## Evaluation Metric  
Submissions will be evaluated using a combination of the \\(\text{F}_\beta\\)-score and Euclidean distance. The goal is to determine whether a tomogram contains a motor and, if it does, to accurately predict its location. 

Let the ground truth be \\(y\\) and the predicted location be \\(\bar{y}\\). The Euclidean distance \\(\| y - \bar{y} \|_2\\) determines classification:  
     - **True Positive (TP):** If \\(\| y - \bar{y} \|_2 \le \tau\\), the prediction is within threshold. 
     - **False Negative (FN):** If \\(\| y - \bar{y} \|_2 > \tau\\), the prediction is outside of threshold.  
where \\(\ \tau = 1000\\) Angstroms.

### \\(\text{F}\_\beta\\)-score  
The \\(\text{F}\_\beta\\)-score balances precision and recall, placing greater weight on recall when \\(\beta > 1\\) and on precision when \\(\beta < 1\\) (in our case we use **\\(\beta = 2\\)**, thus we are weighting recall more than precision). It is defined as:  

\\(\text{F}\_\beta = (1 + \beta^2) \cdot \frac{\text{precision} \cdot \text{recall} }{(\beta^2 \cdot \text{precision}) + \text{recall}} = (1 + \beta^2) \cdot \frac{\text{TP}}{(1 + \beta^2) \cdot \text{TP} + \beta^2 \cdot \text{FN} + \text{FP}}\\)

This metric ensures that both the presence and location accuracy of predicted motors are considered in the final score. 

[Link to metric notebook](https://www.kaggle.com/code/metric/byu-biophysics-91249)

## Submission Format  
Your submission should be a CSV file with one row per tomogram found in the test set.  **IMPORTANT:** If you predict that no motor exists, set `Motor axis 0`, `Motor axis 1`, `Motor axis 2` to `-1`

    tomo_id,Motor axis 0,Motor axis 1,Motor axis 2
    tomo_003acc,501.1,22.8,429.8
    tomo_00e047,-1,-1,-1
    tomo_01a877,395.2,335.4,798.0
    etc.