Overview
This chapter implements K-means from scratch, applies the Elbow method, explores hierarchical clustering with dendrograms, and performs real customer segmentation on the iFood marketing dataset.
You Will Learn
- Writing K-means in NumPy with explicit E- and M-steps
- Using the Elbow method to choose K in practice
- Constructing dendrograms and interpreting them
- Performing and interpreting customer segmentation on real data
Main Content
Implementing K-means from Scratch
You implement functions to (1) initialise centroids, (2) assign points to nearest centroids, and (3) recompute centroids. Running this implementation on Iris confirms that it quickly converges and recovers setosa almost perfectly, with some mixing between versicolor and virginica where their petal features overlap.
Choosing K via the Elbow Method
By running K-means for K = 1…10 and plotting inertia as a function of K, you learn to visually detect elbows. On Iris, K = 3 is usually an obvious elbow. On more complex data the elbow may be subtle, which is a useful reminder that model selection often involves imperfect but pragmatic heuristics.
Hierarchical Clustering and Dendrograms
Using scipy’s linkage and dendrogram functions, you perform agglomerative clustering on Iris and visualise the hierarchy. Cutting the dendrogram at different heights produces varying clusterings that correspond to coarse and fine-grained groupings. Comparing these to K-means cluster assignments shows where methods agree and differ.
Customer Segmentation on iFood
On the iFood marketing dataset, you standardise numeric features, select relevant subsets (e.g., spending by category, channel usage, demographics), and apply K-means with a K chosen via the Elbow method and domain sense. Profiling each cluster by its centroid yields interpretable customer personas (e.g., high-income wine enthusiasts, deal-seeking families), illustrating the practical value of unsupervised learning.
Examples
Running K-means on Iris
Use scikit-learn’s KMeans to confirm your implementation.
from sklearn.datasets import load_iris
from sklearn.cluster import KMeans
X, y = load_iris(return_X_y=True)
km = KMeans(n_clusters=3, random_state=42)
labels = km.fit_predict(X)
print("Cluster centers:\n", km.cluster_centers_)Common Mistakes
Omitting feature scaling before clustering
Why: Unscaled features with different units dominate distance computations, biasing clusters.
Fix: Standardise or normalise features before applying distance-based clustering methods.
Assuming clusters discovered in customer data are static over time
Why: Customer behaviour shifts; segments may drift or split.
Fix: Re-segment periodically and track stability of cluster assignments over time.
Mini Exercises
1. On the iFood dataset, build at least three different K-means segmentations using different feature subsets. How do the inferred personas change?
2. Compare K-means and hierarchical clustering on the same subset of customers. Where do they agree and disagree?