How deeply does The Well-Grounded Data Analyst cover elbow method?

Explains iterative fitting, inertia, plotting, and diminishing returns, while stopping short of treating the metric as a sufficient decision rule.

Elbow method

As explained in The Well-Grounded Data Analyst

The elbow method selects an approximate number of clusters by identifying where additional clusters produce diminishing improvement in a clustering criterion.

The elbow method estimates a useful cluster count by running k-means with several values of k and locating where additional clusters deliver sharply diminishing improvement. section 13.1.4

Use the method by:

Fitting k-means for multiple cluster counts and recording inertia, which measures how closely observations sit to their cluster centers. section 13.1.4
Plotting inertia against k and selecting the bend where further clusters barely reduce the score, then checking whether the resulting groups make practical sense. section 13.1.4

from sklearn.cluster import KMeans

k_values = range(3, 15)
inertia_values = []

for k in k_values:
    kmeans = KMeans(n_clusters=k, random_state=42)
    kmeans.fit(X_scaled)
    inertia_values.append(kmeans.inertia_)

fig, axis = plt.subplots()

axis.plot(k_values, inertia_values)

_ = axis.set(
    title="'Inertia' values for different values of k",
    xlabel="Number of clusters (the 'k' in k-means)",
    ylabel="Inertia"
)

axis.set_ybound(0, 900)

plt.show()

A runnable listing tests k from 3 through 14, collects inertia values, and plots the curve used to identify the elbow. section 13.1.4

How The Well-Grounded Data Analyst covers it

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Also explained in

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Statistics Slam DunkThe within-cluster sum of squares method selects a clustering count by examining how within-cluster squared distances decrease as the number of clusters increases.
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Data Without LabelsThe elbow method is a heuristic for selecting a model complexity value by locating a sharp bend in a curve of objective performance versus that value.
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Advanced Algorithms and Data StructuresThe elbow method is a model-selection technique that chooses a parameter value at the point where additional complexity yields diminishing improvement in an evaluation measure.
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Cyber Threat HuntingThe elbow method is a clustering-validation technique that selects a cluster count by locating a point where additional clusters yield diminishing improvement in within-cluster distance.

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Related concepts

squared lossuses · Squared loss is the square of the difference between a predicted or fitted value and its target or observation, often summed across data points.
k-means++ initializationuses · K-means++ initialization is a procedure that selects initial centroids using probability proportional to squared distance from previously selected centroids.
K-means clusteringconfigures · K-means clustering partitions data into a specified number of groups by assigning observations to representative centers and iteratively updating those centers to reduce within-group distances.
silhouette coefficientalternative to · The silhouette coefficient measures how well a sample fits its assigned cluster compared with the nearest alternative cluster, typically ranging from -1 to 1.
hyperparameterconfigures · A hyperparameter is a setting chosen outside ordinary parameter learning that controls a model, algorithm, or learning procedure.
within-cluster sum of squaresuses · Within-cluster sum of squares is the sum of squared distances between observations and the centroids of their assigned clusters.

This explainer was generated by Manning's knowledge graph from the text of The Well-Grounded Data Analyst. The section links point to the parts of the book it draws on.