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Stage 2 · Intermediate · M4

Finding Groups Nobody Labeled

The model has no answers to copy. It has to invent the categories.

12 lessons · 112 minSteady

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About this chapter

With no labels, a model still has one move: measuring how far apart two things are. That one move builds everything here. You will run k-means by hand until it stops, see the shapes it gets wrong, cut a tree of merges at a sensible height, and meet a method that is allowed to answer nowhere. Then the chapter stops grouping and starts squeezing, from a rotation that keeps the widest view to a grid of scores rebuilt from two thin tables. It ends by burying real groups under columns that mean nothing.

What you will be able to do

  1. 1

    Near Means Similar

    Say why distance is the one tool left without labels, and pick the scale that decides it.

    8 min
  2. 2

    Who Is Nearest

    Find a point's nearest neighbors with no labels, and read how crowded its spot is.

    8 min
  3. 3

    k-Means, Step by Step

    Run assign and update by hand until the centers stop moving.

    10 min
  4. 4

    Where k-Means Breaks

    Spot a bad landing, and predict k-means failing on crescents, rings, long stripes and lopsided groups.

    11 min
  5. 5

    How Many Groups Are There?

    Use elbow and silhouette to argue for a value of k, and admit the ambiguity.

    8 min
  6. 6

    Clusters Inside Clusters

    Read a dendrogram and cut it at a sensible height.

    9 min
  7. 7

    Density, Not Centers

    Tune DBSCAN's two parameters and read which points it calls noise.

    9 min
  8. 8

    PCA Is a Rotation

    Turn the data to its widest directions and read how much of the spread each one keeps.

    11 min
  9. 9

    Maps of High-Dimensional Data

    Read a t-SNE or UMAP map and list what distances on it do not mean.

    10 min
  10. 10

    Points That Belong Nowhere

    Score points for strangeness, catch the odd combination one column misses, and set a line by how many alerts people can check.

    9 min
  11. 11

    A Grid With Less in It

    Rebuild a full grid of scores from a few numbers per row and per column, and say what those numbers are.

    10 min
  12. 12

    The Curse of Dimensionality

    Explain why columns that mean nothing bury real groups, and what people do before they cluster.

    9 min

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