Calinski-Harabasz Index (Variance Ratio Criterion)
A clustering validation metric called the Calinski-Harabasz Index is used to evaluate the quality of clusters within a dataset. Higher values indicate compact and well-separated clusters. It computes the ratio of the within-cluster variance to the between-cluster variance. It helps determine the ideal number of clusters for a given dataset by comparing the index across various clusterings. Improved cluster definition is implied by a higher Calinski-Harabasz Index. This measure is useful for assessing how well clustering algorithms work, which helps choose the best clustering solution for a variety of datasets.
Mathematical Formula:
Calinski-Harabasz Index (CH) is calculated as:
- Here,
- B is the sum of squares between clusters.
- W is the sum of squares within clusters.
- N is the total number of data points.
- K is the number of clusters.
The B and W are calculated as:
- Calculating between group sum of squares (B)
- Here,
- is the number of observation in cluster ‘k’
- is the centroid of cluster ‘k’
- C is the centroid of the dataset
- K is number of clusters
- Calculating within the group sum of squares (W)
- Here,
- is the number of observation in cluster ‘k’
- is the i-th observation of cluster ‘k’
- is the centroid of cluster ‘k’
Interpretation: Higher numbers suggest better-defined clusters.
Clustering Metrics in Machine Learning
Clustering is an unsupervised machine-learning approach that is used to group comparable data points based on specific traits or attributes. It is critical to evaluate the quality of the clusters created when using clustering techniques. These metrics are quantitative indicators used to evaluate the performance and quality of clustering algorithms. In this post, we will explore clustering metrics principles, analyze their importance, and implement them using scikit-learn.
Table of Content
- Silhouette Score
- Davies-Bouldin Index
- Calinski-Harabasz Index (Variance Ratio Criterion)
- Adjusted Rand Index (ARI)
- Mutual Information (MI)
- Steps to Evaluate Clustering Using Sklearn
Clustering Metrics
Clustering metrics play a pivotal role in evaluating the effectiveness of machine learning algorithms designed to group similar data points. These metrics provide quantitative measures to assess the quality of clusters formed, helping practitioners choose optimal algorithms for diverse datasets. By gauging factors like compactness, separation, and variance, clustering metrics such as silhouette score, Davies–Bouldin index, and Calinski-Harabasz index offer insights into the performance of clustering techniques. Understanding and applying these metrics contribute to the refinement and selection of clustering algorithms, fostering better insights in unsupervised learning scenarios.
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