# Discrimination of Chinese Liquors Based on Electronic Nose and Fuzzy Discriminant Principal Component Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Chinese Liquor Samples

#### 2.2. Electronic-Nose System

_{2}, ZnO

_{2}, or Fe

_{2}O

_{3}, as the substrate, and a precious metal, such as platinum or palladium, is added as a catalyst. The catalyst can shorten the response time of the sensor to the chemical reaction equilibrium and accelerate the response speed of the sensor. In addition, the MOS sensor has a simple structure and long service life. It is also inexpensive to manufacture and easily miniaturized and integrated. In addition, MOS sensors respond quickly and are reproducible in a short period of time [40]. The details of the sensor parameters are described in Table 2. The gas sensor array could detect the flavors of Chinese liquors and outputted the analog signals to the data acquisition card, which converted the analog signals into the digital signals processed by the computer. The response curves of the digital signals were examined using the LabVIEW 2013 software (National Instruments Corporation, Austin, TX, USA). Machine-learning algorithms for data analysis were programmed with MATLAB 2014 (MathWorks, Natick, MA, USA).

#### 2.3. Experimental Steps and Data Processing

#### 2.4. Discriminant Principal Component Analysis and Fuzzy Discriminant Principal Component Analysis

_{B}is the between-class scatter matrix; S

_{W}is the within-class scatter matrix; and Ψ and λ are the eigenvector and the corresponding eigenvalue, respectively. According to the above calculation, we have the maximum eigenvalue λ

_{1}and the corresponding eigenvector Ψ

_{1}, which is the first vector of the optimal discriminant vector set.

_{r}

_{+1}and γ are the r + 1th eigenvector and the corresponding eigenvalue, respectively; and Ψ

_{1}, Ψ

_{2},…, Ψ

_{r}are a set of optimal discriminant vectors. According to the set of optimal discriminant vectors Ψ

_{1}, Ψ

_{2},…, Ψ

_{r}(r ≥ 1), the next optimal discriminant vector Ψ

_{r}

_{+1}can be calculated using Equation (2). The p (p > r) optimal discriminant vectors can be obtained through the above calculation. Then, we have an optimal discriminant vector set {Ψ

_{1}, Ψ

_{2}, …, Ψ

_{p}}.

- c is the number of class; n is the number of training samples;
- $\overline{x}$ the mean of training samples;
- T represents the transpose of the matrix.

- ${S}_{fT}^{-1}$ is the inverse of the fuzzy total class scatter matrix;
- Ψ and λ are the eigenvector and the corresponding eigenvalue, respectively. After obtaining the maximum eigenvalue λ
_{1}and the corresponding eigenvector Ψ_{1}, suppose that Ψ_{1}is the first vector of the fuzzy optimal discriminant vectors.

- Ψ
_{r+}_{1}is the r+1th eigenvector; - β is the corresponding eigenvalue;
- I is the identity matrix;
- Ψ
_{1}, Ψ_{2},…, Ψ_{r}is a set of fuzzy optimal discriminant vectors.

_{r}

_{+1}can be obtained according to the fuzzy optimal discriminant vectors Ψ

_{1}, Ψ

_{2}, …, Ψ

_{r}(r ≥ 1). Through the above calculation, the p (p > r) fuzzy optimal discriminant vectors {Ψ

_{1}, Ψ

_{2},…, Ψ

_{p}} can be achieved.

## 3. Results and Discussion

#### 3.1. Data Preprocessing

#### 3.2. PCA Analysis

#### 3.3. Classification with DPCA

#### 3.4. Classification with PCA and FDPCA

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Three-dimensional distribution of data after principal component analysis (PCA). Maotai (MT), Fenjiu (FJ), Kouzijiao (KZJ), Haizhilan (HZL), Yingjiagongjiu (YJ), Gujinggongjiu (GJ).

**Figure 6.**Three-dimensional distribution of data after discriminant principal component analysis (DPCA).

**Figure 8.**Three-dimensional distribution of data after fuzzy discriminant principal component analysis (FDPCA).

Chinese Liquors | Proof | Raw Material | Place of Origin |
---|---|---|---|

Maotai (MT) | 53%vol | Sorghum, wheat, water | Zunyi City, Guizhou Province |

Gujinggongjiu (GJ) | 53%vol | Water, sorghum, rice, wheat, glutinous rice, corn | Haozhou City, Anhui Province |

Yingjiagongjiu (YJ) | 52%vol | Water, sorghum, rice, corn, wheat | Mianzhu City, Sichuan Province |

Haizhilan (HZL) | 42%vol | Water, sorghum, rice, corn, wheat, barley, peas | Suqian City, Jiangsu Province |

Fenjiu (FJ) | 53%vol | Water, sorghum, barley, peas | Fenyang City, Shaanxi Province |

Kouzijiao (KZJ) | 46%vol | Water, sorghum, corn, rice, wheat, barley, peas | Huaibei City, Anhui Province |

Sensor | Target Gas | Standard Test Conditions | |
---|---|---|---|

Circuit Conditions | Preheat Time | ||

TGS2600 | Air pollution (hydrogen, alcohol, etc.) | VC = 5.0 +/− 0.01 V DC VH = 5.0 +/− 0.05 V DC | 7 days or more |

TGS2602 | Air pollution (VOC, ammonia, hydrogen sulfide, etc.) | VC = 5.0 +/− 0.01 V DC VH = 5.0 +/− 0.05 V DC | 7 days or more |

TGS2610 | Butane, LP gas | VC = 5.0 +/− 0.01 V DC VH = 5.0 +/− 0.05 V DC | 7 days or more |

TGS2620 | Ethanol, organic solvents | VC = 5.0 +/− 0.01 V DC VH = 5.0 +/− 0.05 V DC | 7 days or more |

TGS2611 | Methane, natural gas | VC = 5.0 +/− 0.01 V DC VH = 5.0 +/− 0.05 V DC | 7 days or more |

TGS813 | Methane, propane, butane | VC = 10.0 +/− 0.1 DC/AC VH = 5.0 +/− 0.05 DC/AC RL = 4.0 kΩ +/− 1% | 7 days or more |

TGS822 | Alcohol, organic solvents | VC = 10.0 +/− 0.1 V DC/AC VH = 5.0 +/− 0.05 V DC/AC RL = 10.0 kΩ +/− 1% | 7 days or more |

TGS822TF | Coal gas, which includes H_{2} and CO | VC = 10.0 +/− 0.1 V DC/AC VH = 5.0 +/− 0.05 V DC/AC | 7 days or more |

MQ136 | Hydrogen sulfide benzene vapor | VC = 5.0 +/− 0.1 V DC VH = 5.0 +/− 0.05 V DC/AC | More than 48 h |

MQ3 | Alcohol gas (volatile alcohol) | VC = 5.0 +/− 0.1 V DC/AC VH = 5.0 +/− 0.05 V DC/AC | More than 48 h |

Types of Models | Feature Number | k (-Nearest Neighbor Algorithm) | LOO Cross- Validation Accuracy | 5-Fold Cross-Validation Accuracy | 10-Fold Cross-Validation Accuracy | 20-Fold Cross-Validation Accuracy | 25-Fold Cross-Validation Accuracy | Average Validation Accuracy |
---|---|---|---|---|---|---|---|---|

PCA | 5 | 7 | 88.6% | 90.44% | 90.78% | 89.78% | 90.28% | 89.98% |

DPCA | 5 | 7 | 96% | 94.44% | 95.56% | 95.33% | 96.38% | 95.54% |

FDPCA | 5 | 7 | 98.33% | 98.67% | 98.56% | 98.89% | 99.44% | 98.78% |

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**MDPI and ACS Style**

Wu, X.; Zhu, J.; Wu, B.; Zhao, C.; Sun, J.; Dai, C.
Discrimination of Chinese Liquors Based on Electronic Nose and Fuzzy Discriminant Principal Component Analysis. *Foods* **2019**, *8*, 38.
https://doi.org/10.3390/foods8010038

**AMA Style**

Wu X, Zhu J, Wu B, Zhao C, Sun J, Dai C.
Discrimination of Chinese Liquors Based on Electronic Nose and Fuzzy Discriminant Principal Component Analysis. *Foods*. 2019; 8(1):38.
https://doi.org/10.3390/foods8010038

**Chicago/Turabian Style**

Wu, Xiaohong, Jin Zhu, Bin Wu, Chao Zhao, Jun Sun, and Chunxia Dai.
2019. "Discrimination of Chinese Liquors Based on Electronic Nose and Fuzzy Discriminant Principal Component Analysis" *Foods* 8, no. 1: 38.
https://doi.org/10.3390/foods8010038