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Linkage

Linkage is the method for calculating inter-cluster distance.

Linkage types

The "closeness" of two clusters can be defined in different ways:

  • single: the distance between the two closest members; forms long chains.
  • complete: between the two farthest members; tight clusters of similar diameter.
  • average: the mean over all member pairs; in between.
  • ward: the merge that increases within-cluster variance least; round clusters similar to KMeans (default).

The chaining effect

The strength of single linkage is also its weakness: even a single chain of noise points linking two clusters merges them. Ward is more robust to noise but can't split curved shapes:

for l in ["single", "complete", "average", "ward"]:
    e = AgglomerativeClustering(n_clusters=2, linkage=l).fit_predict(Xm)
    print(l, adjusted_rand_score(ym, e))

The right linkage is chosen according to the expected shape of the clusters in the data.

Practice Compare linkages

Run AgglomerativeClustering(n_clusters=2, linkage=l) on the moon data with the four linkage types. On each line print the linkage name and the ARI with round(..., 3).

Starter code

model.py
from sklearn.datasets import make_moons
from sklearn.cluster import AgglomerativeClustering
from sklearn.metrics import adjusted_rand_score

X, y = make_moons(n_samples=200, noise=0.05, random_state=0)

# buraya yaz

Sample solution

model.py
from sklearn.datasets import make_moons
from sklearn.cluster import AgglomerativeClustering
from sklearn.metrics import adjusted_rand_score

X, y = make_moons(n_samples=200, noise=0.05, random_state=0)

for l in ["single", "complete", "average", "ward"]:
    e = AgglomerativeClustering(n_clusters=2, linkage=l).fit_predict(X)
    print(l, round(adjusted_rand_score(y, e), 3))

Expected output

single 1.0
complete 0.433
average 0.433
ward 0.433

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Which linkage gives the best result for two moon-shaped clusters?

  • All the same
  • single Correct answer
  • ward
  • complete

Explanation: single merges along a chain of neighbouring points and follows the curved shape.

2 Merge by the farthest members.

Question 
ag = AgglomerativeClustering(n_clusters=3, linkage=____)
Answer 
ag = AgglomerativeClustering(n_clusters=3, linkage="complete")

Explanation: Complete linkage uses the distance between the two clusters' farthest members.

3 Match the linkages.

Term Meaning
single Closest members, chains
complete Farthest members
average Mean over all pairs
ward Least variance increase

All lessons in Intermediate

1 scikit-learn basics

  1. What is scikit-learn?
  2. Estimator API
  3. The fit method
  4. The predict method
  5. The score method
  6. Summary - scikit-learn

2 Pipeline

  1. What is a Pipeline?
  2. Steps
  3. fit and predict
  4. Advantages
  5. ColumnTransformer
  6. Summary - Pipeline

3 Cross-validation

  1. What is cross-validation?
  2. K-fold
  3. cross_val_score
  4. Stratified
  5. Advantages
  6. Summary - Cross-validation

4 Grid search

  1. What is grid search?
  2. GridSearchCV
  3. param_grid
  4. best_params_
  5. best_score_
  6. Summary - Grid search

5 SVM

  1. What is SVM?
  2. Margin
  3. Kernel
  4. C parameter
  5. Classification
  6. Summary - SVM

6 Project: SVM

  1. Preparing data
  2. Training model
  3. Prediction
  4. Evaluation

7 Random forest

  1. What is random forest?
  2. Ensemble
  3. n_estimators
  4. Bagging
  5. Feature importance
  6. Summary - Random forest

8 Boosting

  1. What is boosting?
  2. AdaBoost
  3. Gradient boosting
  4. Learning rate
  5. Advantages
  6. Summary - Boosting

9 Clustering

  1. What is clustering?
  2. KMeans
  3. Centroid
  4. Elbow method
  5. Labels
  6. Summary - Clustering

10 KMeans in depth

  1. KMeans algorithm
  2. Initialization
  3. n_init
  4. inertia_
  5. random_state
  6. Summary - KMeans

11 Hierarchical clustering

  1. What is hierarchical clustering?
  2. Dendrogram
  3. Agglomerative
  4. Linkage
  5. Advantages
  6. Summary - Hierarchical clustering

12 Project: Clustering

  1. Preparing data
  2. Training KMeans
  3. Label analysis
  4. Printing results

13 PCA

  1. What is PCA?
  2. Variance
  3. n_components
  4. fit_transform
  5. explained_variance_
  6. Summary - PCA

14 Dimensionality reduction

  1. What is dimensionality reduction?
  2. Why reduce?
  3. PCA vs t-SNE
  4. Visualization
  5. Advantages
  6. Summary - Dimensionality reduction

15 Feature selection

  1. What is feature selection?
  2. Variance threshold
  3. SelectKBest
  4. Recursive elimination
  5. Feature importance
  6. Summary - Feature selection

16 Imbalanced data

  1. What is imbalanced data?
  2. SMOTE
  3. Class weight
  4. Oversampling
  5. Metric selection
  6. Summary - Imbalanced data

17 Project: Features

  1. Feature extraction
  2. Feature selection
  3. Training model
  4. Evaluation

18 Ensemble methods

  1. What is ensemble?
  2. Voting
  3. Bagging
  4. Boosting
  5. Stacking
  6. Summary - Ensemble

19 Regularization

  1. What is regularization?
  2. L1 (Lasso)
  3. L2 (Ridge)
  4. alpha
  5. ElasticNet
  6. Summary - Regularization

20 Intermediate final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4