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Glucose Oxidase Biosensor Modeling and Predictors Optimization by Machine Learning Methods^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. ML Models for Regression

- Parametric linear models attempt to find a function defined by:$$\widehat{f}\left(x\right)={\beta}_{0}+\sum _{j=1}^{p}{x}_{j}{\beta}_{j}$$
- Parametric non-linear regression finds a function that is a non-linear combination of the model parameters. For example, for $p=1$:$$\widehat{f}\left(x\right)={\beta}_{0}+{\beta}_{1}{x}^{2}+{\beta}_{2}{x}^{3}+{\beta}_{3}sin\left({\beta}_{4}x\right)$$
- Semi-parametric regression, in which the predictor does not follow a predetermined form or definition; for example, a regression tree.

#### 2.1. Partial Least Squares

#### 2.2. Artificial Neural Networks

#### 2.3. Support Vector Machines

## 3. Experimental Work

#### 3.1. Biosensor Data

#### 3.2. Experimental Settings

#### 3.3. Hardware and Software

^{®}language, Version 2012a, and run on an Ubuntu Linux server, v. 11.10, with an Intel(R) Xeon(R) CPU E5620 @2.40 GHz and eight cores. The SVMR-RBF libraries were embedded into the MATLAB environment using the LIBSVM MATLAB

^{®}Support Vector Machine Toolbox [22].

## 4. Results and Discussion

#### 4.1. Artificial Neural Network Model

#### 4.2. Support Vector Machine RBF Model

## 5. Optimization of Experimental Conditions

- Approximate a third-degree polynomial model by Ordinary Least Squares (OLS) estimation.
- Maximize the polynomial as a function of the input variables.
- Use these values to find the best output or biosensor response.

## 6. Conclusions and Future Work

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Electrochemical biosensor: the analyte is recognized by the bioreceptor followed by detection by the transducer, producing a measurable electric signal.

**Figure 3.**Regression plot for test data: observed target value vs. predicted target values, before and after taking the log the targets.

**Figure 4.**Detailed regression plot for the test data: observed and predicted values rendered by the ANN and the SVMR-RBF models on log data.

**Figure 5.**Observed vs. predicted target values with p-benzoquinone fixed to 0.2 (Columns 1–2) at different glucose values and glucose fixed to four at different p-benzoquinone values (Columns 3–4).

**Figure 7.**Biosensor sensitivity: dependence on the input variables, p-benzoquinone concentration, pH and temperature.

**Table 1.**Input variables describing the Glucose-Oxidase Biosensor (GOB). Each column is the set of available values for each variable.

Glucose | pH | Temperature | p-Benzoquinone |
---|---|---|---|

(mmol/L) | (Celsius) | (mmol/L) | |

4 | 4 | 20 | 1 |

8 | 5 | 37 | 0.8 |

12 | 6 | 47 | 0.4 |

16 | 7 | 57 | 0.2 |

20 | - | - | - |

**Table 2.**Obtained cross-validation Normalized Root Mean Square Error (NRMSE) errors and test ${R}^{2}$ regression coefficients.

Regression Method | Before Log | Log Data | ||
---|---|---|---|---|

NRMSE | ${\mathit{R}}^{2}$ | NRMSE | ${\mathit{R}}^{2}$ | |

PLS | 0.50 | 0.509 | 0.26 | 0.763 |

SVMR-Lin | 1.44 | 0.520 | 0.28 | 0.718 |

SVMR-RBF | 0.03 | 0.999 | 0.01 | 0.999 |

ANN | 0.11 | 0.984 | 0.05 | 0.980 |

**Table 3.**Optimum values for the predictors found by a GA, SA and evaluation of the ANN and SVMR-RBF responses on these values. Biosensor output is in mA.

GA | SA | ANN | SVMR-RBF | |
---|---|---|---|---|

Max Output | 57.86 | 58.01 | 58.10 | 57.96 |

Glucose | 20 | 20 | - | - |

Benzoquinone | 1 | 1 | - | - |

T | 45 | 45 | - | - |

pH | 5 | 5 | - | - |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Gonzalez-Navarro, F.F.; Stilianova-Stoytcheva, M.; Renteria-Gutierrez, L.; Belanche-Muñoz, L.A.; Flores-Rios, B.L.; Ibarra-Esquer, J.E.
Glucose Oxidase Biosensor Modeling and Predictors Optimization by Machine Learning Methods. *Sensors* **2016**, *16*, 1483.
https://doi.org/10.3390/s16111483

**AMA Style**

Gonzalez-Navarro FF, Stilianova-Stoytcheva M, Renteria-Gutierrez L, Belanche-Muñoz LA, Flores-Rios BL, Ibarra-Esquer JE.
Glucose Oxidase Biosensor Modeling and Predictors Optimization by Machine Learning Methods. *Sensors*. 2016; 16(11):1483.
https://doi.org/10.3390/s16111483

**Chicago/Turabian Style**

Gonzalez-Navarro, Felix F., Margarita Stilianova-Stoytcheva, Livier Renteria-Gutierrez, Lluís A. Belanche-Muñoz, Brenda L. Flores-Rios, and Jorge E. Ibarra-Esquer.
2016. "Glucose Oxidase Biosensor Modeling and Predictors Optimization by Machine Learning Methods" *Sensors* 16, no. 11: 1483.
https://doi.org/10.3390/s16111483