Lesson 22 established that “close in embedding space” means close according to whatever the training objective rewarded. Even once you’ve picked the right objective, a second, more mechanical trap is waiting in how you compute “close” in the first place — and it doesn’t need any machine learning at all to demonstrate, just two features and a ruler.
The setup. A product catalog has each item described by two raw numbers: reviews (total review
count, typically in the hundreds to low thousands) and rating (average star rating, 1.0 to 5.0). No
scaling has been applied — these are the numbers exactly as they’d sit in a database column, fed
straight into Euclidean distance: for two points $(r_1, s_1)$ and $(r_2, s_2)$,
$\text{distance} = \sqrt{(r_1 - r_2)^2 + (s_1 - s_2)^2}$.
Three items:
| item | reviews | rating |
|---|---|---|
| Q (query) | 1000 | 4.8 |
| X (candidate) | 1050 | 2.1 |
| Y (candidate) | 200 | 4.7 |
X has 50 more reviews than Q, but a rating that’s wildly different (2.1 vs. 4.8 — a badly-reviewed product). Y has a rating almost identical to Q (4.7 vs. 4.8 — essentially the same quality) but 800 fewer reviews.
Your task: compute the raw Euclidean distance from Q to X, and from Q to Y. Whichever comes out smaller is the one a nearest-neighbor search would return as “most similar” to Q. Enter that smaller distance, rounded to the nearest whole number. (Before you check the solution: does the item this distance points to actually strike you as the more similar product?)