Different SVM Kernel experiment

The experiment is performed with UCF Sport Action Dataset. Each feature vector is normalized visual word frequency histogram of local features extracted from supervoxel region in the video. The split consists of training $$3886$$, testing $$2277$$ instances, respectively with $$20k$$ dimension.

• Linear Kernel
- MAP: $$31.91\%$$ ( Runtime* = $$2.5$$ mins )

• Intersection Kernel
- MAP: $$35.65\%$$ ( Runtime* = $$3.3$$ mins )

• Chi-square Kernel
- MAP: $$39.03\%$$ ( Runtime* = $$2.4$$ mins )

• Jenson-Shannon Kernel
- MAP: $$39.50\%$$ ( Runtime* = $$3.0$$ mins )

Runtime* : Test & Training time

UCF vertex 10

1. Kernel Type: Linear

mAP: 31.91 % Time complexity: 2.5 mins

2. Kernel Type: Intersection

mAP: 35.65 % Time complexity: 3.3 mins

3. Kernel Type: Chi-Square

mAP: 39.03 % Time complexity: 2.4 mins

4. Kernel Type: Jenson-Shannon

mAP: 39.50 % Time complexity: 3.0 mins

UCF vertex 10 bg alfa 0.5

1. Kernel Type: Linear

mAP: 56.96 % Time complexity: 22.3 mins

2. Kernel Type: Intersection

mAP: 58.38 % Time complexity: 20.3 mins

3. Kernel Type: Chi-Square

mAP: 63.08 % Time complexity: 14.8 mins

4. Kernel Type: Jenson-Shannon

mAP: 63.53 % Time complexity: 78.7 mins

UCF vertex 10 bg alfa 0.75

1. Kernel Type: Linear

mAP: 65.29 % Time complexity: 15.1 mins

2. Kernel Type: Intersection

mAP: 60.87 % Time complexity: 16.8 mins

3. Kernel Type: Chi-Square

mAP: 65.96 % Time complexity: 11.2 mins

$$mAP$$ performance with different types of kernel functions vs background histogram weight values, $$\alpha_{bg}$$

 Kernel Type $$\alpha_{bg} = 0$$ $$\alpha_{bg} = 0.5$$ $$\alpha_{bg} = 0.75$$ $$Linear$$ 31.91 % 56.69 % 65.29 % $$Intersection$$ 35.65 % 58.98 % 60.89 % $$Chi-Square$$ 39.03 % 63.08 % 65.96 % $$Jenson-Shannon$$ 39.50 % 63.53 %

The runtime evaluation (in mins) with different types of kernel functions vs background histogram weight values, $$\alpha_{bg}$$

 Kernel Type $$\alpha_{bg} = 0$$ $$\alpha_{bg} = 0.5$$ $$\alpha_{bg} = 0.75$$ $$Linear$$ 2.5 22.3 15.1 $$Intersection$$ 3.3 20.3 16.8 $$Chi-Square$$ 2.4 14.8 11.2 $$Jenson-Shannon$$ 3.0 78.7