Not every question comes with labels. Cartwheel’s marketing team asks: “What kinds of customers do we have?” Nobody has tagged customers with types, so there’s no target to predict. Unsupervised learning looks for structure in the features alone. The two tools you’ll use most are clustering, which groups similar rows, and dimensionality reduction, which summarises many columns with a few.
\nk-means needs one decision from you: the number of clusters, k. Then it repeats two steps:
\nWhen assignments stop changing, it’s done. Different starting centres can give different results, so scikit-learn runs the whole thing n_init times and keeps the tightest solution.
Because “nearest” is a distance, the same lesson from k-nearest neighbours applies: scale first, or total_spent in thousands decides everything.
Use behaviour columns only and leave churned out: a segmentation should describe customers, not their outcome. You’ll look at churn afterwards to see whether the segments mean anything.
import pandas as pd\nfrom sklearn.cluster import KMeans\nfrom sklearn.metrics import silhouette_score\nfrom sklearn.pipeline import make_pipeline\nfrom sklearn.preprocessing import StandardScaler\n\nchurn = pd.read_csv(\"churn.csv\")\nbehaviour = [\"orders\", \"total_spent\", \"avg_order_value\", \"days_since_last_order\",\n \"tenure_days\", \"mobile_share\"]\nX = StandardScaler().fit_transform(churn[behaviour])\nfor k in range(2, 7):\n labels = KMeans(n_clusters=k, n_init=10, random_state=42).fit_predict(X)\n print(f\"k={k} silhouette {silhouette_score(X, labels):.3f}\")\n\nsegments = make_pipeline(StandardScaler(), KMeans(n_clusters=4, n_init=10, random_state=42))\nchurn[\"segment_id\"] = segments.fit_predict(churn[behaviour])\nprofile = churn.groupby(\"segment_id\").agg(\n customers=(\"orders\", \"size\"), orders=(\"orders\", \"mean\"),\n avg_order=(\"avg_order_value\", \"mean\"), days_since=(\"days_since_last_order\", \"mean\"),\n tenure=(\"tenure_days\", \"mean\"), churn_rate=(\"churned\", \"mean\"))\nprint(profile.round(2))First, the honest part. The silhouette score measures how much closer each customer is to its own cluster than to the next one, from -1 to 1. Scores around 0.25 for every k mean the customers don’t fall into crisp natural groups; they form a continuum. That’s typical for behavioural data. It doesn’t make clustering useless, but it means k is your choice, made for usefulness, not a fact you discovered.
\nThen the useful part. Profiling the four clusters gives segments a marketer can name:
\nChurn rates differ sharply between segments even though k-means never saw churned. That’s evidence the segments capture something real, and it gives marketing four different conversations to have instead of one.
k-means isn’t the only option. It assumes roughly round clusters of similar size, an assumption that is usually good enough for behavioural segments. Hierarchical clustering (AgglomerativeClustering) shows how groups merge at different levels, and DBSCAN finds dense regions of any shape and labels outliers as noise. Start with k-means for segmentation; switch when its assumptions clearly don’t fit your data.
Many datasets have dozens of correlated columns. The breast cancer data has 30 measurements of cell nuclei, many of them variations on size. Principal component analysis finds new axes, each a weighted mix of the original columns, ordered by how much of the data’s variation they capture. Keep the first few and you have a compact summary.
\nimport numpy as np\nfrom sklearn.datasets import load_breast_cancer\nfrom sklearn.decomposition import PCA\nfrom sklearn.pipeline import make_pipeline\nfrom sklearn.preprocessing import StandardScaler\n\nX, y = load_breast_cancer(return_X_y=True)\npca = make_pipeline(StandardScaler(), PCA()).fit(X)\nratios = pca[-1].explained_variance_ratio_\nprint(\"first two components keep:\", ratios[:2].round(3), \"=\", round(ratios[:2].sum(), 3))\nprint(\"components needed for 90%:\", int(np.argmax(np.cumsum(ratios) >= 0.90)) + 1)\n\ncoords = make_pipeline(StandardScaler(), PCA(n_components=2)).fit_transform(X)\nfor label, name in [(0, \"malignant\"), (1, \"benign\")]:\n print(name, \"average position:\", coords[y == label].mean(axis=0).round(2))Two components keep 63% of the variation in 30 scaled columns, and seven keep 90%. Plot the two coordinates and malignant and benign tumours sit on opposite sides of the first axis, even though PCA never saw the labels. That’s why a 2D PCA plot is a standard first look at any wide dataset.
\n\nBoth techniques here are classic and cheap. The next lesson is about models that learn their own features from raw inputs: neural networks.
\n","toc":[{"id":"sec-1","text":"k-means in two moves","level":2},{"id":"sec-2","text":"Segmenting Cartwheel’s customers","level":2},{"id":"sec-3","text":"PCA: fewer columns, most of the information","level":2}],"takeaways":["k-means alternates two steps, assign each point to its nearest centre and move each centre to the mean of its points, until nothing changes.","Clustering uses distances, so scale features first, and setn_init and random_state for repeatable results.","Clusters are only useful if you can describe them; profile each one with group means before giving it a name.","A low silhouette score means the data has no crisp natural groups; segments can still be useful, but they’re a choice, not a discovery.","PCA finds new axes that capture the most variance; explained_variance_ratio_ tells you how much each component keeps."],"further":[{"title":"Clustering: K-means","url":"https://scikit-learn.org/stable/modules/clustering.html#k-means"},{"title":"KMeans","url":"https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html"},{"title":"Principal component analysis (PCA)","url":"https://scikit-learn.org/stable/modules/decomposition.html#pca"}],"quiz":[{"q":"You run k-means on raw churn columns without scaling. Which column will dominate the clusters?
","options":[{"text":"used_coupon, because binary columns separate groups cleanly.","why":"A 0/1 column contributes at most 1 to a squared distance, which is nothing next to dollar amounts."},{"text":"days_since_last_order, because it’s the best churn predictor.","why":"k-means never sees the target; it only sees distances, which are driven by scale."},{"text":"All columns contribute equally, because k-means normalises internally.","why":"KMeans does no scaling of its own; you have to add a StandardScaler."},{"text":"total_spent, because its values in the thousands swamp every other distance.","why":"Correct. Unscaled, k-means mostly clusters customers by spend."}],"answer":3},{"q":"Silhouette scores for k = 2 to 7 all sit between 0.25 and 0.27. What does that tell you?
","options":[{"text":"The data has no strong natural grouping, so pick k for usefulness and explainability.","why":"Correct. Flat, low scores mean no k stands out; the segmentation is a modelling choice."},{"text":"k = 7 is best because it has the highest score.","why":"Differences this small are noise, and seven segments are harder for a team to use than four."},{"text":"k-means has failed and must be replaced by a supervised model.","why":"Weak cluster structure doesn’t make clustering useless, and a supervised model needs labels you don’t have for segments."}],"answer":0},{"q":"PCA on the 30 breast cancer features gives explained_variance_ratio_ of 0.44 and 0.19 for the first two components. What does a 2D plot of them show?
segments so the customers are scaled before k-means (4 clusters, n_init=10, random_state=42), and get one label per customer in labels.churn_by_cluster: the churn rate of each cluster, as a Series indexed by cluster label. highest_rate: the largest of those rates.wine_var_2: the share of variance that the first two principal components keep for the wine dataset’s 13 features, after standard scaling.StandardScaler() before KMeans(...) in make_pipeline.","churn.groupby(labels)["churned"].mean() groups by the label array directly.","Fit make_pipeline(StandardScaler(), PCA(n_components=2)) on X_wine and sum pipe[-1].explained_variance_ratio_."],"explanation":"Scaled k-means finds the four segments from the lesson (129, 41, 79 and 149 customers), and the lapsed occasionals churn at 79% even though the target was never used for clustering. Unscaled, total_spent would have dominated and the segments would mostly sort customers by spend. On the wine data, two components keep about 55% of the variance in 13 measurements: enough for a useful map, not enough to replace the original columns.