### Scoring with Top-K Accuracy

Top-K Accuracy can be used as a scoring function by measuring whether the correct scene label appears in the top **K** predictions for each video clip. This allows evaluation of both strict (Top-1) and more tolerant (Top-5, Top-10) classification performance.

For a given value of $ K $, the **Top-K Accuracy score** is calculated as:

$$
\text{Top-}K = \frac{1}{N} \sum_{i=1}^{N} \mathbb{1}\left[y_i \in \hat{Y}_i^{(K)}\right]
$$

Where:

- $ N $: total number of video clips in the test set  
- $ y_i $: ground-truth label for the $ i $-th clip  
- $ \hat{Y}_i^{(K)} $: set of top $ K $ predicted labels for the $ i $-th clip  
- $ \mathbb{1}[\cdot] $: indicator binary function that returns 1 if the condition is true, 0 otherwise