MATH 170 · Clustering · Movie Preferences for k-Means
Clustering what you can't plot k-means · L1
You are the data point. Rate sixteen movies and your whole taste
becomes a list of sixteen numbers — a vector with no picture. Then run one loop of
k-means on yourself: assign (which taste-cluster are you nearest?)
and update (your joining moves the cluster's center).
No scatterplot on this page — that's the point.
Two movies you could draw. Sixteen movies means sixteen axes: nowhere to draw them,
and nothing stops the math. Every number below comes from the same L1 recipe you
met with the digit grids: distance = |u1−v1| + |u2−v2| + … + |u16−v16|.
1 · Rate the movies
Rate the movies — pick 0 if you haven't seen it.
2 · Assign — which persona are you nearest?
Three taste-personas act as the k=3 starting centroids. "Place me" runs one
assign step: your disagreement with each persona, movie by movie, summed left to right.
step 0 — rate
Rate above, then press Place me ▸ to run the assign step.
3 · The roster — nearest and farthest classmate
Six classmates already rated the same movies. Every distance below is the same
left-to-right sum — no plot needed to say who's near you.
4 · Update — the refit step
The other half of the k-means loop: each cluster's centroid becomes the
per-movie average of everyone assigned to it — including you.
Want to do this with your whole class
instead of six fictional students? The Shared Plane — the classroom app — has a
rate & cluster movies mode. Everyone rates the movie list on their own
device, the instructor locks the ratings and steps k-means in every dimension at once, and
the projector shows the clusters as named lists with each cluster's mean rating underneath.
Still no scatterplot, for the same reason as here: there is nowhere to draw that many axes, and
nothing stops the math. One difference worth saying out loud: the room version still runs on the
original eight titles — the first eight in the list above — because its copy of the
list has not been extended yet.
Try: place yourself, then flip one rating from +1 to −1 — each persona distance changes by at most 2, so from an all-zero row it takes at least three changed ratings to join a different cluster.