Why is evaluating clustering harder than evaluating classification?

Clustering is unsupervised, so there is no single correct answer

Clustering has too few attributes

Clustering always gives one cluster

How does the elbow method choose k?

Plot SSE against k and pick where the curve bends

Pick the k equal to number of attributes

What does a clustering tendency test such as Hopkins statistic check?

Whether the data contain non-random structure rather than being uniformly random

Which are internal measures?

Cohesion, separation and silhouette

Precision and recall against labels

Year not given

Short note: Evaluation of clustering

Short answer

Clustering evaluation uses external measures (purity, Rand index) with known labels, internal measures (SSE, silhouette, Dunn index) without labels, and relative measures (elbow method, silhouette comparison) to compare clusterings. It also assesses clustering tendency (e.g., Hopkins statistic) and determines optimal cluster count via gap statistic or silhouette analysis.

Write a short note on Evaluation of Clustering.

Evaluation of clustering (cluster validity) assesses whether a clustering is meaningful and how good it is. Since clustering is unsupervised there is no single correct answer, so evaluation is more difficult than for classification. It answers four questions: Is there any non-random structure in the data (clustering tendency)? What is the right number of clusters? How well do the clusters fit the data without external information? How do they compare with the known labels or with another clustering?

Measures

External (supervised) measures: compare with known class labels. Purity, entropy, precision/recall/F-measure, Rand index, adjusted Rand index, normalised mutual information.
Internal (unsupervised) measures: use only the data.
- Cohesion = within-cluster sum of squares (SSE), lower is better.
- Separation = between-cluster sum of squares, higher is better.
- Silhouette coefficient s = (b − a)/max(a, b), where a is the mean distance to objects in the same cluster and b is the mean distance to the nearest other cluster; range −1 to 1.
- Dunn index, Davies-Bouldin index.
Relative measures: compare different clusterings (e.g. different k or algorithm). Example: the elbow method plots SSE against k and picks the k where the curve bends; or choose k with the best silhouette.

Other aspects

Determining the number of clusters (elbow, silhouette, gap statistic).
Clustering tendency test (e.g. Hopkins statistic) to check that the data is not uniformly random.
Evaluation depends on the algorithm: compactness suits k-means, but density-based clusters of arbitrary shape need other indices.

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