The below methods are used in cluster analysis to determine the optimal number of clusters in a dataset. Determining the right number of clusters is crucial for accurate clustering results and meaningful interpretation of the data. Each method provides a quantitative measure or heuristic approach to help identify the optimal number of clusters based on the inherent structure and distribution of the data.
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Elbow Method: The Elbow Method aids in determining the optimal number of clusters in a dataset by plotting the variance explained as a function of the number of clusters. The "elbow" point indicates the optimal number of clusters where adding more clusters doesn't significantly decrease the variance explained.
Silhouette Method: The Silhouette Method evaluates the quality of clustering by measuring the coherence within clusters and separation between clusters. It calculates silhouette scores for each data point, where higher scores indicate better cluster separation and cohesion. The optimal number of clusters is determined by maximizing the average silhouette score across all data points.
Gap Statistic Method: The Gap Statistic Method compares within-cluster dispersion with that expected under a null reference distribution. It measures the gap between the observed within-cluster dispersion and that of a random data distribution. The optimal number of clusters is determined by identifying the number of clusters where the gap statistic is maximized.
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