A Non-Invasive and Highly Accurate Multi-Wavelength Light Near-Infrared Glucose Sensor Using A Multilevel Metric Learning–Back Propagation Network

Abstract

Non-invasive near-infrared (NIR) human glucose sensors have attracted great interest in managing diabetes mellitus and those with complex sensing backgrounds due to glucose absorption spectrum overlap. Here, we propose a non-invasive and highly accurate multi-wavelength light NIR glucose sensor using a multilevel metric learning-back propagation network, i.e., “HMML-BP”, based on the narrowband multi-wavelength light NIR system. Our human glucose sensing method combines the advantages of this system and an HMML-BP network. The latter is composed of multilevel metric learning modules and a BP network to predict blood glucose concentrations. The narrowband multi-wavelength light NIR sensing system consists of six-channel NIR filters with center wavelengths of 850 nm, 940 nm, 1300 nm, 1400 nm, 1550 nm, and 1650 nm and a spectral resolution below 12 nm. The six NIR channels measured were first entered into the MML modules to build 3D multi-wavelength light data. Next, 3D multi-wavelength light data were optimized by stochastic neighbor embedding. Diffusion maps and factor analysis algorithms were used to retain effective NIR information. Finally, the optimized data were utilized as the BP network input to predict blood glucose concentrations. The predicted results showed that the factor analysis algorithm had the best performance in our HMML-BP network and that all the predicted glucose values fell into region A, with a mean absolute relative difference of 9.98%, meeting the requirements of daily glucose monitoring. Our blood glucose sensing method provides a new way of utilizing multi-wavelength light and hyperspectral information for smart human glucose monitoring.

1. Introduction

Traditional human blood glucose sensors are commonly based on the electrochemical method, where samples have to be obtained through the finger-prick method, which is painful, expensive, and susceptible to shortcomings [1,2,3]. The demand for non-invasive, cheap, and user-friendly glucose monitors, which are critical in diabetes, is rapidly growing. People with diabetes need frequent blood glucose management [4,5]. Advanced optical glucose sensors could take advantage of non-contact optical measurements, which have attracted great interest both in research and on the commercial market [6,7]. There have been many reports of such optical method-based sensors, such as near-infrared (NIR) absorption [8,9], mid-infrared (MIR) absorption [10], Raman shift [11,12,13], and NIR photoacoustic sensors [14,15], and so on. NIR glucose sensors employ the intrinsic NIR spectral absorption properties of glucose molecules and human tissue’s NIR light penetration ability to sense human glucose. Many researchers have applied on-chip waveguides [16], micro-fibers [17], and hydrogel-coated layers [18] to fabricate NIR glucose sensors, which commonly need complex, slower, and expensive experimental methods, limiting the application of low-cost blood glucose sensing in practical, commercial fields. Taking advantage of low-cost NIR LED/LD sources and Si/Ge/InGaAs photodiodes, NIR glucose sensors are convenient to use, providing a potential application method for emerging non-invasive human glucose monitors [19]. However, the intrinsic NIR absorption spectra of the glucose molecule overlap severely with other human biomaterials such as water, fat, protein, and so on, leading to complex, noisy backgrounds for non-invasive blood glucose monitors [20,21]. As a result, removing these backgrounds and improving glucose sensing accuracy are crucial for developing non-invasive daily NIR human glucose monitors.

Many groups have analyzed the NIR absorption properties of glucose in human tissue [22] and utilized advanced artificial intelligence (AI) algorithms to remove complex noising backgrounds [23,24], achieving non-invasive glucose measurement through AI algorithms and electronic control systems [25,26,27]. Yucen Yang et al. reported daily blood glucose detection based on the infrared pulsed sensing (IPS) method using NIR LED and a deep hybrid feature neural network to predict blood glucose concentrations [28]. Kiseok Song et al. reported the use of multi-modal spectroscopy where three NIR channels of 850 nm, 950 nm, and 1300 nm were input into the artificial neural network (ANN) to sense the glucose concentration [29]. Jain and coworkers proposed a dual (940 nm and 1300 nm) short-wavelength NIR-wave-based detection system that was validated on 200 individual subjects [30]. Dai et al. reported on a blood glucose detection system using a 1550 nm NIR absorbance spectrum and particle swarm optimization (PSO) with two ANNs [31]. Joshi et al. proposed a wearable, non-invasive consumer glucose device that applied 940 nm and 1300 nm NIR lights, which combined with the deep neural network regression algorithm to sense glucose levels [32]. Ramasahayam et al. designed a non-invasive blood glucose spectroscopy method that consisted of 1070 nm, 950 nm, and 935 nm NIR LEDs and combined this with an ANN [33]. Hina et al. proposed a single 940 nm wavelength glucose sensor using different machine learning algorithms that were trained using extracted features and reference glucose values [34]. Po-Lei Lee and coworkers proposed a non-invasive blood glucose sensor and applied dual-channel photoplethysmography (PPG) with values of 530 nm and 1550 nm LED and pulse arrival velocity (PAV) [35]. Jinxiu Cheng et al. reported on a nonlinear auto-regressive method with exogenous (NARX) input using seven parameters, including 1550 nm NIR absorbance information, ambient temperature, ambient humidity, systolic pressure, diastolic pressure, pulse rate, and body temperature, to predict human glucose levels [36]. These reported NIR glucose sensors commonly have very few NIR channels and broad-spectrum bandwidths caused by simple LED sources, which leads to rough NIR multi-wavelength light information and large measurement errors, limiting their use in terms of accurate glucose sensing. As a result, their predicted network algorithms must become increasingly complex, typically requiring large datasets and a long time to predict human glucose. The critical parameters of typical NIR glucose sensors are summarized and compared in

Table 1. Comparison of the critical parameters of typical NIR glucose sensors.

Reference	Measurement Site	Wavelength	Model	Results
[26]	Palm	1050, 1219, 1314, 1409, 1550, 1609	PLSR-SAE 1	Region A: 97.96%; Rp: 0.9216
[29]	Wrist	850, 950, 1300	IMPS and mNIRS 2-ANN	MARD: 8.3%; Region A: 90%
[31]	Finger	1550	PSO-2ANN	Regions A and B: 98.28%
[33]	Finger	935, 950, 1070	FPGA 3-ANN	Error: 1.02 mg/dL
[35]	Finger	530, 1500	PPG and PAV	RMSE: 7.46 ± 2.43 mg/dL
[36]	Finger	1550	SA 4 and NARX	RMSE: 0.72 mmol/L CORR: 0.85
This work	Finger	850, 940, 1300, 1400, 1550, 1650	HMML-BP	MARD: 9.98%; Region A: 100%

¹ Partial least squares regression–stacked auto-encoder; ² impedance spectroscopy and multi-wavelength near-infrared spectroscopy; ³ field-programmable gate array; ⁴ sensitivity analysis.

. These traditional sensors suffer from limited NIR multi-wavelength light information and complex predicted networks, meaning they fall short in terms of the development trends of real-time, highly accurate, and highly sensitive daily glucose monitoring. A non-invasive NIR glucose sensor with more efficient multi-wavelength light optical information and using a predicted algorithm shows promise for application in these regards; however, this remains an open question.

In this paper, we propose a non-invasive and highly accurate multi-wavelength light NIR glucose sensor using a multilevel metric learning–back propagation network, i.e., an “HMML-BP” network, based on the multi-wavelength light narrowband NIR sensing system. The HMML-BP network is composed of multilevel metric learning modules and a BP network, meaning it can remove complex sensing backgrounds and predict human blood glucose concentration. Our method distinguishes itself from prior approaches through its physics-informed design and hierarchical processing, offering unique advantages for non-invasive glucose monitoring. Most reported glucose sensing methods rely on single-step predictive models with direct preprocessing [29,32,33,34,36,37]. These models often require increasingly complex architectures, large datasets, and extended training times due to the intrinsic NIR absorption spectra of glucose heavily overlapping with those of other biomolecules, as well as the high complexity of sensing backgrounds in vivo. Our method leverages the distinct absorption properties of human tissue and blood glucose; low tissue absorption regions (850 nm and 950 nm channels) serve as reference signals to mitigate background noise and glucose absorption bands (1300 nm, 1400 nm, 1550 nm, and 1650 nm) containing target-specific information. By systematically integrating multilevel metric learning with a BP network, our method achieves high accuracy while maintaining physical interpretability. Different from conventional approaches that directly process overlapped glucose absorption spectra, our hierarchical design enables the independent verification of the embedding space’s physical consistency, as well as the convenient extraction of effective information from complex backgrounds. In addition, these physics-aware architectures show more transparency, reduced joint optimization information loss, and better computational efficiency, all of which are critical for practical daily human blood glucose sensing.

Our highly accurate narrowband multi-wavelength light NIR sensing system consists of six-channel NIR filters with center wavelengths of 850 nm, 940 nm, 1300 nm, 1400 nm, 1550 nm, and 1650 nm and a spectral resolution below 12 nm. The measured information is entered into the multilevel metric learning modules to build 3D multi-wavelength light data. The multilevel metric learning module is made of the first-level metric learning elements of 1D tissue absorption and 3D glucose absorption data, which are further connected to the second-level metric learning element to remove complex sensing backgrounds. Several metric learning algorithms of stochastic neighbor embedding (SNE) [38], diffusion maps [39], and factor analysis [40] are used to optimize 3D multi-wavelength light data. Furthermore, these data are input into the BP network to predict blood glucose concentration. The predicted results produced by our HMML-BP network are evaluated via comparative absolute relative difference (ARD), Clarke error grid analysis (EGA), Bland–Altman analysis, and so on. These results show that the factor analysis algorithm has the best performance in our HMML-BP network, with all falling in region A with a mean absolute relative difference (MARD) of around 9.97%, thus satisfying the requirements of human daily glucose sensing.

2. Methods

In human biomedical tissue, the NIR-I window of 700–900 nm shows low tissue absorption, while that of 900–1700 nm presents a higher penetration depth due to reduced scattering [41]. Considering the absorption properties of glucose (C₆H₁₂O₆), with bands of 1100–1300 nm and 1500–1800 nm, 6-channel multi-wavelength NIR lights of 850 nm, 950 nm, 1300 nm, 1400 nm, 1550 nm, and 1650 nm are used as $I_{sig}$ to characterize the NIR optical performance of human tissue. In order to account for potential interference from analytes such as lactate and urea, Table S1 in the Supplementary Materials lists the NIR absorption peaks of key blood components. The primary absorption bands of urea and protein are primarily associated with N–H bonds, whereas glucose molecules exhibit absorption at C–H and O–H bonds. The selected wavelengths (850 nm, 940 nm, 1300 nm, 1400 nm, 1550 nm, and 1650 nm) are distinct from the absorption peaks of most interfering analytes.

Considering distinct optical absorption properties of human tissue and glucose, the low tissue absorption regions (850 nm and 940 nm channels) serve as reference signals to mitigate background noise; glucose absorption bands (1300 nm, 1400 nm, 1550 nm, and 1650 nm) containing target-specific information serve as the signal. This measured multi-channel optical information is systematically integrated by multilevel metric learning with a BP network. The designed multilevel metric learning module is used to extract effective optical information, while the BP network is applied to predict human blood glucose concentrations. These 6-channel multi-wavelength NIR lights are divided into two groups: 850 nm and 950 nm for low tissue absorption, and 1300 nm, 1400 nm, 1550 nm, and 1650 nm for obvious absorption. According to the multi-wavelength absorption model, based on the Lambert–Beer law [42], the intensity of 6-channel multi-wavelength NIR light $I_{\mathrm{s}\mathrm{i}\mathrm{g}}\left({\lambda }_i\right)$ can be calculated by

$$I_{\mathrm{s}\mathrm{i}\mathrm{g}}\left({\lambda }_i\right)=I_{0}exp\left[{\epsilon }_{sig}\left({\lambda }_i\right)c_{i}L\left({\lambda }_i\right)+G\right],$$

(1)

where $I_0$ represents the intensity of incident light, $c_i$ is the concentration of the measured sample, $G$ donates the absorption of the sensing background, and ${\epsilon }_{sig}\left({\lambda }_i\right)$ and $L\left({\lambda }_i\right)$ describe the extinction factor and optical path for the wavelength ${\lambda }_i$. To remove complex sensing background $G$, the scattered light of the ground glass diffuser serves as the reference light $I_{ref}$ and can be described as follows:

$$I_{ref}=I_{0}exp\left[G\right]$$

(2)

Then, the normalized multi-wavelength light ${NI}_{SR}\left({\mathsf{\lambda }}_{\mathrm{i}}\right)$ can be calculated as

$${NI}_{SR}({\mathsf{\lambda }}_{\mathrm{i}})={\displaystyle \frac{I_{sig}}{I_{ref}}}=exp\left[{\epsilon }_{sig}\left({\lambda }_i\right)c_{i}L\left({\lambda }_i\right)\right]$$

(3)

Furthermore, normalized multi-wavelength lights ${NI}_{SR}\left({\mathsf{\lambda }}_{\mathrm{i}}\right)$ are introduced into the proposed HMML-BP network to remove complex human tissue noise and predict glucose concentration. As shown in Figure 1, our HMML-BP network consists of four critical parts:

• Removing sensing background: Measured 6-channel human intensity $I_{\mathrm{s}\mathrm{i}\mathrm{g}}\left({\lambda }_i\right)$ is normalized according to the measured reference scattering intensity $I_{\mathrm{s}\mathrm{i}\mathrm{g}}\left({\lambda }_i\right)$, using Equations (1)–(3), in order to remove the influence of the sensing background and obtain normalized 6-channel multi-wavelength light information, ${NI}_{SR}$;
• First level of metric learning elements: Normalized 850 nm ${NI}_{SR}$(850) and 940 nm ${NI}_{SR}$(940) channels are trained by the metric learning elements to form the 1D human tissue low absorption data (TData 1). SNE, diffusion maps, and factor analysis algorithms are utilized to optimize TData 1 to effectively extract NIR optical information. Similarly, normalized 1300 nm ${NI}_{SR}$(1300), 1400 nm ${NI}_{SR}$(1400), 1550 nm ${NI}_{SR}$(1550), and 1650 nm ${NI}_{SR}$(1650) glucose absorption band channels are tested by other metric learning elements to build 3D data (GData 3), which are also optimized using SNE, diffusion maps, and factor analysis algorithms;
• Second level of metric learning elements: According to the self-comparison effect between 1D tissue absorption data (TData 1) and 3D glucose absorption data (GData 3), these (both TData 1 and GData 3) are further input into the second-level metric learning elements to build 3D multi-wavelength light data (MData 3). Furthermore, these data (MData 3) are also optimized by SNE, diffusion maps, and factor analysis algorithms to remove tissue absorption interference and extract glucose absorption information effectively;
• Glucose prediction of BP network: The predicted glucose BP network, with 3 initial input variables of MData 3, is constructed using the following method. The architecture of our proposed network consists of three layers: one input, one hidden, and one output layer. The number of input layer neurons is the same as the number of input variables, and the 3D multi-wavelength light data (MData 3) serve as the input layer. The number of hidden layer neurons is adjusted to 36. The output layer has a neuron that represents the predicted concentration of human blood glucose. The network was trained using the Bayesian Regularization algorithm, in which the maximum number of training rounds was set to 20,000. The learning rate was set to 0.01 and the minimum error of the training target was set to 0.0000001. The total 135 samples were split into two sets: 115 samples were randomly selected as the training set for generating and training the network, and the remaining 20 samples were used to evaluate the performance of the trained model. In addition, the performance of the established model was evaluated according to MARD, the root mean square error (RMSE), Bland–Altman analysis, and EGA.

3. Materials and Experiments

Six NIR multi-wavelength light property channels of 850 nm, 940 nm, 1300 nm, 1400 nm, 1550 nm, and 1650 nm were examined via a human finger using the constructed reflectance NIR multi-wavelength light system (Figure 2). As can be seen in Figure 2a, incident light from a halogen lamp (Thorlabs, Newton, NJ, USA, OSL2IR) travels through the collimated lens L1 and forms parallel light. Then, the parallel incident light is tuned by switching the monolithic multi-wavelength light electric filter wheel, forming narrowband multi-wavelength light. From the schematic diagram of the monolithic multi-wavelength light electric filter wheel in Figure 2b, 6 NIR filters of 850 nm (Thorlabs, FBH850-10), 940 nm (Thorlabs, FBH940-10), 1300 nm (Thorlabs, FBH1300-12), 1400 nm (Thorlabs, FBH1400-12), 1550 nm (Thorlabs, FBH1550-12), and 1650 nm (Thorlabs, FBH1650-12) are embedded into the monolithic electric wheel (Thorlabs, FW102C). Channel filters of 850 nm and 940 nm have a half of the maximum (FWHM) of 10 nm, while the other four filters have the larger value of 12 nm. This narrowband monolithic multi-wavelength light filter is used to extract highly accurate narrowband NIR light, avoiding broadband light absorption interference from other biomaterials. This light is further focused on the human finger by lens L2, and the reflected light is collected by lens L3. Finally, the intensity I of reflected light is recorded by the power meter (Thorlabs, PM16-122).

In accordance with biomedical ethics protocols, all study participants were fully informed of the experimental procedures and potential risks associated with the non-invasive glucose-monitoring methodology. Informed consent was obtained prior to initiating human experiments. The experimental protocol comprised the following sequence: Participants’ fingertips were disinfected using sterile alcohol swabs and allowed to air-dry until complete ethanol evaporation. The human fingertip was then placed on the test location of our custom NIR multi-wavelength light imaging system, as shown in Figure 2a, in order to measure diffuse reflectance spectroscopy. Each experiment lasted for 6 s. To establish ground-truth reference values, capillary blood samples were concurrently collected via aseptic lancet puncture and analyzed using a clinically validated glucometer (Johnson, New Brunswick, NJ, USA, OneTouch VerioVue).

When the electric filter wheel selects different wavelengths, the power meter automatically feeds back the optical power in real time to achieve circuit integration. The tissue exposure time is about 0.5 s for each wavelength, while the multiplexing time of each wavelength is approximately 500 ms. Through this standardized protocol, we acquired 130 paired datasets comprising multi-wavelength light NIR signatures, as well as corresponding blood glucose concentrations, enabling the comprehensive characterization of optical fingertip properties under varying glycemic conditions.

Since human blood glucose sensing is complex, many critical factors (motion artifacts, stray light, sweat, temperature, and so on) have been analyzed: (1) Motion artifacts: To improve stability, our glucose system uses the highly accurate electric wheel, all optical information was tested after achieving system stability, and the experiments were conducted immediately for about 6 s to maintain this stability. (2) Stray light: To minimize the interference of stray light, the whole experimental system was enclosed in a black box, with only a small hole opened at the finger acquisition site to allow placement. The incident and reflection paths were separated by a black baffle. Furthermore, diffuse light from frosted glass was obtained after each human measurement, serving as the reference light for removing system fluctuations. (3) Sweat: To remove sweat interference from human fingers, disinfection with alcohol and air-drying were carried out before each experiment. (4) Temperature: Considering the influence of temperature, all experiments were tested under room temperature.

Compared to existing NIR-based glucose sensing technologies [26,29,31,33,35,36], our system exhibits two primary limitations in terms of hardware and AI algorithms. First, the multi-wavelength NIR configuration (6 discrete channels) incurs higher hardware costs compared to conventional single- or dual-wavelength systems. Second, the hybrid architecture integrating metric learning and BP networks demands greater memory resources and longer training durations than simpler prediction algorithms, necessitating deployment on high-performance computing platforms.

4. Results and Discussion

4.1. Multi-Wavelength Light Metric Learning

Six multi-wavelength signal light ${NI}_{SR}\left({\mathsf{\lambda }}_{\mathrm{i}}\right)$ channels of ${NI}_{SR}$(850), ${NI}_{SR}$(940), ${NI}_{SR}$(1300), ${NI}_{SR}$(1400), ${NI}_{SR}$(1550), and ${NI}_{SR}$(1650) are input into the multilevel metric learning module to build multi-wavelength light data. Figure 3a–c show the TData 1 made by SNE, diffusion maps, and factor analysis algorithms, respectively. As can be seen in Figure 3a–c, all these TData 1 exhibit low linear properties that can be attributed to the intrinsic random absorption properties of various biomaterials constituting the artificial human tissue background. Furthermore, Figure 3d–f exhibit the GData 3 optimized by SNE, diffusion maps, and factor analysis algorithms, respectively, displaying a certain degree of linearity compared to TData 1 (Figure 3a–c). The constructed GData 3_Fact made by the factor analysis algorithm shows improved linearity compared to that obtained by SNE and diffusion map algorithms. In addition, these 3D multi-wavelength light metric data, MData 3, in Figure 3g–i show improved linear properties compared to the GData 3 shown in Figure 3d–f, indicating that the artificial human background TData 1 play a critical role in removing random biomaterial interference. Furthermore, MData 3_Fact obtained by the factor analysis algorithm (Figure 3i) exhibit the best linearity in contrast to all these results, showing that the multilevel metric learning module achieved using this algorithm shows the best performance in reducing biomaterial interference and effectively extracting glucose NIR absorption information. The construction of multi-wavelength light data using other algorithms is shown in Figure S1.

In view of the multidimensional distribution characteristic of 3D multi-wavelength light data, the standardized Euclidean distance is calculated and compared to quantitatively characterize GData 3 and MData 3. As shown by the silver spots in Figure 3d–i, measured 3D glucose concentration data are made by expanding the measured glucose concentration $c_n$ into the 3D space; the three axes describe the measured glucose concentration $c_n$. Utilizing the pdist2 (pairwise distance between two sets of samples) algorithm in MATLAB (MATLAB R2023b, The MathWorks, Inc., Natick, MA, USA), the similarity $\alpha$ and the difference $\beta$ between 3D multi-wavelength light data and glucose concentration data can be calculated as follows:

$$\alpha ={\displaystyle \frac{\sum _{i=1}^n{d}_{ii}}{n}},$$

(4)

$$\beta ={\displaystyle \frac{\sum _{i,j=1}^n{d}_{ij}}{n(n-1)}},$$

(5)

where $d_{i,i}$ and $d_{i,j}$ donate the inner and outer term of standardized Euclidean distance, and n is the measured human glucose. In general, the smaller similarity $\alpha$ and larger difference $\beta$ typically indicate the better performance of 3D data. As shown in

Table 2. Comparison of similarity $\alpha$ and difference $\beta$ of 3D multi-wavelength light data made by SNE, diffusion maps, and factor analysis.

	$\mathit{\alpha }$			$\mathit{\beta }$			Δ
	$\mathit{\alpha }$GData	$\mathit{\alpha }$MData	Δ1	$\mathit{\beta }$GData	$\mathit{\beta }$MData	Δ2
SNE	8.487	8.5422	0.0552	8.4869	8.542	0.0552	0.0001
Diffusion maps	8.2276	8.2604	0.0328	8.2276	8.2606	0.033	0.0002
Factor analysis	8.609	8.861	0.252	8.6086	8.861	0.2524	0.0004

, the calculated differences ${\beta }_{SNE}$, ${\beta }_{diff}$, and ${\beta }_{\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}}$ of MData 3 are 8.542, 8.2606, and 8.861; all these values are larger than those of GData 3, with calculated difference ${\beta }_{\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}}$ of MData showing the largest improvement of 0.2524. However, the calculated similarities ${\alpha }_{SNE}$,${\alpha }_{diff}$, and ${\alpha }_{\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}}$ of MData 3 show a similar improvement in contrast those of GData 3. When ${∆}_1$ denotes the difference between the calculated ${\alpha }_{\mathrm{M}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}3}$ and ${\alpha }_{\mathrm{G}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}3}$ (${∆}_1$= ${\alpha }_{\mathrm{M}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}3}$ − ${\alpha }_{\mathrm{G}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}3}$) and ${∆}_2$ denotes the difference between the calculated ${\beta }_{\mathrm{M}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}3}$ and ${\beta }_{\mathrm{G}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}3}$ (${∆}_2$= ${\beta }_{\mathrm{M}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}3}$ − ${\beta }_{\mathrm{G}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}3}$), then the improvement trend between ${∆}_1$ and ${∆}_2$ can be described as $∆$ = |${∆}_1$ − ${∆}_2$|. As can be seen in Table 2, the calculated ${∆}_{fact}$ shows the largest value of 0.0004 in comparison with the calculated ${∆}_{SNE}$ and ${∆}_{diff}$. This indicates that the improvement $\beta$ of MData 3 made by the factor analysis algorithm can effectively compensate for the weakness of a larger $\alpha$. All these improvements indicate that our multilevel metric learning module, constructed using the factor analysis algorithm, is quite effective in utilizing multi-wavelength light information and building a 3D multi-wavelength light metric space. The calculation results of other algorithms are detailed in Table S2.

4.2. Prediction of Human Glucose Concentration

These 3D multi-wavelength light data, made by multilevel metric learning modules through SNE, diffusion maps, and factor analysis algorithms, were further input into the BP network to predict blood glucose concentration. The predicted results were characterized and analyzed through a comparison of ARD, EGA, and Bland–Altman analysis, among others; the results of this analysis are shown in

Table 3. Comparison of blood glucose prediction results from different algorithms.

	MARD	RMSE	MD	Clark EGA
				Region A	Region B
SNE	11.29%	0.742	0.2445	90%	10%
Diffusion maps	10.49%	0.787	0.1197	95%	5%
Factor analysis	9.98%	0.789	−0.0092	100%	0

.

4.2.1. Comparison Analysis of ARD, MARD, and RMSE

A comparison of the calculated ARD of predicted $\widehat{y_i}$ and measured glucose concentrations $y_i$ is shown in Figure 4. Figure 4a–c show the calculated ARD = ${\displaystyle \frac{\left|y_i-\widehat{y_i}\right|}{y_i}}$ of the predicted results made by our HMML-BP network using SNE, diffusion maps, and factor analysis algorithms. As shown in Figure 4a, those using the SNE algorithm show that samples 9# and 19# are obviously far away from the measured results, the calculated ARD values of which are around 27% and 30%, respectively (Figure 4b). Furthermore, Figure 4c exhibits the prediction results obtained by our network using the diffusion maps algorithm, showing that only sample 19# emerges as obviously different from the measured results, with an ARD of 21% (Figure 4d). The predicted results and ARD achieved by our network using the factor analysis algorithm, as shown in Figure 4e–f, show that all the predicted results are closer to the measured concentrations, with ARD at less than 20%.

The MARD is calculated to evaluate the predicted accuracy as follows:

$$\mathrm{M}\mathrm{A}\mathrm{R}\mathrm{D}={\displaystyle \frac{1}{n}}\times \sum _{i=1}^n\left({\displaystyle \frac{\left|y_i-\widehat{y_i}\right|}{y_i}}\right)$$

(6)

The calculated MARD of the predicted results made by our network using the factor analysis algorithm is 9.98%, displaying the best value in contrast to those achieved using the diffusion map and SNE algorithms (10.49% and 11.29%, respectively). Furthermore, the RMSE characterizes the prediction accuracy and is calculated as

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{(y_i-\widehat{y_i})}^2}{n}}}$$

(7)

The calculated RMSE made by our network using the factor analysis algorithm is around 0.742, showing the best performance in contrast to those achieved using diffusion maps and SNE algorithms (0.787 and 0.789, respectively).

4.2.2. Bland–Altman Analysis

These predicted results were also characterized using Bland–Altman analysis in order to assess the practical use of medical instruments in more detail [43]. As can be seen from Figure 5a, when applied to our network using the SNE algorithm, this analysis shows that the mean difference (MD) between the predicted and measured glucose concentrations is 0.2445 mmol/L, as well as that the 100% limit of agreement region is located within [−1.2638 mmol/L, 1.7529 mmol/L], the 95% limit of agreement. Also, a Bland–Altman analysis of predicted results produced by our network using the diffusion map algorithm, as shown in Figure 5b, shows how the smaller MD of 0.1197 mmol/L and 95% of the predicted points are situated in [−1.4436 mmol/L, 1.6829 mmol/L], thus meeting the 95% limit of agreement. Furthermore, Figure 5c presents a Bland–Altman analysis of predicted results produced by our network using the factor analysis algorithm, showing that the smallest MD of −0.0092 mmol/L and the 100% limit of agreement region are located in [−1.5011 mmol/L, 1.4827 mmol/L], thus falling within the 95% limit of agreement acceptable for medical instruments.

4.2.3. Clarke EGA

Clarke EGA, the “gold standard” for blood glucose sensing, shows regions A and B with clinically acceptable errors of less than 20% and 40%, while regions C, D, and E present significant clinical risks that must be avoided in blood glucose sensing [44]. Figure 6a shows the Clarke EGA image (left) and error distribution fan diagram (right) of predicted results made by the HMML-BP network using the SNE algorithm, showing that 90% of the predicted results fall in region A, while 10% fall in region B. In addition, the Clarke EGA image of the predicted results obtained by the HMML-BP network using the diffusion map algorithm, as shown in Figure 6b, exhibits improved predicted accuracy, with regions A and B at 95% and 5%, respectively. Furthermore, Figure 6c presents the EGA image of predicted results made by the HMML-BP network using the factor analysis algorithm; here, all tested results are located in region A, showing the highest predicted accuracy compared to those produced with SNE and diffusion maps. All these improvements obtained using the factor analysis algorithm show higher accuracy in human glucose sensing, offering a more effective way of monitoring human daily glucose.

The predicted results of our method fall exclusively in region A, outperforming commercial continuous glucose-monitoring (CGM) systems (e.g., Dexcom and Abbott Libre), whose results are distributed across both regions A and B. Our system achieves a MARD of 9.98%, which is comparable to commercial CGMs (typically ~9%) [45]. In addition, for daily blood glucose sensing in humans, long-term cost is one of the most critical considerations. Current CGM systems, which involve inserting electrodes under the skin for 7–14 days [46], can cause physical discomfort and impose financial burden on users. In contrast, our system eliminates the recurring expenses associated with sensor replacements, offering a more affordable and patient-friendly solution.

4.3. Translational Value

Inspired by the current methodology, our wearable prototype blood glucose monitor is covered by our invention patent (CN 202510450345), which consists of a circular monolithic integrated structure with tunable NIR LEDs, centrally located photodiodes, and electronic modules (e.g., Bluetooth). This prototype is compatible with mature, low-cost elements that can be built for practical applications. However, the system may face critical challenges due to the significant noise introduced by these cost-effective components, which could be calibrated through optimization algorithms. The power consumption of our wearable prototype is worthy of discussion. Tunable NIR LEDs, photodiodes, and wireless modules (e.g., Bluetooth) constitute the major power consumption sources in wearable systems of this nature. Typically, the power cost of NIR LEDs ranges from 50 to 100 mW, photodiodes consume 5–10 mW, and Bluetooth Low Energy (BLE) modules require 5–15 mW during active transmission. With optimized power management, the entire system can be supported by a 300–500 mAh lithium polymer battery, which is compatible with commercial portable blood glucose monitors like Freestyle Libre (Abbott) and Guardian Connect (Medtronic). In addition, our system is compatible with major market platforms (e.g., Apple Health, Google Fit), enabling remote parameter adjustment and demonstrating potential for telemedicine and IoT-based glucose monitoring. As our experiments were conducted in China, localization requirements are currently a priority for National Medical Products Administration (NMPA) approval. Furthermore, the system consists of mature optical/electrical components that can be easily obtained through mass production.

Therefore, the translational value of the current methodology can be summarized as follows: (1) Non-invasive real-time glucose monitoring: Our method leverages the distinct absorption properties of human tissue and blood glucose, where low-absorption regions (850 nm and 940 nm channels) serve as reference signals for mitigating background noise, while glucose absorption bands (1300 nm, 1400 nm, 1550 nm, and 1650 nm) provide target-specific information. By systematically integrating multilevel metric learning with a BP network, our method achieves high accuracy while maintaining physical interpretability. Taking advantage of a hierarchical design guided by physical properties, our approach requires fewer computational resources and offers a novel pathway for real-time glucose monitoring. (2) Cost-effectiveness: Long-term cost is one of the most critical considerations for daily blood glucose sensing in humans. Current CGM systems, which involve inserting electrodes under the skin for 7–14 days, can cause physical discomfort and impose financial burden on users. In contrast, our system eliminates the recurring expenses associated with sensor replacements, offering a more affordable and patient-friendly solution. (3) Future applications: By expanding the method to other spectral information, biomarkers such as blood oxygen could also be detected. This versatility aligns with the development of advanced portable wearables and IoT-enabled devices, demonstrating promising potential for remote smart healthcare applications.

5. Conclusions

In conclusion, we propose a non-invasive and highly accurate multi-wavelength light NIR glucose sensor using an HMML-BP network based on the multi-wavelength light narrowband NIR sensing system. Our human glucose sensing method combines the advantages of both this system and an HMML-BP network. The latter is composed of multilevel metric learning modules and a BP network to remove complex sensing backgrounds and achieve highly accurate blood glucose predictions. The highly accurate narrowband multi-wavelength light NIR sensing system consists of six-channel NIR filters with center wavelengths of 850 nm, 940 nm, 1300 nm, 1400 nm, 1550 nm, and 1650 nm, with a spectral resolution of less than 12 nm. The measured six-channel multi-wavelength light information is entered into multilevel metric learning modules to build 3D multi-wavelength light data; these are then optimized using SNE, diffusion maps, and factor analysis algorithms, before being further utilized as the BP network input to predict human glucose. The predicted results of the HMML-BP network optimized using the factor analysis algorithm show the best performance; all the predicted values fall within region A and the MARD is around 9.98%, meeting the requirements of daily human glucose monitoring.

Our current system is still subject to many limitations in terms of hardware, data processing, and predicted results. To enhance portability for practical applications, the following issues should be addressed: (1) Hardware system: The system is limited by bulky halogen lamps and the experimental platform of the filter wheel. Therefore, it is crucial to reduce the size of these lamps in order to build a portable system. Future work could focus on designing wearable prototypes developed using low-cost and compact components such as NIR LEDs, photodiodes, and Bluetooth modules. (2) Data processing: To a certain extent, multilevel metric learning increases calculation complexity, so the real-time performance of blood glucose prediction still needs to be improved. (3) Predicted results: The system is in the theoretical verification stage, and the sample size is relatively small; in the future, human blood glucose measurements could be conducted in clinical settings in order to expand the dataset, enhance its diversity, and thus verify the system’s long-term stability.

Further work on non-uniform HMML-BP networks with different heterogeneous algorithms, including multilevel metric learning elements, could be pursued in order to improve predication accuracy and broaden the working range. Additional dynamic physiological variations, such as sweat-induced light-scattering changes and temperature-dependent blood flow dynamics, could also be investigated to explore more complex tissue properties and enhance prediction accuracy. In the future, more electric feedback modules could also be added to achieve automatic correction and further improve prediction accuracy. Moreover, miniature, portable, and highly accurate multi-wavelength light NIR glucose sensors could be applied to on-chip multi-wavelength light NIR systems using integrated, narrowband NIR LED–filter–photodiodes. The proposed non-invasive glucose sensing method allows for the convenient measuring and effective use of highly accurate multi-wavelength light NIR information to achieve non-invasive, precise blood glucose prediction, offering a new way of utilizing multispectral—or even hyperspectral—information in smart human glucose sensors. Our proposed method thus shows promise for application in non-invasive daily blood glucose monitoring.