In K-means clustering, determining the **optimal number of clusters**, K, is a critical decision. Choosing the right K is essential to uncover meaningful patterns in your data. Too few clusters might **oversimplify the data**, while too many might create **overly specific** and **less useful clusters**. Therefore, methods to guide your choice of K are important. 

One popular technique for finding the optimal K is the **within-sum-of-squares (WSS) metric**. WSS measures the sum of squared distances between each data point and its assigned centroid within a cluster. Essentially, WSS indicates how **compact** the clusters are. Lower WSS values suggest tighter, more compact clusters.

To use WSS to find the optimal K, you would typically follow these steps:

This elbow is often considered a strong indicator of the optimal K for the following reasons: 

- **It suggests diminishing returns:** adding more clusters beyond the elbow does not lead to a **substantial improvement** in WSS, meaning clusters are not getting significantly more compact; 

- **It balances granularity and simplicity:** the elbow often represents a good balance between capturing the essential structure in the data **without overfitting** or creating unnecessarily fine-grained clusters.

Keep in mind that the elbow method is a **heuristic**. The elbow point may not always be sharply defined, and other factors might influence your final choice of K. **Visual inspection** of the resulting clusters and your **domain knowledge** are valuable supplements to the elbow method. 

When using the WSS method to choose the number of clusters in K-means, what does the elbow point on the WSS plot typically represent?

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Cluster Analysis

Finding Optimal Number of Clusters Using WSS