best outcomes achieved by various models, are depicted in Figure 12, while the top-performing metrics of different models are summarized in

Table 4. Comparative Results of Performance of Different Detection Models.

Model Type	Feature Selection Method	Number of Features	MAE (g/L)	RMSE (g/L)	R2 (0–1)
RF	mRMR	10	8.44	12.04	0.22
		20	8.60	11.57	0.28
		30	8.18	11.06	0.37
SVM	mRMR	10	8.92	11.87	0.24
		20	10.06	13.41	0.11
		30	11.72	15.32	0.05
XGB	mRMR	10	9.51	13.02	0.14
		20	10.72	13.32	0.11
		30	11.01	13.85	0.06
SVM-XGB	mRMR	10	7.06	9.28	0.63
		20	7.94	10.15	0.54
		30	8.25	10.92	0.49
SVM-LGBM	mRMR	10	6.70	8.21	0.64
		20	7.00	8.66	0.58
		30	7.30	8.83	0.57

. The box plot in Figure 12 visually represents the distribution of model performance indicators across various models. The Bland–Altman plot of predicted results from categorical regression stacking of models is shown in Figure 13.

4. Discussion

This study explores the application of various complex network techniques for non-invasive Hb detection. The findings indicate that utilizing the clustering results of multi-sample weighted undirected graphs as features for Hb interval classification significantly enhances performance, demonstrating the effectiveness of these clustering outcomes in facilitating Hb interval categorization. Moreover, in a multi-sample weighted undirected graph composed of morphological features of multiple PPG signals, four clusters can be obtained by using Louvin’s algorithm to cluster the network. Comparison of the clustering results with the Hb index shows that the clusters are highly correlated with the physiological index of Hb, which indicates that the morphology of PPG signals is highly correlated with the Hb index, and the clustering results based on the morphology of PPG signals can also reflect the interval distribution of Hb.

Furthermore, the comparison experiments reveal that while visibility graph methods exhibit some beneficial effects in the field of Hb detection, their contribution to improving the accuracy of Hb concentration measurement is limited. Among the visibility graph transformation methods, the Natural Visibility Graph (NVG) outperforms the Horizontal Visibility Graph (HVG) in Hb detection. The inferior performance of HVG compared to NVG can be attributed to HVG’s tendency to discard edge connections during the transformation process to expedite the generation of complex networks [36]. While this characteristic reduces transformation time, it also results in the loss of crucial distinguishing information for Hb interval discrimination in the context of non-invasive Hb detection, ultimately leading to suboptimal model performance.

Subsequently, this study compares the prediction effects of two prediction frameworks, direct regression and classification-regression two-stage stacking, in terms of using complex network features as inputs. In the comparison of the prediction results, it can be found that if the complex network features and pulse wave morphological features are regressed directly after feature selection, the fitting effect is poor and the model performance results obtained are not optimistic. In contrast, the model framework of classification-regression stacking will achieve better prediction results, of which the best result is SVM-LGBM with an MAE of 6.67 g/L, an RMSE of 8.21 g/L, and an R2 of 0.64. This result can likewise prove that the network features obtained by the complex network technique are more recognizable in interval classification, and thus also prove that when the network technique is applied, the modeling framework of classification regression stacking is superior to direct regression and will achieve better model fit and model accuracy. From the regression results of the model, we can also find that the model performance obtained by using ten features for prediction is better compared to the model performance obtained by twenty and thirty features. This proves that the visibility graph features are of limited help to the regression model and that even the low relevance of the features at the bottom of the feature filtering order can adversely affect the model results. This study also compares the results obtained using the previous prediction framework with the new prediction framework based on the new dataset, and it can be seen that as the expansion of the sample interval is gradually widened, the regression effect of the morphological features using only the PPG signals deteriorates. The overall robustness and stability of the algorithm can be improved, and more accurate performance results can be obtained by using the complex network technique to find the connection between different samples.

A comprehensive comparison of the model performance, practicality, robustness, and other metrics is made between this study and other studies using human body part images for Hb detection, multispectral detection, and the method using MW-PPG. The specific metrics are shown in

Table 5. Comparison of results from another research.

Research	Input Features	Model Use	Subject	MAE (g/L)	RMSE (g/L)	R2 (0–1)
Acharya S, Swaminathan D, Das S et al., 2019 [15]	MW-PPG (4 channel)	Stacked Regressor	1583	-	13.53	-
Lakshmi M, Manimegalai P, Bhavani S 2020 [37]	PPG 7 features	Linear regression	47	7.3	9.5	0.53
Kumar, R. D., Guruprasad, S., Kansara, K et al., 2021 [38]	MW-PPG (4 channel)	Stacked Regressor	1005	-	14.7	-
Zhao X, Meng L, Su H et al., 2022 [39]	Image	ASModel _UWF	4512	8.3	-	-
Lychagov V, Semenov V, Volkova E, et al., 2023 [40]	MW-PPG (6 channel)	CNN	170	13.6	-	0.43
Xu L, Chen Y, Lu S et al., 2024 [5]	Image	ResNet101	1244	11.9	14.8	0.12
Previous Studies	MW-PPG (4 channel)	XGboost	58	7.56	10.22	0.53
This work	MW-PPG (4 channel)	SVM-LGBM	152	6.7	8.21	0.64

, from which the comparison shows that the model proposed in this paper has the lowest error and the best fit. In this table, the number of samples used in the model training using human body part images is higher because of the need for deep learning technology, but its prediction performance is average, and there is no practical application of the model, only the training and prediction of the theoretical model. Compared with the model results obtained for the same MW-PPG, we demonstrate a clear advantage in the model result. Of these studies, the ones with larger samples have used public datasets for subsequent manipulation and research. The most similar study to this paper is the Hb prediction performed by Lychagov V et al. in 2023, which used six-wavelength MW-PPG data from 170 of the autonomous clinical collections. A comparison of the results with that study shows that the model efficacy obtained in this study is better.

In this study, we have conducted relevant research to compare the parameters of our designed Hb non-invasive detection system with the common Hb non-invasive detectors on the market, and the results are shown in

Table 6. Comparison of common instruments in the market.

Equipment Type	Measuring Range (g/L)	Relative Error (g/L)	Confidence Upper Interval (95%)	Confidence Lower Interval (95%)
Masimo Rad-67	80–170	-	20.7	−18.2
NBM200	110–170	9.9	-	-
Masimo Pronto	60–180	10	-	-
Our Equipment	110–170	8.21	18.7	−15.25

. It can be seen that the relevant accuracy obtained in this study is not inferior to most of the Hb devices available in the market, so the detection system designed in this study is a promising candidate to contribute to large-scale Hb detection.

5. Conclusions

In this study, we explored the application of complex network technology in the non-invasive detection of Hb, designed a ‘classification-regression stacking’ model framework based on multi-sample weighted undirected graph clustering features and visibility features, and developed a Hb prediction system based on this model. Based on the comparison with previous studies and conventional instruments available on the market, it can be concluded that the present study has improved the accuracy of PPG signals for non-invasive Hb detection in general. However, this study is limited by the hardware equipment and experimental environment, as well as the limitations of data acquisition. It is difficult to achieve a wider range of acquisition, and our system can only be used as a basis for experimentation and research. In the future, we can continue to increase the collection of clinical data on MW-PPG signals and increase the number of samples of moderate anemia and severe anemia to obtain a wider prediction accuracy and prediction range; plateau anemia, thalassemia, and other special types of anemia may also correlate with MW-PPG signals. In terms of hardware improvement, this study can investigate the detection of methemoglobin and hemoglobin monoxide by increasing the wavelength of low frequency bands, such as 500–600 nm; and at the same time, it can reduce the size of the probe by increasing the degree of integration, such as making it into a watch to make it more convenient to carry. The roadmap for future improvements is shown in Figure 14, and these are the directions in which the study can advance to obtain more comprehensive conclusions and explanations.