# Classification of Knee Joint Vibration Signals Using Bivariate Feature Distribution Estimation and Maximal Posterior Probability Decision Criterion

^{*}

## Abstract

**:**

## 1. Introduction

## 2. VAG Signal Acquisition and Feature Description

#### 2.1. Dataset

#### 2.2. Features Description

## 3. Bivariate Probability Distribution Modeling

## 4. Signal Classification

#### 4.1. Fisher’s Linear Discriminant Analysis

#### 4.2. Maximal Posterior Probability Decision Criterion

#### 4.3. Support Vector Machine

## 5. Results

**Figure 1.**Distributions of the bivariate features for the normal and abnormal knee joint vibration signals. The distribution of the normal signals is shown with the cold color map (blue representing the highest density), whereas the distribution of the abnormal signals is illustrated with the hot color map (red representing the highest density).

**Figure 2.**Decision boundaries provided by the Fisher’s linear discriminant analysis (FLDA), the support vector machine (SVM) with polynomial kernels, and the maximum posteriori probability (MPP) estimation method.

**Table 1.**The confusion matrix and area under the receiver operating characteristic (ROC) curve of the Fisher’s linear discriminant analysis (FLDA). ${A}_{z}$: area under ROC curve. SE: standard error.

actual group | ||||
---|---|---|---|---|

Total number | positive | negative | ||

28 | 47 | |||

classified group | positive | 24 | 19 | 5 |

negative | 51 | 9 | 42 | |

sensitivity | $19/28=0.6786$ | |||

specificity | $42/47=0.8936$ | |||

${A}_{z}$± SE | $0.8564\pm 0.0447$ |

**Table 2.**The confusion matrix and area under the receiver operating characteristic (ROC) curve of the support vector machine (SVM) with polynomial kernels. ${A}_{z}$: area under ROC curve. SE: standard error.

actual group | ||||
---|---|---|---|---|

Total number | positive | negative | ||

28 | 47 | |||

classified group | positive | 25 | 18 | 7 |

negative | 50 | 7 | 43 | |

sensitivity | $18/28=0.6429$ | |||

specificity | $43/47=0.9149$ | |||

${A}_{z}$± SE | $0.8533\pm 0.0467$ |

**Table 3.**The confusion matrix and area under the receiver operating characteristic (ROC) curve of the maximal posterior probability (MPP) decision. ${A}_{z}$: area under ROC curve. SE: standard error.

actual group | ||||
---|---|---|---|---|

Total number | positive | negative | ||

28 | 47 | |||

classified group | positive | 27 | 21 | 6 |

negative | 48 | 4 | 44 | |

sensitivity | $21/28=0.75$ | |||

specificity | $44/47=0.9362$ | |||

${A}_{z}$± SE | $0.9096\pm 0.0332$ |

**Figure 3.**Segments of the knee joint vibration signals associated with (

**a**) Grade I–II chondromalacia and (

**b**) lateral meniscus tear.

## 6. Discussion and Conclusions

## Acknowledgment

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**MDPI and ACS Style**

Wu, Y.; Cai, S.; Yang, S.; Zheng, F.; Xiang, N.
Classification of Knee Joint Vibration Signals Using Bivariate Feature Distribution Estimation and Maximal Posterior Probability Decision Criterion. *Entropy* **2013**, *15*, 1375-1387.
https://doi.org/10.3390/e15041375

**AMA Style**

Wu Y, Cai S, Yang S, Zheng F, Xiang N.
Classification of Knee Joint Vibration Signals Using Bivariate Feature Distribution Estimation and Maximal Posterior Probability Decision Criterion. *Entropy*. 2013; 15(4):1375-1387.
https://doi.org/10.3390/e15041375

**Chicago/Turabian Style**

Wu, Yunfeng, Suxian Cai, Shanshan Yang, Fang Zheng, and Ning Xiang.
2013. "Classification of Knee Joint Vibration Signals Using Bivariate Feature Distribution Estimation and Maximal Posterior Probability Decision Criterion" *Entropy* 15, no. 4: 1375-1387.
https://doi.org/10.3390/e15041375