1 Introduction
1.1 Background
1.2 Purpose
1.3 Related work
2 Hierarchical Bayesian HMM for event detection
2.1 Data and hidden variables
2.2 Observation model
2.3 Prior distribution for parameter set
2.4 Settings for hyperparameter set
2.4.1 Reparameterization of \(\beta_{f_{l},i}\)
2.4.2 Prior distribution for λ f l and η f l
3 Implementation of event prediction
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Problem: Predict an event e t new in test data, when the feature variable sequence \(f_{1:t}^{\text{new}} :=(f_1^{\text{new}},\ldots, f_t^{\text{new}})\) in the test data and a training data set Y are given.
3.1 Bayesian predictive probability for target event
3.2 Calculation of predictive probability
4 Event detection experiment for soccer games
4.1 Target data sequences
4.1.1 Target soccer games
# | Length [s] | Number of events | Training/testing | ||||
---|---|---|---|---|---|---|---|
KO | CK | FK | TI | GK | |||
1 | 2,390 | 2 | 1 | 14 | 27 | 9 | For training |
2 | 2,389 | 2 | 4 | 22 | 25 | 11 | |
3 | 2,454 | 1 | 3 | 4 | 24 | 20 | |
4 | 2,479 | 4 | 10 | 7 | 15 | 14 | |
5 | 2,460 | 3 | 1 | 10 | 19 | 10 | For testing |
4.1.2 Players’ positions
4.1.3 Feature variables
4.2 Settings
4.3 Experimental results
Event | Method | Difference | |
---|---|---|---|
without hyperparameter learning | with hyperparameter learning | ||
KO | 6.539 × 10−2
| 6.313 × 10−2
| 2.261 × 10−3
|
CK | 8.659 × 10−3
| 7.661 × 10−3
| 9.973 × 10−4
|
FK | 5.121 × 10−1
| 4.884 × 10−1
| 2.374 × 10−2
|
TI | 2.028 × 10−1
| 2.024 × 10−1
| 4.484 × 10−4
|
GK | 1.639 × 10−1
| 1.626 × 10−1
| 1.336 × 10−3
|
4.4 Performance comparison
Index | Method | Reduction (%) | |
---|---|---|---|
without hyperparameter learning | with hyperparameter learning | ||
Cross entropy | 7.891 × 10−1
| 7.866 × 10−1
| 0.32 |
Perplexity | 1.728 × 10−1
| 1.725 × 10−1
| 0.18 |
5 Conclusion
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Model extensions: In many cases of sequential data modeling, model extensions with generalized HMMs, also known as hidden semi-Markov Models, can improve the modeling performance, and they have been successfully applied to several problems (e.g., [27, 28]). Model extensions, including such a generalized HMM-based approach, are expected to be effective for event detection problems.
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Incomplete information: There are cases where some of the data is missing. Such a situation is called incomplete information" and is common in Bayesian HMM learning framework and is solvable. We would like to deal with this as the subject of a future research project.
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Problems with wider scope: In this paper, we focused on the event detection problem based on a small number of professional soccer game data. Currently we are in a process of obtaining a larger data set of soccer game videos of a professional league. Applications of the proposed method, with modifications, to problems other than event detection problems, such as sports strategy/situation analysis, may be interesting.
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Other sports: Although we applied the proposed method only to soccer games in this paper, the proposed method is not limited to soccer games. Applications to other sports can be considered, e.g., rugby football, ice hockey, and basketball, among others.