Unsupervised clustering with unknown number of clusters

Unsupervised Clustering with Unknown Number of Clusters

Unsupervised clustering is a machine learning technique used to group data points into clusters based on their similarity. A common challenge in clustering is determining the optimal number of clusters. In this article, we will explore methods for unsupervised clustering when the number of clusters is unknown.

Challenges of Unknown Cluster Numbers

1. Suboptimal Clustering:

If the number of clusters is misspecified, the clustering algorithm may produce suboptimal results, leading to incorrect grouping of data points.

2. Difficulty in Evaluation:

Evaluating the performance of clustering algorithms is challenging without a ground truth label for the number of clusters.

Methods for Determining the Number of Clusters

1. Elbow Method

The elbow method involves plotting the within-cluster sum of squares (WCSS) against the number of clusters. The WCSS represents the sum of squared distances between each data point and its cluster centroid. The plot typically exhibits an elbow shape, where the rate of decrease in WCSS slows down after a certain number of clusters. The elbow point is considered the optimal number of clusters.

In this example, the elbow point appears to be at 3 clusters, as the rate of decrease in WCSS slows down significantly after this point.

2. Silhouette Analysis

Silhouette analysis measures the similarity of data points within their cluster compared to other clusters. The silhouette score ranges from -1 to 1, where a higher score indicates better clustering.

• A score close to 1 suggests that the data point is well-clustered.
• A score close to -1 indicates that the data point might be misclassified.
• A score close to 0 indicates that the data point lies close to the boundary between two clusters.

The optimal number of clusters is typically identified by the number that maximizes the average silhouette score.

3. Gap Statistic

The gap statistic measures the difference between the within-cluster dispersion in the data and the expected dispersion in a random sample. A large gap statistic indicates that the clustering structure is statistically significant.

The optimal number of clusters is chosen as the one that maximizes the gap statistic.

4. Model Selection with Cross-Validation

For more complex clustering algorithms, model selection can be performed using cross-validation. This involves splitting the data into training and validation sets. Different numbers of clusters are evaluated on the training data, and the model with the best performance on the validation set is chosen.

Code Example (Python)

from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

# Load the dataset
data = ...

# Elbow method
wcss = []
for i in range(1, 11):
  kmeans = KMeans(n_clusters=i, random_state=42)
  kmeans.fit(data)
  wcss.append(kmeans.inertia_)

# Silhouette analysis
silhouettes = []
for i in range(2, 11):
  kmeans = KMeans(n_clusters=i, random_state=42)
  kmeans.fit(data)
  silhouettes.append(silhouette_score(data, kmeans.labels_))

# Choose the optimal number of clusters
optimal_clusters = ...  # Based on elbow method or silhouette analysis

# Fit the final model
kmeans = KMeans(n_clusters=optimal_clusters, random_state=42)
kmeans.fit(data)

# Get cluster labels
labels = kmeans.labels_

Conclusion

Determining the optimal number of clusters in unsupervised clustering is a crucial step. The methods discussed above provide valuable tools for identifying the appropriate number of clusters, ensuring optimal clustering results.