How deeply does Statistics Slam Dunk cover elbow method?

Explains scree plots and diminishing returns, but stops short of an objective rule when the elbow is ambiguous.

Elbow method

The within-cluster sum of squares method selects a clustering count by examining how within-cluster squared distances decrease as the number of clusters increases.

The elbow method helps choose K for K-means clustering. Plot the number of clusters against within-cluster sum of squares; the curve usually drops quickly, then shows diminishing returns. The bend, or elbow, suggests a practical cluster count. section 11.5.2

Use the method as a guided decision rather than an automatic answer:

Compute within-cluster squared distances for increasing values of K. section 11.5.2
Plot K on the x-axis and within-cluster sum of squares on the y-axis. section 11.5.2
Look for the point where additional clusters produce noticeably smaller improvements. section 11.5.2
Compare the result with another criterion because the elbow may be unclear or subjective. section 11.5.2

NBA payrolls and wins

For adjusted team payrolls and regular-season wins from 2000 through 2017, the elbow method suggested six clusters, while the silhouette method suggested two. The analysis chose four clusters as a compromise. The resulting K-means model isolated the New York Knicks and grouped the San Antonio Spurs with ten other teams. section 20.1

How Statistics Slam Dunk covers it

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Also explained in

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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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The Well-Grounded Data AnalystThe elbow method selects an approximate number of clusters by identifying where additional clusters produce diminishing improvement in a clustering criterion.
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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 Statistics Slam Dunk. The section links point to the parts of the book it draws on.