When K-Means geometry misleads

Understand the idea

Different starting centres can find different local solutions. Multiple starts help, but do not remove the preference for compact centroid-based groups or resolve the meaning of k.

Illustrative data

Illustrative data
Column	Values
`x`	0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
`y`	-0.1, 0.25, 0.5, 1.45, 2.3, 3.85, 5.3, 7.45, 9.5, 12.249999999999998, 14.9, 18.25

Click the highlighted code to change the result.

scaled = StandardScaler().fit_transform(example[["x", "y"]])
example_model = KMeans(n_clusters=4, n_init=, random_state=)
example_model.fit(scaled)
inertia = example_model.inertia_

Seed 2 · four groups, one start · inertia 1.538. Crosses mark centroids; group IDs are not known classes.

What the syntax does

n_init=1: Uses a single initialisation so seed sensitivity is visible in this exercise.
n_init: "auto", 10, 20
model.inertia_: Records each fit’s compactness so instability can be compared.

Supplied for this practice

These objects are prepared afresh before your editor runs.

X: Feature dataframe for the declared population, preserving row indices.
X = df.copy()
scaler: Already fitted coordinate system learned from X; transform reuses its statistics without fitting again. Fitted on X; reuse without refitting.
scaled: Standardised features in the same row/column order as X.
scaled = scaler.fit_transform(X)

Outputs you create

answer: The requested result, with the values, labels and row order described by this task.

CLUSTER45_ANISO · first 8 rows
`length_mm`	`width_cm`
5820.15	45.332
2911.98	36.4235
3023.77	37.199
3616.25	38.4231
4037.74	41.4146
4313.07	43.8337
5331.02	48.9987
3962.73	38.9743

Your task

On CLUSTER45_ANISO’s unequal-size elongated clouds
Fit four-cluster K-Means with one initialisation for each seed 1, 2 and 3.
Store each inertia in answer in seed order.

answer

Hints

Think: Different initial centres can lead to different local solutions.

Tools: KMeans with n_init=1, random_state and inertia_.

Approach: Keep k and data fixed while fitting each declared seed, then compare the objectives.

Explained solution

answer=[]
for seed in [1,2,3]:
    model=KMeans(n_clusters=4,n_init=1,random_state=seed).fit(scaled)
    answer.append(model.inertia_)

One start exposes initialisation sensitivity that a multi-start run is designed to reduce.