# Basketball Action Data Processing Method Based on Mode Symmetric Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Algorithm Definitions

#### 2.1. Basketball Action Data Detection Algorithm Based on Symmetric Difference and Background Reduction

#### 2.1.1. Calculation of Symmetric Difference

#### 2.1.2. Background Subtraction Calculation

#### 2.1.3. Basketball Action Detection

#### 2.2. Pole Symmetric Mode Decomposition (ESMD) and Basketball Action Modal Data Generation

- The maximum and minimum values of the original basketball action data are separated because in the ESMD algorithm, adjacent equal extremes are treated as one point;
- The ESMD method proposes decomposition methods for optimal data screening times and determines the suspension criteria;
- The ESMD method can obtain a better adaptive global mean (AGM) curve and optimize the AGM curve by least squares to optimize the number of data screenings.

- Find the midpoint of all adjacent extreme points of the original basketball action data $x(t)$ [21], and add the boundary midpoints of the left and right sides;
- Using the midpoints of the above extreme points, construct p difference curves ${L}_{1},\dots {L}_{p}(p\ge 1)$ and calculate the mean curves ${L}^{*}=({L}_{1}+\dots +{L}_{p})/p$;
- Subtract the mean envelope from the original basketball action sequence $x(t)$ to obtain a new sequence $h(t)$, as shown in Equation (5):$$h(t)=x(t)-{L}^{*}$$
- Verify if the new sequence $h(t)$ satisfies the following two conditions: $\left|{L}^{*}\right|\le \epsilon $ (allowed to be an error); the number of data screenings reaches the expected maximum $K$, and if the above two conditions are met, it is treated as a mode, otherwise, $h(t)$ is set as the original data to iterate the above three steps until the above two conditions are met;
- With $x(t)-{\displaystyle \sum {M}_{i}}$, ${M}_{i}$ as the maximum fixed number, repeat the above four steps until the last residual amount has no more than a fixed number of extremes;
- Change the value of the expected maximum value $K$ of the number of screenings, repeat the above five steps, calculate the variance ${\sigma}^{2}$ of $x(t)-R$, and plot the relationship between $\sigma /{\sigma}_{0}$ and $K$, where ${\sigma}_{0}$ is the standard deviation of $x(t)$;
- According to the minimum value of $\sigma /{\sigma}_{0}$, find $\sigma /{\sigma}_{0}$ and then repeat the previous six steps through ${K}_{0}$ to output the entire mode. Then, the last residual $R$ is an optimized AGM curve.

#### 2.3. Basketball Action Mode Data Processing

#### 2.3.1. Cleaning and Integration of Basketball Action Mode Data

#### 2.3.2. Basketball Action Mode Data Integration and Data Reduction

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**The accuracy rate (%) of the three methods to process different types of basketball movement data.

Round | Technical Action in Basketball Court |
---|---|

5 | Rebound, block, dribble, dribble, pass, block, 2 points |

20 | Block, dribble, dribble, assists, block, 3 goals |

100 | Fast break, long pass, technical foul, steal, free throw |

Round | Technical Action in Basketball Court |
---|---|

5 | Backboard, Removal, Dribble, Pass the Ball, Removal, 2 Points In |

20 | Removal, Dribble, Dribble, Assists, Removal, 3 Points In |

100 | Fast Break, Long Pass, Technical Foul, Steals, Penalty Shot |

Data Volume/Piece | The Basketball Movement | ||||
---|---|---|---|---|---|

In Situ Shooting | Three-Step Layup | The Ball Breakthrough | Personal Defense | Rob Basket Ball | |

20 | 0.42 | 0.76 | 0.55 | 0.54 | 0.78 |

40 | 0.43 | 0.85 | 0.70 | 0.72 | 0.56 |

60 | 0.41 | 0.63 | 0.64 | 0.66 | 0.65 |

80 | 0.43 | 0.87 | 0.88 | 0.45 | 0.64 |

100 | 0.54 | 0.76 | 0.79 | 0.54 | 0.86 |

120 | 0.80 | 0.65 | 0.50 | 0.86 | 0.40 |

140 | 0.73 | 0.58 | 0.84 | 0.75 | 0.87 |

160 | 0.61 | 0.86 | 0.73 | 0.61 | 0.46 |

180 | 0.75 | 0.64 | 0.85 | 0.83 | 0.84 |

200 | 0.53 | 0.84 | 0.64 | 0.97 | 0.57 |

220 | 0.84 | 0.76 | 0.44 | 0.45 | 0.76 |

240 | 0.45 | 0.88 | 0.56 | 0.51 | 0.84 |

260 | 0.64 | 0.43 | 0.85 | 0.66 | 0.68 |

280 | 0.75 | 0.54 | 0.75 | 0.89 | 0.67 |

300 | 0.85 | 0.67 | 0.65 | 0.70 | 0.56 |

Average | 0.61 | 0.71 | 0.69 | 0.68 | 0.68 |

Data Volume/Piece | The Basketball Movement | ||||
---|---|---|---|---|---|

In Situ Shooting | Three-Step Layup | The Ball Breakthrough | Personal Defense | Rob Basket Ball | |

20 | 2.12 | 3.21 | 4.25 | 2.27 | 4.14 |

40 | 2.29 | 2.32 | 4.45 | 3.22 | 5.25 |

60 | 2.51 | 1.68 | 4.36 | 1.25 | 2.35 |

80 | 2.24 | 2.57 | 4.27 | 2.55 | 3.25 |

100 | 2.24 | 2.87 | 4.84 | 5.54 | 4.27 |

120 | 2.28 | 1.67 | 5.57 | 4.26 | 5.34 |

140 | 2.53 | 3.57 | 5.35 | 3.65 | 2.29 |

160 | 2.21 | 4.46 | 4.54 | 5.21 | 3.46 |

180 | 2.45 | 2.28 | 5.65 | 2.23 | 2.74 |

200 | 2.53 | 3.57 | 4.24 | 3.28 | 4.67 |

220 | 2.24 | 2.64 | 3.74 | 5.28 | 2.36 |

240 | 2.25 | 2.55 | 5.14 | 4.28 | 2.54 |

260 | 2.64 | 3.58 | 5.12 | 5.26 | 1.98 |

280 | 2.75 | 3.35 | 4.54 | 2.57 | 3.77 |

300 | 2.24 | 2.24 | 3.59 | 3.25 | 2.56 |

Average | 2.37 | 2.84 | 4.64 | 3.61 | 3.40 |

Data Volume/Piece | The Basketball Movement | ||||
---|---|---|---|---|---|

In Situ Shooting | Three-Step Layup | The Ball Breakthrough | Personal Defense | Rob Basket Ball | |

20 | 0.05 | 0.03 | 0.08 | 0.06 | 0.12 |

40 | 0.06 | 0.03 | 0.10 | 0.06 | 0.13 |

60 | 0.08 | 0.02 | 0.09 | 0.06 | 0.13 |

80 | 0.09 | 0.03 | 0.11 | 0.06 | 0.14 |

100 | 0.07 | 0.04 | 0.11 | 0.08 | 0.15 |

120 | 0.07 | 0.05 | 0.12 | 0.08 | 0.16 |

140 | 0.08 | 0.06 | 0.12 | 0.08 | 0.15 |

160 | 0.08 | 0.06 | 0.13 | 0.09 | 0.14 |

180 | 0.09 | 0.07 | 0.13 | 0.10 | 0.16 |

200 | 0.10 | 0.07 | 0.14 | 0.11 | 0.13 |

220 | 0.12 | 0.07 | 0.13 | 0.13 | 0.15 |

240 | 0.13 | 0.08 | 0.12 | 0.14 | 0.14 |

260 | 0.12 | 0.08 | 0.15 | 0.13 | 0.17 |

280 | 0.11 | 0.09 | 0.14 | 0.14 | 0.16 |

300 | 0.09 | 0.09 | 0.13 | 0.15 | 0.15 |

Average | 0.09 | 0.06 | 0.12 | 0.10 | 0.15 |

The Serial Number | In Situ Shooting | Three-Step Layup | The Ball Breakthrough | Personal Defense | Rob Basket Ball | |||||
---|---|---|---|---|---|---|---|---|---|---|

Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | |

1 | 11 | 0.32 | 25 | 0.48 | 32 | 0.43 | 35 | 0.37 | 14 | 0.31 |

2 | 15 | 0.44 | 26 | 0.50 | 24 | 0.32 | 24 | 0.25 | 16 | 0.36 |

3 | 16 | 0.47 | 18 | 0.35 | 35 | 0.47 | 32 | 0.34 | 20 | 0.44 |

4 | 13 | 0.38 | 24 | 0.46 | 40 | 0.54 | 45 | 0.47 | 24 | 0.53 |

5 | 17 | 0.50 | 26 | 0.50 | 26 | 0.35 | 42 | 0.44 | 11 | 0.24 |

6 | 22 | 0.65 | 31 | 0.60 | 35 | 0.47 | 40 | 0.42 | 11 | 0.24 |

7 | 20 | 0.59 | 35 | 0.67 | 30 | 0.41 | 26 | 0.27 | 13 | 0.29 |

8 | 20 | 0.59 | 27 | 0.52 | 26 | 0.35 | 36 | 0.38 | 14 | 0.31 |

9 | 19 | 0.56 | 29 | 0.56 | 24 | 0.32 | 27 | 0.28 | 15 | 0.33 |

10 | 16 | 0.47 | 30 | 0.58 | 20 | 0.27 | 30 | 0.32 | 18 | 0.40 |

average | 17 | 0.49 | 27 | 0.52 | 29 | 0.39 | 34 | 0.35 | 16 | 0.34 |

The Serial Number | In Situ Shooting | Three Steps Layup | The Ball Breakthrough | Personal Defense | Rob Basket Ball | |||||
---|---|---|---|---|---|---|---|---|---|---|

Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | |

1 | 20 | 0.59 | 30 | 0.58 | 42 | 0.57 | 63 | 0.66 | 26 | 0.58 |

2 | 19 | 0.56 | 34 | 0.65 | 40 | 0.54 | 65 | 0.68 | 25 | 0.56 |

3 | 21 | 0.62 | 33 | 0.63 | 43 | 0.58 | 63 | 0.66 | 24 | 0.53 |

4 | 23 | 0.68 | 32 | 0.62 | 45 | 0.61 | 64 | 0.67 | 26 | 0.58 |

5 | 21 | 0.62 | 35 | 0.67 | 41 | 0.55 | 65 | 0.68 | 26 | 0.58 |

6 | 20 | 0.59 | 36 | 0.69 | 46 | 0.62 | 66 | 0.69 | 25 | 0.56 |

7 | 24 | 0.71 | 33 | 0.63 | 42 | 0.57 | 62 | 0.65 | 28 | 0.62 |

8 | 25 | 0.74 | 35 | 0.67 | 43 | 0.58 | 64 | 0.67 | 27 | 0.60 |

9 | 21 | 0.62 | 34 | 0.65 | 41 | 0.55 | 63 | 0.66 | 26 | 0.58 |

10 | 26 | 0.76 | 32 | 0.62 | 45 | 0.61 | 64 | 0.67 | 26 | 0.58 |

Average | 22 | 0.65 | 33 | 0.64 | 43 | 0.58 | 64 | 0.67 | 26 | 0.58 |

The Serial Number | In Situ Shooting | Three-Step Layup | The Ball Breakthrough | Personal Defense | Rob Basket Ball | |||||
---|---|---|---|---|---|---|---|---|---|---|

Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | Times | Ratio/% | |

1 | 30 | 0.88 | 50 | 0.96 | 74 | 1.00 | 95 | 1.00 | 44 | 0.98 |

2 | 31 | 0.91 | 52 | 1.00 | 73 | 0.99 | 94 | 0.99 | 44 | 0.98 |

3 | 32 | 0.94 | 51 | 0.98 | 74 | 1.00 | 94 | 0.99 | 44 | 0.98 |

4 | 34 | 1.00 | 50 | 0.96 | 74 | 1.00 | 94 | 0.99 | 44 | 0.98 |

5 | 34 | 1.00 | 52 | 1.00 | 71 | 0.96 | 94 | 0.99 | 43 | 0.96 |

6 | 34 | 1.00 | 53 | 1.02 | 72 | 0.97 | 95 | 1.00 | 41 | 0.91 |

7 | 33 | 0.97 | 52 | 1.00 | 73 | 0.99 | 93 | 0.98 | 42 | 0.93 |

8 | 33 | 0.97 | 53 | 1.02 | 74 | 1.00 | 93 | 0.98 | 42 | 0.93 |

9 | 33 | 0.97 | 51 | 0.98 | 73 | 0.99 | 92 | 0.97 | 43 | 0.96 |

10 | 31 | 0.91 | 53 | 1.02 | 72 | 0.97 | 94 | 0.99 | 43 | 0.96 |

Average | 33 | 0.96 | 52 | 0.99 | 73 | 0.99 | 94 | 0.99 | 43 | 0.96 |

Different Action | Average Error | T Test Value | Average Error | T Test Value | ||
---|---|---|---|---|---|---|

In This Paper Methods | Based on Data Mining Method | In This Paper Methods | Based on Big Data Processing Platform Method | |||

In situ shooting | 0.04 | 0.07 | −2.132~2.132 | 0.03 | 0.06 | −1.372~1.372 |

Three-step layup | 0.03 | 0.08 | −2.356~2.356 | 0.02 | 0.07 | −2.112~2.112 |

The ball break through | 0.02 | 0.09 | −2.149~2.149 | 0.02 | 0.08 | −1.932~1.932 |

Personal defense | 0.02 | 0.07 | −1.132~1.132 | 0.04 | 0.05 | −0.132~0.132 |

Rob basket ball | 0.24 | 0.09 | −1.956~1.956 | 0.04 | 0.06 | −1.031~1.031 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, F.; Jiang, Y.
Basketball Action Data Processing Method Based on Mode Symmetric Algorithm. *Symmetry* **2019**, *11*, 560.
https://doi.org/10.3390/sym11040560

**AMA Style**

Zhang F, Jiang Y.
Basketball Action Data Processing Method Based on Mode Symmetric Algorithm. *Symmetry*. 2019; 11(4):560.
https://doi.org/10.3390/sym11040560

**Chicago/Turabian Style**

Zhang, Fei, and Yi Jiang.
2019. "Basketball Action Data Processing Method Based on Mode Symmetric Algorithm" *Symmetry* 11, no. 4: 560.
https://doi.org/10.3390/sym11040560