Human Activity Recognition with an HMM-Based Generative Model
Abstract
:1. Introduction
2. Hidden Markov Model
- Transition probability, which is the probability of altering the state at time t to the same state or another state at the time step . The sum of all transition probabilities at the current state is equal to 1.
- Emission probability, which indicates the probability of an observation generated from a particular state.
- Initial probability , in which HMM starts at time step of 0. The sum of all probabilities is equal to 1.
- A sequence of observations: generated by hidden states . K indicates the number of states.
- Transition matrix: .
- Emission matrix: for . M indicates the number of mixture components associated with the state j.
- : Initial probability to start the sequence from state j.
3. Parameter Estimation with Variational Inference
Algorithm 1: Variational learning of the SD-HMM model. |
|
4. Experimental Results
4.1. Opportunity Dataset
- Oversampling: Both datasets have 108 features; as illustrated in Table 1, there are considerable inequalities in the distribution of instances per cluster. As shown in the first run of the test, the percentages of four activities are 59.7%, 17.4%, 19.9%, and 3% for standing, walking, lying, and sitting, respectively. These shares for the second run are 41%, 23.8%, 5.1%, and 30%. As this challenge results in frequency bias, the model may be affected by the dominant class and learn from clusters, including more observations. We tackled this challenge with oversampling using a method called the synthetic minority over-sampling technique (SMOTE). In this method, new data points were generated by interpolating between observations in the original dataset. Thus, we obtain a balanced dataset. After this step, we had equal observations in 4 clusters with 22,380 and 10,379 in the first and second runs, respectively.
- Missing values: In both datasets, we have several missing values, which are shown in Table 2 for the first and second runs, respectively. This is a typical issue, especially when we work on real datasets. We replaced missing values with the median of each feature to minimize the effects of the outliers. As we mentioned, we have 108 features.
4.2. UCI Dataset
5. Results and Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Standing | Walking | Lying | Sitting | |
---|---|---|---|---|
First run | 60% | 20% | 17% | 3% |
Second run | 41% | 24% | 5% | 30% |
Feature | Numbers of Nan in Each Feature |
---|---|
1, 2, 3 | 454 |
4, 5, 6, 10, 11, 12, 28, 29, 30 | 20 |
13, 14, 15 | 92 |
19, 20, 21 | 1681 |
22, 23, 24 | 311 |
34, 35, 36 | 37,507 |
Method | Accuracy | Precision | Recall | F1-Score |
---|---|---|---|---|
SD-HMM | 89.33 | 86.54 | 85.51 | 86.02 |
D-HMM | 85.96 | 86.28 | 85.18 | 85.72 |
GMM-HMM | 86.08 | 83.54 | 82.37 | 82.95 |
Method | Accuracy | Precision | Recall | F1-Score |
---|---|---|---|---|
SD-HMM | 87.12 | 87.28 | 85.44 | 86.35 |
D-HMM | 85.96 | 86.28 | 85.18 | 85.72 |
GMM-HMM | 85.14 | 82.24 | 83.75 | 82.99 |
Method | Accuracy | Precision | Recall | F1-Score |
---|---|---|---|---|
SD-HMM | 86.17 | 85.05 | 86.83 | 85.93 |
D-HMM | 85.22 | 84.38 | 85.57 | 84.97 |
GMM-HMM | 84.31 | 82.47 | 82.33 | 82.39 |
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Manouchehri, N.; Bouguila, N. Human Activity Recognition with an HMM-Based Generative Model. Sensors 2023, 23, 1390. https://doi.org/10.3390/s23031390
Manouchehri N, Bouguila N. Human Activity Recognition with an HMM-Based Generative Model. Sensors. 2023; 23(3):1390. https://doi.org/10.3390/s23031390
Chicago/Turabian StyleManouchehri, Narges, and Nizar Bouguila. 2023. "Human Activity Recognition with an HMM-Based Generative Model" Sensors 23, no. 3: 1390. https://doi.org/10.3390/s23031390
APA StyleManouchehri, N., & Bouguila, N. (2023). Human Activity Recognition with an HMM-Based Generative Model. Sensors, 23(3), 1390. https://doi.org/10.3390/s23031390