Mattia Zanon, 1 Giovanni Sparacino, 1 Andrea Facchinetti, 1 Mark S. Talary, 2 Andreas Caduff, 2 and Claudio Cobelli 1. 1.

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1 Alied Mathematics Volume 13, Article ID , 1 ages htt://dx.doi.org/1.1155/13/ Research Article Regularised Model Identification Imroves Accuracy of Multisensor Systems for oninvasive Continuous Glucose Monitoring in Diabetes Management Mattia Zanon, 1 Giovanni Saracino, 1 Andrea Facchinetti, 1 Mark S. Talary, Andreas Caduff, and Claudio Cobelli 1 1 Deartment of Information Engineering, University of Padova, Via Gradenigo 6B, Padova, Italy Biovotion AG, Technoarkstrasse 1, 85 Zurich, Switzerland Corresondence should be addressed to Claudio Cobelli; cobelli@dei.unid.it Received 14 March 13; Acceted 1 June 13 Academic Editor: Kiwoon Kwon Coyright 13 Mattia Zanon et al. This is an oen access article distributed under the Creative Commons Attribution License, which ermits unrestricted use, distribution, and reroduction in any medium, rovided the original work is roerly cited. Continuous glucose monitoring (CGM) by suitable ortable sensors lays a central role in the treatment of diabetes, a disease currently affecting more than 35 million eole worldwide. oninvasive CGM (I-CGM), in articular, is aealing for reasons related to atient comfort (no needles are used) but challenging. I-CGM rototyes exloiting multisensor aroaches have been recently roosed to deal with hysiological and environmental disturbances. In these rototyes, signals measured noninvasively (e.g., skin imedance, temerature, otical skin roerties, etc.) are combined through a static multivariate linear model for estimating glucose levels. In this work, by exloiting a dataset of 45 exerimental sessions acquired in diabetic subjects, we show that regularisation-based techniques for the identification of the model, such as the least absolute shrinkage and selection oerator (better known as LASSO), Ridge regression, and Elastic-et regression, imrove the accuracy of glucose estimates with resect to techniques, such as artial least squares regression, reviously used in the literature. More secifically, the Elastic-et model (i.e., the model identified using a combination of l 1 and l norms) has the best results, according to the metrics widely acceted in the diabetes community. This model reresents an imortant incremental ste toward the develoment of I-CGM devices effectively usable by atients. 1. Introduction Diabetes consists of a malfunction of the glucose-insulin regulatory system leading to the onset of long and short term comlications, like retinoathy, neuroathy, and cardiovascular and hearth diseases, due to sustained blood glycaemic levels exceeding the normal range of 7 18 mg/dl [1]. According to the International Diabetes Federation, diabetes is estimated to currently affect more than 35 million eole worldwide, and this number is raidly growing []. ot surrisingly, in the last few decades, diabetes has received an increasing attention both for its social and economic imlications [3]. Standard theray of tye 1 diabetes is based on a combination of diet, hysical activity, and exogenous insulin injections, modulated on the basis of individual atient levels of glucose concentration in the blood. Accurate and frequent monitoring of glucose concentrations by ortable sensor devices lays a crucial role in the diabetes theray [4]. Self-monitoring blood glucose (SMBG) sensors require the collection of a blood samle by ricking the skin with a lancet device. An external ocket device is then used to analyze the blood and determine glucose concentration for instance by the glucose oxidase rincile [5]. These sensors are uncomfortable for the atient and are tyically used no more than 3-4 times er day. Such sarseness of samling does not allow the observation of glucose dynamics and glucose excursions outside the safety range, and dangerous nocturnal hyoglycaemic swings are often not detected. To overcome these roblems, ortable continuous glucose monitoring (CGM) sensors, measuring blood glucose values every 1 to 5 minutes for u to 7 consecutive days, have been roosed in the

2 Alied Mathematics early s and are now of great interest for the tuning and otimization of diabetes theray [6, 7]. In articular, online alications of CGM sensors include revention of hyer- /hyoglycaemic events; see for examle [8, 9], and closedloo glucose control aimed at determining otimal automatic insulin infusion in the so-called artificial ancreas systems; see [1 14]. otably, dealing with these online alications requires facing nontrivial signal rocessing issues connected to denoising [15], calibration [16], and rediction [17 1](see [, 3] for reviews) calling for the develoment of the socalled smart CGM sensor architecture [4]. Most of the CGM sensors requiring the lacement of a small needle in the subcutaneous tissue use an enzyme-based glucose-oxidase electrode and thus are invasive, albeit minimally. To limit atients discomfort, in the last decade, several noninvasive continuous glucose monitoring (I-CGM) sensors have been rototyed. Many different hysical rinciles have been considered to ursue I-CGM, but none of them has clearly outerformed the others so far; see for examle [5 7]. One major difficulty with I-CGM is the fact that environmental (e.g., temerature) and hysiological (e.g., sweat, blood oxygenation, etc.) rocesses act as erturbing factors and often allow blood glucose changes to be tracked only in highly controlled conditions (e.g., during in-hosital studies) [8 3]. To tackle this issue, an aroach gaining increasing attention in the last years is the multisensor aroach to I-CGM; that is, instead of focusing on a single hysical rincile, these devices resort to a combination of technologies. For instance, the GlucoTrack [31] exloits a mix of thermal, acoustic, and electromagnetic technologies and comares the three measurements, assuming they all reflect a glucose-related measurement. A different, yet recent, multisensor rototye [3] emloys a combination of dielectric sectroscoy (DS) and mid-infrared-based sensors. A further examle of multi-sensor device, roosed by Solianis Monitoring AG (Zürich, Switzerland, technology taken over by Biovotion AG, Zurich, Switzerland), embeds sensors of different nature for the biohysical characterisation of skin and underlying tissue in order to track glucose-related and erturbing factors searately [3, 33]. Multisensor aroaches to I-CGM require a model to connect the hysical quantities measured by the sensors with blood glucose concentrations. For instance, in the Solianis Monitoring AG rototye (from now on named Solianis for the sake of readability) considered in this work, a multivariate linear regression model is used to combine 15 signals recorded noninvasively for estimating a glucose concentration rofile (see Section 3.1 for more details). As described in [33, 34], the linear regression model is identified on a dataset collected in a oulation of subjects and comrising multi-sensor channels measurements and reference blood glucose (RBG) values collected in arallel by a gold standard technique. Previous work [35] has shown that a regularised identification method, based on l 1 norm (least absolute shrinkage and selection oerator LASSO), rovidedaglucoserofilemoreaccuratethanthatofothermodels identified with aroaches controlling comlexity such as subset selection method or artial least squares (PLS). In the resent work, by using the same dataset of 45 exerimental sessions used in [35], we demonstrate that the accuracy of glucose estimates can be further imroved by considering l norm regularization (Ridge regression) and a combination of l 1 and l norms (Elastic-et E regression), roviding a further incremental ste toward the develoment of an I-CGM effectively usable by diabetic atients.. Database The database consists of 45 exerimental sessions recorded from 6 tye 1 diabetic subjects, during which lasma glucose was induced to vary according to different redetermined rofiles to cause different hyo- and hyerglycaemic excursions. During each session, multi-sensor data and RBG were acquired in arallel, with a time samling of seconds and 1 15 minutes, resectively. The RBG samles were acquired by means of a SMBG device. The study was erformed at the University Hosital Zurich according to the requirements of good clinical ractice and was aroved by the local ethical commission. More clinically related information can be found in [33]. For the analysis, the database was slit into two data subsets of and 3 exerimental sessions, resectively. If the first data subset is used for identifying the models with the different techniques, the second is used to test the models over unseen multi-sensor data (1 >) and vice versa ( >1). For the sake of sace, we will not discuss results of the alicationofthemodelonthesamedatasetusedfortheir identification, and only model test results will be considered. Multi-sensor data in the identification data subset undergoes a rerocessing ste described in detail in [35]. Briefly, each multi-sensor channel is normalized to have zero mean and unitary standard deviation. These values are then used to standardize the same channels in the test data subset to ermit simulation of real-time glucose monitoring. Moreover, the first RBG value available at the beginning of each recording session is used to calibrate the estimated glucose rofiles by the model setting a baseline adjustment, to allow for a real-time consideration/imlementation. 3. Methods 3.1. Glucose Determination by a Multisensor System. In stating the roblem, we deliberately make only a brief descrition of the framework we are working on and we refer the reader to the quoted bibliograhy for details. Rather than focusing on a single hysical rincile, the Solianis multi-sensor device resorts to a combination of technologies, embedded into the substrate in contact with the skin for the biohysical characterisation of the skin and underlying tissue in order to account for confounding factors, which can significantly deteriorate the accuracy of glucose measurements [3, 36 38]. In articular, glucose-related signals are obtained from DS fringing field caacitive electrodes, with different geometrical roerties, roviding a sectrum of the frequency-deendent comlex dielectric roerties of skin and underlying tissue including blood, which can be easily arameterised by its magnitude and hase [39]. Environmental and hysiological rocesses that can interfere

3 Alied Mathematics 3 Mag. (a.u.) Mag. (a.u.) Tem. (a.u.) Channel no. 1 6: 9: 1: 15: 18: Channel no. 6: 9: 1: 15: 18:. Channel no. 15 6: 9: 1: 15: 18: Model 3 1 6: 9: 1: 15: 18: Multisensor channels X Glucose concentrations y Figure 1: A model (center) is needed to roerly combine the 15 multisensor channels (left, deicted with lines of different colours) for estimating blood glucose concentration rofile (right, magenta stars). with the measurements of the main glucose-related signals aremeasuredwithtemerature,otical,humidity,accelerometer, and additional DS sensors incororated into the same device substrate [3]. About 15 channels are thus rovided by the multi-sensor device (Figure 1, left), which have to be roerly combined through a mathematical model (Figure 1, middle) for estimating glucose concentrations in the blood (Figure 1, right). Since a mechanistic descrition comrising the hysical rinciles, linking measured channels with hysical/hysiological rocesses, in articular, related to glucose changes, has not yet been fully develoed, a blackbox multivariate linear regression model is used. Formally, if is the number of data oints available and is the number of measured channels, the model to identify from the identification dataset is described as y = Χβ + ^, (1) where y reresents the ( 1) target vectorcontainingrbg values, X is the ( ) matrix collecting the multi-sensor channels, β is the ( 1) vector containing the coefficients of thelinearmodel,and^ is the ( 1) term reresenting the error. The vector β in (1) can be identified by minimizing the cost function F(β) given by the residual sum of squares (RSS): F(β) =RSS (β) = y Xβ = (y i X i β), () measuring the distance between data and model redictions. Since this cost function has a quadratic form, a closedform solution, the so-called ordinary least squares (OLS) estimate, can be obtained. In the case under consideration, OLS suffers from overfitting due to the high dimensionality of the measurement sace and to the correlation between subsets of inut channels (well visible in the channels showed in Figure 1, left). Recent work [34] showed that further imroved results can be obtained by exloiting subset selection techniques. Then, further work [35] investigated the use of other methods controlling model comlexity, including PLS (widely used in chemometrics and related fields dealing with sectroscoy data) and the LASSO regularization technique. It has been shown that regularization techniques, in articular, the LASSO, outerform PLS since it sets many coefficients to zero being less sensitive to occasional noise in the multi-sensor channels. Formally seaking, regularized model identification techniques add a term L(β) to the cost function of (), leading to F(β) =RSS (β)+l(β), (3) where L(β) is a function of β reflecting comlexity. DeendingontheformandonthearametersofL(β) in (), the resulting model will resent different well-known features, as will be briefly reviewed in the following section. Thus, the β minimizing (3) is identified establishing a trade off between adherence to the data and model comlexity,usuallybyacross-validationrocedureasbetterdiscussed next. 3.. Model Identification by Regularisation Techniques l 1 orm: LASSO. In the L(β) term of (3), the l 1 norm can be used. In the literature, this l 1 norm has been roosed in signal rocessing (under the name of basis ursuit) [4] and in statistics[41] for its main feature of inducing sarse solutions. Formally, in (3), the l 1 norm leads to define L(β) as the sum of the absolute values of the coefficients of the model L (β) =λ β 1 =λ β j (4) multilied by the scalar nonnegative arameter, hereafter referred to as regularization arameter for the sake of reasoning. Thus, the solution is found by minimizing β LASSO = arg min β (y i X i β) +λ β } j } } (5)

4 4 Alied Mathematics andisknownastheleastabsoluteshrinkageandselection oerator (LASSO), for its roerties of shrinking many coefficients to zero selecting only few inut variables. In articular,in our alicationdocumented in [35], the LASSO was shown to outerform PLS since it sets many coefficients to zero being less sensitive to occasional noise in multi-sensor channels. Equation (5) does not have a closed-form solution because the cost function is not differentiable when some coefficients β j are zero, and a lethora of methods have been develoed to calculate aroximate solutions numerically; see [4, 43] for reviews. In articular, an efficient technique for comuting the LASSO solution is obtained by modifying theleastangleregressionalgorithm[44]. With this technique, the arameter that has to be fixed reresents the number of inutvariablesallowedtoenterthemodel,indicatedwithj in Section 3. Remark 1. The regularization arameter weighting the L(β) term in (5) isobtainedbymeansofastandardrocedure known as K-fold cross-validation [45]. Briefly, the identification dataset is slit into K aroximately equal arts. Then, the model is identified on K 1arts and tested over the ortion of data not considered for deriving the model, calculating the mean squared error (MSE): MSE = 1 K 1 (y i ŷ ı ), (6) where y and ŷ reresent the true and estimated outut, resectively, and K 1 reresents the number of data oints in the K 1ortion of data. This rocedure is reeated K times and for a range of values of the arameter that has to be determined. Then, the cross-validation curve is lotted, resenting the MSE as a function of the regularization arameter. Emirical evidence suggests choosing its value in corresondence with a clear dro of the cross-validation curve l orm: Ridge Regression. The l norm involves the enalization of the sum of squares of the coefficients of the model multilied by a scalar nonnegative arameter: L(β) =λ β =λ β j. (7) The so-called Ridge regression solution, from now on ridge, is thus given by β ridge = arg min β (y i X i β) +λ β j } }. (8) } The quadratic nature of the cost function in (7) entailsa closed-form solution for β deendent on the arameter λ: β ridge =(X T X +λi x ) 1 X T y. (9) Also, in this case, the regularization arameter λ can be fixed by means of cross-validation. According to [45], as an indication of the model comlexity, the degrees of freedom (df)canbeused: df (λ) = tr [X(X T X +λi) 1 X T ]= dj d j +λ, (1) where the d j s are the singular values of X. Thus, to determine the regularization arameter by cross-validation, the MSE is lotted against df in (1) l 1 +l orms: Elastic et-regression. The so-called Elastic-et regression, from now on E, resorts to a weighted sum of the two reviously described norms, defining L(β) as L(β) =λ(α β 1 + (1 α) β ) =λ(α (11) β j + (1 α) β j ), where α weighs the contribution of the two norms while λ sets the amount of regularization [46]. Hence, the E model arameters are obtained solving the following: β E = arg min β (y i X i β) +λ(α β j +(1 α) β j )} }. } (1) Problem (1) does not have a closed-form solution, and severalnumericalalgorithmshavebeenroosedtocomutean aroximate solution (some of them are simle adatations of those develoed for the LASSO [46]). The algorithm that has been used in this work is the one based on cyclical coordinate descent originally develoed for the LASSO [47] and adated to roblem (1) following[48 5]. The arameters λ and α are determined by cross-validation, following a rocedure similarto thatofremark Criteria for Model Assessment. The accuracy of estimated glucose rofiles in the model test is measured through a set of indexes widely used in the diabetes research community. In articular, we consider the root mean squared error (RMSE) RMSE = 1 ((y i ŷ i ) ), (13) the mean absolute difference (MAD), indicating how much estimated glucose values are lower or higher than the reference, MAD = 1 y i ŷ i, (14)

5 Alied Mathematics 5 MSE umber of active variables MSE λ= df(λ) MSE λ = Log (λ) (a) (b) (c) Figure : 1-fold cross-validation curves for the choice of the otimal comlexity arameters for LASSO (a), Ridge (b), and E for α =.4 (c). The MSE (mean value and one standard deviation) is reresented as a function of the model comlexity arameter for each method. The red crosses reresent the values of the comlexity arameter chosen according to the dro in the error curve. The vertical red dashed line is for a better visual identification of the comlexity arameters. and the mean absolute relative difference (MARD), which characterizes the relative errors (in %) of the estimated glucose: MARD = 1 y i ŷ i y i, (15) where y i and ŷ i,fori = 1,...,,are,resectively,the reference RBG samles and the glucose estimates rovided by the models (all the exerimental sessions are simultaneously considered). Finally, a oular method used in the diabetes community to judge on the oint accuracy of glucose sensors istheerrorgridanalysis(ega)roosedbyclarkeand coworkers [51].The area where estimated glucose by the model and RBG values are dislayed as a scatterlot is broken down into five regions (labeled from A to E). Zone A reresents those glucose values within % of the RBG values and so on. The most dangerous situations are those where estimated glucose values fall into zones C/D/E because, from a clinical oint of view, they will lead to unnecessary or even wrong and otentially dangerous treatments. An evolution of EGA develoed for CGM sensors is the continuous EGA (CEGA) that also measures the accuracy of estimated glucose trends by creating a grid which is broken down into regions labeled from A R to E R ;see[5] for details. To give an idea of the values of these indexes for the current state-of the-art, minimally invasive (needle-based) commercial CGM sensors, a recent study [11]reorted mean MARD levels ranging from 11.8 to.% and a ercentage of data oints in the A+B region ranging from 98.9 to 96.9 under controlled conditions, comaring CGM measurements to gold standard blood glucose samling. 4. Results 4.1. Regularization Parameter Determination by Cross-Validation. Thefirststeintheanalysisissettingthevaluesforλ in (5), (8), and (1)andforα in (1). These were determined by finding where the cross-validation curve resents a clear dro in sloe, as exlained in Remark 1. Figure shows the values obtained when identification data subset art 1 is considered, and the red cross, together with a vertical red dashed line for visualization urose, highlights the selected otimal value (cross-validation lots for identification data subset art arenotshowedforthesakeofsace).secifically, ak-fold cross-validation strategy has been alied, with K=1, for having a good comromise between bias and variance of the estimated error [45].The left sublot shows the error curve as a function of the number of latent variables for the LASSO model, indicating a dro of the cross-validation curve around 15. The choice of the regularization arameter for ridge followed a similar aroach, with the crossvalidation curve (middle anel) resenting a dro when the degree of freedom, defined in (1), aroximately equals 5, corresonding to λ = 5. Similarly for E, the ending art of the dro in the error curve can be noticed for log(λ) 4.5 (Figure(c)), corresonding to λ =.1. For E, different cross-validation curves for different values of α were examined. The most reasonable choice seemed to be that obtained with α =.4. Indeed, this combination of arameters is the one roviding a good trade off between the l 1 and l norms allowing a reasonable comromise for the E model to be achieved. A value of α=.4can suggest that, although it is imortant to shrink channel weights to zero in order to lower the robability of occasional jums or sikes entering the model, allowing a grouing effect over correlated redictors is also imortant for a more robust estimation of glucose rofiles. 4.. Model Test. Figure3 shows examles of estimated blood glucose concentration rofiles (continuous line) versus reference RBG samles (oen bullets) for two reresentative exerimental sessions. Visual insection suggests that the rofiles rovided by the E model (bottom anels) outerform, in terms of accuracy, those rovided by LASSO (to) and Ridge (middle). The same observation alies for the examles deicted in Figure 4, which reresents a more challenging situation because of the resence of wider

6 6 Alied Mathematics 4 Subject: AA, session no. 8 LASSO 4 Subject: AA4, session no. LASSO : 1: 15: 18: 1: 15: 18: 4 Subject: AA, session no. 8 Ridge 4 Subject: AA4, session no. Ridge : 1: 15: 18: 1: 15: 18: 4 Subject: AA, session no. 8 E 4 Subject: AA4, session no. E : 1: 15: 18: 1: 15: 18: (a) (b) Figure 3: Reresentative recording sessions of Subjects AA (a) and AA4 (b). LASSO, Ridge, and E models test over indeendent test data subset (continuous lines) versus RBG levels (oen bullets). MARD values for the exerimental session on the right are of 16.7% (LASSO), 16.9% (Ridge), and 16.5% (E), while for the exerimental session on the left of 1.7% (LASSO), 11.% (Ridge), and 9.1% (E). disturbances, as witnessed by the sikes and jums affecting the reresentative multi-sensor raw channels dislayed in an additional fourth row of anels. This qualitative observation is suorted from the analysis of the MARD values obtained for the reresentative sessions in Figure3, that is,16.7%, 16.9%, and 16.5% (exerimental session deicted in the left anels) and 1.7%, 11.%, and 9.1% for the LASSO, Ridge, and E models, resectively. When occasional noise is affecting some of the multi-sensor channels, the MARD values slightly worsen, as can be seen for the exeriment deicted in Figure 4(a) resenting MARD of 53% for the LASSO, 4.5% for Ridge, and.6 for E. However, the E model still rovides blood glucose estimation rofiles more accurately than Ridge and LASSO. This is confirmed, in general, by Table 1, which shows the aggregate results over the test data subset. By analysing the results in more detail, the LASSO model seems to have a slight advantage in estimating glucose trends (last column of Table 1). The reason is twofold: first, the regularization erformed by the l 1 norm revents the modelcoefficientsfromassuminglargevaluesthusredicting glucose rofiles that are more flat than the other models, as it haens for examle in Figures 3(b) and 4(b); second, channels more sensitive to noise that contain also glucoserelated information are considered by Ridge and E exloiting the effect of the l norm but are less robable to be selected by LASSO, thus yielding smoother estimates. This fact can clearly be seen from Figure 4, where artifacts are resent (e.g., in channel no.) for the session of left data and in channel no.3 for the session of the right data. Interestingly, the LASSO model seems more robust than the other models to these jums in the data, reserving the glucose rofile with elevated smoothness and reasonably accurate trend. Indeed the l 1 norm shrinks many coefficients to zero allowing an easier interretation of the results with a reduced number of original variables, reresenting the strongest effects, considered imortant for estimating glucose rofiles. This is a tyical feature of the LASSO to act as

7 Alied Mathematics Subject: AA3, session no. 8 LASSO 9: 1: 15: 18: Subject: AA3, session no. 8 Ridge 9: 1: 15: 18: Subject: AA3, session no. 8 E 9: 1: 15: 18: Subject: AA5, session no. 5 4 LASSO 3 1 9: 1: 15: 18: Subject: AA5, session no. 5 4 Ridge 3 1 9: 1: 15: 18: Subject: AA5, session no. 5 4 E 3 1 9: 1: 15: 18: 1 Subject: AA3, session no. 8 Channel no. 1 Subject: AA5, session no. 5 Channel no. 3 (a.u.).5 (a.u.).5.5 9: 1: 15: 18: (a) 9: 1: 15: 18: (b) Figure 4: Reresentative recording sessions of Subjects AA3 (a) and AA5 (b). LASSO, Ridge, and E models test over indeendent test data subset (continuous lines) versus RBG levels (oen bullets). Bottom anels dislay two reresentative channels (no. and no.3 for subject on the left and on the right, res.) entering the models, where occasional sikes and jums are evident. MARD values for the exerimental session on the right are of 53% (LASSO), 4.5% (Ridge), and.6% (E), while for the exerimental session on the left of 55.7% (LASSO), 34.8% (Ridge), and 34.7% (E). a variable selection method. If, from one side, smoother estimates of glucose rofiles are obtained with the shrinking roerties of the LASSO, sometimes this can lead to biased estimates (see Figure4(a)). The Ridge model is identified minimizing the RSS cost function subject to a bound on the l norm of the coefficients. This norm does not have the ability of inducing sarseness on the coefficients of the multivariate linear regression model; thus a arsimonious model is not identified and all the redictors are ket in the model. This might cause the estimated glucose rofiles by the Ridge model to be sensitive to occasional sikes or jums in the multi-sensor channels, as can be seen in Figure 4(b), where the Ridge model is the one more sensitive among the three. However, estimated glucose rofiles by the Ridge model show accuracy indicators slightly better than those of LASSO. This might indicate that (a) channels discharged by the l 1 norm because sensitive to occasional sikes or jums actually contain useful glucoserelated information and (b) that retaining information from all the inut channels may hel in comensating noisy

8 8 Alied Mathematics Table1:Modeltesterformancewhen art1 ofthedataset is used for model identification and art for model test. In brackets is the comlexity model arameter chosen by means of cross-validation. Mean and standard deviation (in brackets) over the exerimental sessions for root mean squared error (RMSE), mean absolute difference (MAD), mean absolute relative difference (MARD), error grid analysis (EGA (Clarke)) (A + B (A) C/D/E regions whose sum accounts for 1% of data oints), continuous error grid analysis (CEGA) (A R +B R (A R )C R /D R /E R regions whose sum accounts for 1% of data oints). EGA CEGA RMSE MAD MARD A+B(A) A (mg/dl) (mg/dl) (%) R +B R (A R ) C/D/E C R /D R /E R LASSO (4.) 89. (6.1) (j =15) (7.1) (3.7) ().9/9.6/.1 6.3/.5/ Ridge (58.7) 88 (63) (λ =5) (.8) (19.) (17.7).1/8.9/ 4.9/4.8/.3 E (59.9) 88.6 (65) (λ =.1; α =.4) (4.3) (.5) (17.).1/7.6/ 4.9/4.4/.1 channels thanks to the grouing effect induced by the l norm.thus,itisreasonabletoexectthatacombination of the l 1 and l norms could identify a model sharing both roerties of sarseness and grouing effect. Indeed, as mentioned before, the E model results outerform those of Ridge and LASSO allowing a reasonably accurate estimation of the glucose rofile concentrations also when occasional noise is affecting some multi-sensor channels (see Figure 4), resenting lower MARD values than LASSO and Ridge. Thus, E is the model resenting the best indicators and is only slightly worse than LASSO in accuracy for glucose trends (see CEGA results). Moreover, its clinical accuracy in terms of Clarke error grid, with a ercentage of oints within the A + Bof9.3(seeTable 1), is substantially close to that of minimally invasive devices, sanning from 98.9 to 96.9 [53]. The good results obtained by the E model are likely due to the combination of the l 1 and l norms, giving to this model both the advantages of LASSO and Ridge. Indeed, a limitation of the LASSO is that, if there is a grou of correlated variables, then it tends to select only one variable from the grou and does not care which one is selected, thus lacking the ability of revealing grouing information. On the oosite, the l norm allows all coefficients to enter the model, resulting in more sensitivetonoisychannels.thus,thel 1 norm shrinks channel weights to zero (eliminating multi-sensor channels not useful for redicting glucose), while the l norm encourages a grouing effect (automatically including whole grous into the model once one channel among them is selected). This combination results in indicators outerforming those of the other models and in estimated glucose rofiles with a good trade off between sarseness of the model coefficients and robustness due to the grouing effect (see, e.g., Figure 4(a)). Model test results when data subset art is used for model identification and data subset art 1 for model test arecomarablewiththoseintable 1 (not shown here for the sake of sace). 5. Conclusions In diabetes management, tight monitoring of glycaemic levels by CGM sensors is imortant for avoiding both long and short term comlications related to hyer-and hyoglycaemic excursions. I-CGM devices are otentially more aealing than the minimally invasive sensors based on needle electrodes, but their develoment is challenging for several technological and methodological reasons. In the last years, the idea of embedding sensors of different nature within the same device in order to obtain a better biohysical characterisation of the skin and underlying tissues has gained articular attention to develo I-CGM. In these multisensor aroaches, a model linking the measured multisensor channels to glucose is needed, together with a set of techniques that can be used to identify its arameters. In this work, we investigated the use of regularisation-based methods to identify the linear regression model emloyed in the multi-sensor device for I-CGM roosed in [3]. Results on 45 exerimental sessions indicate that the E model generally outerforms the other models: thanks to the combination of the l 1 and l norms, it allows to take the advantage of the LASSO shrinking many model weights to zero being more robust to ossible occasional jums or sikes occurring on the multi-sensor data and of the Ridge model averaging the contribution of correlated channels allowing a more robust estimation of glucose rofiles. With resect to the revious sensor literature, where PLS reresents the current state of the art (see [34, 54, 55] tomentionjust a few), we showed that E can become very useful with multi-sensor data. While retaining information from a grou of variables (as PLS does), E also automatically selects those channels reresenting the strongest effects, giving more insight into the secific roblem at hand. To conclude, in this work, we showed that further increased oint accuracy can be obtained through suitable techniques for the identification of the multivariate model, reresenting an imortant incremental ste towards the develoment of I-CGM devices. While most of the accuracy indices of Table 1 have not yet reached a fully comarable level with those of current enzyme-based needle sensors [53], glucose trends estimated by the considered I-CGM device exhibit an accetable accuracy (last column of Table 1). This result could be otentially imortant in the treatment of diabetes since the glucose trend can be valid adjunctive information to comlement standard SMBG devices that measure glucose by fingerstick, for examle, heling the diabetic atient in reventing the occurrence of critical events, such as hyoglycaemia, by exloiting the dynamic risk concet recently develoed in [56]. References [1] M. 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