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Dendrogram

A dendrogram visualizes hierarchical clustering results as a tree.

Dendrogram

A dendrogram is the drawing of the merge tree: a plot where the leaves are examples, the horizontal lines merges and the line height the merge distance. Cut with a horizontal line, the number of vertical lines it crosses gives the number of clusters.

from scipy.cluster.hierarchy import dendrogram
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
dendrogram(Z, ax=ax)
ax.axhline(4, color="r", linestyle="--")   # cut at this height

Long vertical branches are the sign of well-separated clusters.

Cutting with fcluster

To cut the tree from code, fcluster is used: either with a distance threshold (criterion="distance") or with the desired number of clusters (criterion="maxclust"):

from scipy.cluster.hierarchy import fcluster
etiket = fcluster(Z, t=4, criterion="distance")   # cut merges above 4
etiket2 = fcluster(Z, t=3, criterion="maxclust")  # at most 3 clusters

fcluster starts labels at 1; scikit-learn starts at 0.

Practice Cut the tree

Build the tree with Ward linkage. Make a cut with fcluster first using t=3, criterion="maxclust", then t=10, criterion="distance"; print the two label arrays on separate lines.

Starter code

model.py
import numpy as np
from scipy.cluster.hierarchy import linkage, fcluster

X = np.array([[0, 0], [0, 1], [1, 0], [5, 5], [5, 6], [6, 5], [12, 0], [12, 1]])

# buraya yaz

Sample solution

model.py
import numpy as np
from scipy.cluster.hierarchy import linkage, fcluster

X = np.array([[0, 0], [0, 1], [1, 0], [5, 5], [5, 6], [6, 5], [12, 0], [12, 1]])

Z = linkage(X, method="ward")
print(fcluster(Z, t=3, criterion="maxclust"))
print(fcluster(Z, t=10, criterion="distance"))

Expected output

[2 2 2 3 3 3 1 1]
[2 2 2 3 3 3 1 1]

Questions and answers

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

1 If a horizontal cut crosses 3 vertical lines in a dendrogram, how many clusters result?

  • 2
  • 4
  • It can't be determined
  • 3 Correct answer

Explanation: Each independent branch below the cut is a cluster.

2 Cut the tree so there are at most 2 clusters.

Question 
etiket = fcluster(Z, t=2, criterion=____)
Answer 
etiket = fcluster(Z, t=2, criterion="maxclust")

Explanation: "maxclust" interprets t as the number of clusters.

3 Match the concepts.

Term Meaning
leaf A single example
line height Merge distance
horizontal cut Sets the cluster count
long branch Well-separated cluster

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