# Identification of Green, Oolong and Black Teas in China via Wavelet Packet Entropy and Fuzzy Support Vector Machine

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## Abstract

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## 1. Introduction

Category | Characteristics |
---|---|

White Tea | wilted and unoxidized |

Yellow tea | unwilted and unoxidized, with sweltering |

Green tea | unwilted and unoxidized |

Oolong tea | wilted, bruised, and partially oxidized |

Black tea | wilted and fully oxidized |

Post-fermented tea | fermented green tea |

_{l}, Z

_{n}, C

_{a}, M

_{n}, B

_{a}, M

_{g}, C

_{u}, and K) as chemical descriptors to differentiate three tea classes. They proved the back propagation-artificial neural network (BP-ANN) achieved an almost 95% recall rate. Zhao et al. [11] utilized near-infrared (NIR) spectroscopy for fast identification of green, oolong, and black tea. They extracted five principal components (PCs), which were sent to SVM classifiers. For all categories, their identification accuracies were no less than 90%. Chen et al. [12] proposed using NIR reflectance spectroscopy to identify three types of tea. They used RBF-SVM as the classifier, and found the best identification for green, black, and oolong teas were 90%, 100%, and 95%, respectively. Wu et al. [13] put forward a new nondestructive method based on multispectral digital image texture feature. The sample images were obtained via a red waveband, NIR waveband and green waveband multispectral digital imager. They combined DCT and LS-SVM as the classifier. Chen et al. [14] developed a portable electronic nose, by an odor imaging sensor array, with the aim of tea classification of three different fermentation degrees. Liu et al. [15] used electronic tongue technique to analyze 43 samples of green and black tea. A class of metallic oxide-modified nickel foam electrodes (SnO

_{2}, ZnO, TiO

_{2}, Bi

_{2}O

_{3}) was compared. The signals obtained by cyclic voltammetry underwent multivariate data analysis that consisted of principal component analysis (PCA) and SVM.

## 2. Proposed Method

#### 2.1. Tea Preparation

Category | Number | Origins |
---|---|---|

Green tea | 100 | Henan; Guizhou; Jiangxi; Anhui; Zhejiang; Jiangsu |

Black tea | 100 | Yunan; Hunan; Hubei; Fujian |

Oolong tea | 100 | Fujian; Guangdong |

#### 2.2. Image Acquiring

#### 2.3. Feature Processing

#### 2.3.1. Color Histogram

#### 2.3.2. Discrete Wavelet Packet Transform

**Figure 3.**Diagram of two-level one-dimensional wavelet packet transform. Here, a and b represent the low-pass and high-pass filters, respectively. L and H represent the low-frequency and high-frequency subbands, respectively.

#### 2.3.3. Shannon Entropy

_{n}the probability of n-th greylevel, and G the total number of greylevels [33].

Pseudocode of WPE | |
---|---|

Step A | Input Image. Read the 2D Image. |

Step B | 1D-DWPT. Pass the image through low-pass and high-pass filters and perform downsampling along x-axis and y-axis in sequence. Obtain four subbands. |

Step C | 2D-DWPT. For the four subbands obtained in 1D-DWPT, we continually implement 1D-DWPT to each subband, and finally obtained 16 subbands. |

Step D | WPE. Extract Shannon entropy from the 16 subbands obtained by 2D-DWPT, and output the final feature vector of 16 elements. |

#### 2.3.4. Principal Component Analysis

#### 2.4. Classification

#### 2.4.1. Support Vector Machine

_{n}denotes a training point that is a z-dimensional vector, y

_{n}is the realistic class of p

_{n}taking the value of either +1 or −1, which corresponds to the class 2 or 1, respectively [42]. The hyperplane with maximum-margin that separates the two classes is the desired SVM. Considering that any hyperplane is in the form of

**w**represents the weights and b the bias. We need to select the optimal values of

**w**and b to maximize the distance between the two parallel hyperplanes to the full degree, while it can yet separate the data of the two classes.

**ξ**= (ξ

_{1}, …, ξ

_{n}, …, ξ

_{N}) are added to measure the misclassification degree of sample p

_{n}. Hence, the mathematical formula of the optimal SVM can be deduced by solving:

_{n}disappear, with only the constant L be an additional constraint on the Lagrange multipliers.

#### 2.4.2. Fuzzy SVM

_{n}denotes the altitude of the corresponding training point towards one class and (1 − s

_{n}) is the attitude of meaning less. The optimal hyperplane problem of FSVM is defined as:

**s**= (s

_{1}, s

_{2}, …, s

_{N}) represents the membership vector of FMF. A smaller s

_{n}decreases the influence of the parameter ξ

_{n}, such that the corresponding sample p

_{n}is regarded less substantial. In a similar way, the Lagrangian is constructed as:

#### 2.4.3. Fuzzy Membership Function

_{+}and p

_{−}, respectively. Then, we can get the radius of class +1 and class −1 as

_{+}and r

_{−}represents the radius of class +1 and −1, respectively. The fuzzy membership s

_{n}is defined as a function of both the radius and the mean of both classes [43]

_{n}> 0.

#### 2.4.4. Multiclass Technique

#### 2.5. Statistical Setting

## 3. Results and Discussions

#### 3.1. Feature Extraction

Green | Oolong | Black | |
---|---|---|---|

Sample Image | |||

Color Histogram | |||

Discrete Wavelet Transform (DWT) | |||

Discrete Wavelet Packet Transform (DWPT) |

#### 3.2. PCA Result

# of PC | 1 | 2 | 3 | 4 | 5 |

Variance Explained | 93.91% | 99.08% | 99.49% | 99.78% | 99.90% |

#### 3.3. Classification Performance Comparison

Existing Approaches | |||||||

# of Original Features | # of Reduced Features | Classifier | Green Tea | Oolong Tea | Black Tea | Overall | Rank |

8 metal features | 8 | BP-ANN [10] | N/A | N/A | N/A | 95% | 6 |

3735 spectrum features | 5 | SVM [12] | 90% | 100% | 95% | 95% | 6 |

12 color + 12 texture features | 11 | LDA [17] | 96.7% | 92.3% | 98.5% | 95.8% | 5 |

2 color + 6 shape features | 8 | GNN [18] | 95.8% | 94.4% | 97.9% | 96.0% | 4 |

64 CH + 7 texture + 8 shape features | 14 | FSCABC-FNN [21] | 98.1% | 97.7% | 96.4% | 97.4% | 2 |

Proposed Approaches | |||||||

64 CH + 16 WPE features | 5 | SVM + WTA | 95.7% | 98.1% | 97.9% | 97.23% | 3 |

64 CH + 16 WPE features | 5 | FSVM + WTA | 96.2% | 98.8% | 98.3% | 97.77% | 1 |

#### 3.4. Optimal Wavelet

Wavelet | Recall Rate |
---|---|

db1 | 96.37% |

db2 | 96.60% |

db3 | 96.57% |

bior2.2 | 96.53% |

bior3.3 | 97.10% |

bior4.4 | 97.77% |

**Figure 6.**Decomposition functions for bior4.4, (

**a**) Scaling Function, (

**b**) Wavelet Function, (

**c**) low-pass filter (LPF), (

**d**) high-pass filter (HPF).

**Figure 7.**Reconstruction functions for bior4.4, (

**a**) Scaling Function, (

**b**) Wavelet Function, (

**c**), low-pass filter (LPF), (

**d**) high-pass filter (HPF).

#### 3.5. Further Discussion of Methods

## 4. Conclusion

## Acknowledgment

## Author Contributions

## Abbreviation

(A)(BP)(F)NN | (Artificial) (Back-propagation) (Feed-forward) neural network |

(D)W(P)T | (Discrete) wavelet (packet) transform |

(FSC)ABC | (Fitness-scaled Chaotic) Artificial bee colony |

(F)SVM | (Fuzzy) support vector machine |

(L)(H)PF | (Low-) (High-) Pass Filter |

CCD | charge-coupled device |

CH | Color Histogram |

FMF | Fuzzy membership function |

GNN | Genetic neural-network |

LDA | Linear discriminant analysis |

NIR | Near-infrared |

SCV | Stratified cross validation |

SE | Shannon entropy |

WPE | Wavelet packet entropy |

WTA | Winner-Takes-All |

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Wang, S.; Yang, X.; Zhang, Y.; Phillips, P.; Yang, J.; Yuan, T.-F.
Identification of Green, Oolong and Black Teas in China via Wavelet Packet Entropy and Fuzzy Support Vector Machine. *Entropy* **2015**, *17*, 6663-6682.
https://doi.org/10.3390/e17106663

**AMA Style**

Wang S, Yang X, Zhang Y, Phillips P, Yang J, Yuan T-F.
Identification of Green, Oolong and Black Teas in China via Wavelet Packet Entropy and Fuzzy Support Vector Machine. *Entropy*. 2015; 17(10):6663-6682.
https://doi.org/10.3390/e17106663

**Chicago/Turabian Style**

Wang, Shuihua, Xiaojun Yang, Yudong Zhang, Preetha Phillips, Jianfei Yang, and Ti-Fei Yuan.
2015. "Identification of Green, Oolong and Black Teas in China via Wavelet Packet Entropy and Fuzzy Support Vector Machine" *Entropy* 17, no. 10: 6663-6682.
https://doi.org/10.3390/e17106663