A bank trains a linear support vector machine to sort loan applications into approve and deny, using two features: , the applicant's yearly income in units of $10,000, and , the length of their credit history in years.
The trained model gives every applicant a score
The decision boundary is the line . The two edges of the "street" around it are the lines on the approve side and on the deny side, and the support vectors sit exactly on those edges. The weight vector points straight across the street, at right angles to all three lines. For any vector , the distance covers in the direction of is , where is the length of .
Two of the training applicants are support vectors:
| applicant | score | ||
|---|---|---|---|
| P | 5.2 | 2.0 | |
| Q | 3.6 | 1.0 |
How wide is the street? That is, what is the distance from the edge to the edge, measured at right angles to them? Give your answer rounded to 2 decimal places.