K-Means is the most popular clustering method any learner should know. In this note, we will understand the idea of KMeans and how to use it with Scikit-learn. Besides that, we also learn about its variants (K-medois, K-modes, K-medians).
- Randomly choose centroids ().
- Go through each example and assign them to the nearest centroid (assign class of that centroid).
- Move each centroid (of each class) to the average of data points having the same class with the centroid.
- Repeat 2 and 3 until convergence.
A simply basic steps of K-Means.
A gif illustrating the idea of K-Means algorithm. Source.
How to choose k? #
Using "Elbow" method to choose the number of clusters .
- A type of Partitioning clustering.
- K-means is sensitive to outliers ⇒ K-medoids clustering or PAM (Partitioning Around Medoids) is less sensitive to outliers[ref]
K-Means in code #
from sklearn.cluster import KMeans
kmeans = KMeans(n_clusters=10, random_state=0) # default k=8
Some notable parameters (see full):
max_iter: Maximum number of iterations of the k-means algorithm for a single run.
kmeans.labels_: show labels of each point.
kmeans.cluster_centers_: cluster centroids.
K-Means in action #
- K-Means clustering on the handwritten digits data.
- Image compression using K-Means -- Open in HTML -- Open in Colab.
K-medoids clustering #
- It is simple to understand and easy to implement.
- K-Medoid Algorithm is fast and converges in a fixed number of steps.
- PAM is less sensitive to outliers than other partitioning algorithms.
- The main disadvantage of K-Medoid algorithms is that it is not suitable for clustering non-spherical (arbitrary shaped) groups of objects. This is because it relies on minimizing the distances between the non-medoid objects and the medoid (the cluster centre) – briefly, it uses compactness as clustering criteria instead of connectivity.
- It may obtain different results for different runs on the same dataset because the first k medoids are chosen randomly.
- Different from K-Means:
- Final centers no need to be points in data.
- Measure generally requires Euclidean distance.
- Sensitive to outliers.
- Final Centers is actual points in data. They're called medoids or exemplars.
- Measures can be arbitrarily dissimilar.
- Robust to outliers.
- (Like KMeans'): choose randomly points (no need to be a point in data)
- (Like KMeans'): assign labels to points based on chosen points in step 1.
- (Different from KMeans):
- (Like KMeans'): repeat the steps.
Choose k by Silhouette #
It's better than Elbow method to choose the number of clusters .
👉 Check this note.