A recycling plant's camera sorts every item into one of 5 bins: paper, glass, metal, plastic and food. Logistic regression answers a yes-or-no question, so the engineers extend it to five categories the usual way: train several binary classifiers behind the scenes and combine them. They try both of the standard ways of doing that.
One-vs-rest (OvR). One binary model per bin, each trained to answer "is it this bin, or any of the others?" Each model gives a probability for its own bin, and the system picks the bin whose model gives the highest probability.
One-vs-one (OvO). One binary model for every pair of bins, each trained only on items from its own two bins. Each model gives the probability that the item belongs to the first bin named in its pair, and votes for that bin if the probability is above 0.5, or for the second bin otherwise. The system picks the bin with the most votes.
For one crumpled item, the OvR models report:
| paper | glass | metal | plastic | food |
|---|---|---|---|---|
| 0.38 | 0.09 | 0.47 | 0.45 | 0.06 |
and the OvO models report:
| pair (first vs second) | probability for the first bin |
|---|---|
| paper vs glass | 0.81 |
| paper vs metal | 0.58 |
| paper vs plastic | 0.36 |
| paper vs food | 0.88 |
| glass vs metal | 0.62 |
| glass vs plastic | 0.27 |
| glass vs food | 0.71 |
| metal vs plastic | 0.44 |
| metal vs food | 0.93 |
| plastic vs food | 0.85 |
In the OvO vote, how many more votes does the OvO winner get than the bin OvR picked? Enter a whole number, and enter 0 if both systems pick the same bin.