46  Module 13 Cheat Sheet

Key concepts, definitions, and code from Chapters 31–32

A quick-reference summary of the essential ideas from Module 13. Click any section heading to jump to the full coverage in the book.

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Supervised vs. Unsupervised

Unsupervised learning has no target variable. Nobody tells the algorithm what the right answer is, so there is no accuracy score — evaluation depends on whether the result is useful and interpretable.

	Clustering	Dimension reduction
Question	Which observations belong together?	Which features can be combined?
Operates on	Rows	Columns
Output	A cluster label per row	New constructed features
Method here	K-Means	PCA

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K-Means Clustering

K-Means partitions observations into k groups by repeatedly assigning each point to its nearest centroid and then recomputing each centroid as the mean of its members, until assignments stop changing.

from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler

X_scaled = StandardScaler().fit_transform(X)     # scaling is mandatory here

km = KMeans(n_clusters=4, n_init=10, random_state=123)
labels = km.fit_predict(X_scaled)

km.cluster_centers_    # centroid coordinates (in scaled units)
km.inertia_            # within-cluster sum of squares
km.labels_             # cluster assignment per row

Parameter	Meaning
n_clusters	k, the number of groups — you must choose it
n_init	Random restarts; keeps a bad initialization from winning
random_state	Reproducibility

K-Means measures distance, so unscaled features let large-magnitude columns dominate. Always scale first, or income in dollars will drown out visit counts.

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Choosing k

import matplotlib.pyplot as plt
from sklearn.metrics import silhouette_score

inertias, silhouettes = [], []
ks = range(2, 11)

for k in ks:
    km = KMeans(n_clusters=k, n_init=10, random_state=123).fit(X_scaled)
    inertias.append(km.inertia_)
    silhouettes.append(silhouette_score(X_scaled, km.labels_))

plt.plot(ks, inertias, marker='o')   # elbow plot

Method	Reading it
Elbow	Plot inertia against k; look for the bend where gains flatten
Silhouette	Ranges −1 to 1; higher means tighter, better-separated clusters

Both are heuristics. When they disagree or the elbow is smooth, the data may not have natural clusters — say so rather than forcing a number.

Profiling clusters is the step that makes the result useful:

df['cluster'] = labels
df.groupby('cluster').agg(['mean', 'count'])

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Dimension Reduction with PCA

PCA finds new axes — principal components — that are linear combinations of the original features, ordered so the first captures the most variance. It is feature extraction: the components are constructed, not selected from the originals.

from sklearn.decomposition import PCA

X_scaled = StandardScaler().fit_transform(X)     # required — PCA follows variance

pca = PCA(n_components=0.90)     # keep enough components for 90% of variance
X_pca = pca.fit_transform(X_scaled)

pca.explained_variance_ratio_            # variance share per component
pca.explained_variance_ratio_.cumsum()   # running total
pca.components_                          # loadings: components x original features

Scree plot — how many components to keep:

plt.plot(range(1, len(pca.explained_variance_ratio_) + 1),
         pca.explained_variance_ratio_, marker='o')

Reading loadings: each component’s loadings show which original features it weights most heavily. That is how you name a component — a first component loading on income, spend, and basket size is a “spending power” axis.

pd.DataFrame(pca.components_[:3].T, index=X.columns,
             columns=['PC1', 'PC2', 'PC3'])

Extraction (PCA)	Selection
Builds new combined features	Keeps a subset of original features
Components are hard to explain	Retains original meaning
Uses information from all columns	Discards columns entirely

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Common Pitfalls

Mistake	Fix
Running K-Means or PCA on unscaled data	StandardScaler() first — both are variance/distance driven
Treating cluster numbers as meaningful	Labels are arbitrary; cluster 0 is not “first” or “best”
Forcing k when no elbow appears	Report that the structure is ambiguous
Interpreting components without loadings	A component means nothing until you read what loads on it
Keeping components to hit a variance target blindly	Balance variance retained against interpretability
Expecting an accuracy score	There is no ground truth; judge by usefulness