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KMeans

KMeans is a popular clustering algorithm that divides data into k clusters.

KMeans

KMeans assigns each example to the nearest cluster centre and moves the centres to the mean of the assigned examples; these two steps repeat until the centres stop changing. The goal is to minimise the sum of squared distances of examples to their centres.

km = KMeans(n_clusters=3, n_init=10, random_state=0).fit(X)
print(km.cluster_centers_)   # 3 centres
print(km.predict([[0, 0]]))  # the cluster of a new point

predict assigns new examples to the nearest centre; that is why KMeans can be applied to new data.

KMeans's assumptions

KMeans assumes clusters are round, of similar size and similar density. It fails on moon-shaped or nested ring clusters:

from sklearn.datasets import make_moons
Xm, ym = make_moons(200, noise=0.05, random_state=0)
print(adjusted_rand_score(ym, KMeans(2, n_init=10).fit_predict(Xm)))   # low

The number of clusters n_clusters must be given beforehand; you'll see how to choose it in the elbow method lesson.

Practice Find the centres

Train a KMeans(n_clusters=3, n_init=10, random_state=0) on small data with three clear groups. Sort the centres by their first coordinate (c[np.argsort(c[:, 0])]) and print them with np.round(..., 2). Then print that the cluster of [[5, 5]] equals that of [[5.2, 4.9]].

Starter code

model.py
import numpy as np
from sklearn.cluster import KMeans

X = np.array([[0, 0], [0, 1], [1, 0], [5, 5], [5, 6], [6, 5], [10, 0], [10, 1], [11, 0]])

# buraya yaz

Sample solution

model.py
import numpy as np
from sklearn.cluster import KMeans

X = np.array([[0, 0], [0, 1], [1, 0], [5, 5], [5, 6], [6, 5], [10, 0], [10, 1], [11, 0]])

km = KMeans(n_clusters=3, n_init=10, random_state=0).fit(X)
c = km.cluster_centers_
print(np.round(c[np.argsort(c[:, 0])], 2))
print(km.predict([[5, 5]])[0] == km.predict([[5.2, 4.9]])[0])

Expected output

[[ 0.33  0.33]
 [ 5.33  5.33]
 [10.33  0.33]]
True

Questions and answers

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

1 Where is a centre moved in the KMeans update step?

  • To the mean of the assigned examples Correct answer
  • To the farthest example
  • To a random point
  • To the origin

Explanation: The point minimising the sum of squared distances is the mean.

2 Train and get the labels in one step.

Question 
etiket = KMeans(n_clusters=3, n_init=10).____(X)
Answer 
etiket = KMeans(n_clusters=3, n_init=10).fit_predict(X)

Explanation: fit_predict is the same as fit + labels_.

3 Match the steps.

Term Meaning
assignment To the nearest centre
update Move to the mean
cluster_centers_ Centres
predict Assign a new example

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