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Data Science and Machine Learning

How to Define the Number and Types of Clustering (2): Using Data Methods to Find a Reasonable Number of Clusters

2026-05-22

How to Define the Number and Types of Clustering (2): Using Data Methods to Find a Reasonable Number of Clusters
Clustering is an unsupervised learning method used to automatically discover natural groupings among similar data points when the data has no predefined labels. It groups data points based on similarity or distance, placing similar items into the same group. Common examples include customer segmentation, user behavior analysis, and content classification. The course material also explains that clustering discovers natural groupings in data based on similarity.

When defining the number of clusters, we should not rely only on intuition. A more reliable approach is to combine business objectives with data-driven methods. For example, we first clarify the purpose of the analysis, then use methods such as the Elbow Method and Silhouette Score to identify a more reasonable K value.

For K-means, K represents the number of clusters we want to divide the data into. The algorithm then assigns each data point to the nearest centroid based on distance.

About the purpose of the analysis, more detail please see How to Define the Number and Types of Clustering (1) - Building Segmentation Hypotheses with Business Logic

Method 1: Elbow Method

Elbow Method is a method used to help us decide how many clusters K-means should divide the data into, which is the K value.

Because K-means requires us to specify K in advance, and one of the limitations of K-means is that it is not easy to identify the correct K value, the Elbow Method is commonly used as a supporting method. The Elbow Method mainly observes whether the within-cluster error decreases significantly under different K values. When K increases, the data points within each cluster usually become more concentrated, and the error typically decreases. However, when the rate of decrease begins to slow down, that turning point looks like an elbow, so it is called the elbow point.

For example, after understanding the business context, we may identify around 4–5 candidate user groups. Therefore, we can test from K = 2 to K = 6.

What does the Elbow Method look at?

K ValueClustering Interpretation
K = 2Too broad; can only roughly separate high-activity and low-activity users
K = 3Starts to reveal major behavioral differences
K = 4Clusters become clearer
K = 5Can correspond to a more complete set of business user types
K = 6May start to over-segment, increasing the cost of business interpretation

If the error does not decrease much after K=5, then K=5 can be considered as one candidate number of clusters.

How should we interpret the Elbow Method score?

The core idea of the Elbow Method is:

When K increases, the clustering error decreases. However, after a certain point, adding more clusters brings only very small improvement. This turning point looks like an elbow, so it is called the Elbow.

Simply put, it helps us find:

The point where adding more clusters no longer brings much benefit.

For example:

KInertia / Error
11000
2650
3420
4280
5250
6240

You can see that the error drops significantly from K=1 to K=4, but after K=5 and K=6, the improvement becomes much smaller.

elbow_method_k_inertia.png

This means:

K=4 may be a reasonable candidate, because adding more clusters does not bring much additional benefit.

Method 2: Silhouette Score

Silhouette Score is another method used to determine how many clusters K-means should select.

If the Elbow Method looks at whether the error still decreases significantly when K increases, then the Silhouette Score looks at:

Whether the resulting clusters are clear and well separated.

Silhouette Score checks:

  1. Whether users within the same cluster are similar
  2. Whether different clusters are sufficiently separated

What does Silhouette Score look at?

Check ItemMeaning
Whether users within the same cluster are similarWhether users inside the cluster have similar behavior
Whether different clusters are separatedWhether different clusters have clear differences

Simply put:

Good clustering should mean that users within the same cluster are very similar, while users in different clusters are very different.

How should we interpret Silhouette Score?

Silhouette Score usually ranges from -1 to 1.

ScoreInterpretation
Close to 1Good clustering; users within a cluster are similar, and clusters are well separated
Close to 0Cluster boundaries are unclear; some users may be difficult to assign to a clear group
Less than 0Possible incorrect clustering; users may be closer to another cluster

For example:

KSilhouette Score
20.42
30.51
40.58
50.55
60.48
output.png

In this example, K=4 has the highest score, so K=4 is a reasonable candidate.

In practice, the K value should not be decided by a single method alone. The Elbow Method can first be used to narrow down the reasonable range of K values by identifying where the improvement starts to slow down after adding more clusters. Then, the Silhouette Score can be used to compare the clarity of different clustering results and confirm which clustering result best achieves “high similarity within clusters and clear separation between clusters.”

Final Considerations: Reasonable Cluster Number and Business Segments

Finally, we still need to apply UX / Business judgment to make sure every cluster can be named, understood, and translated into a concrete product strategy.

If the data methods suggest that K=4 is more reasonable, but the initial business logic defined 5 user types, this means that among the original 5 business hypotheses, two groups may behave too similarly in the actual data and should be merged. Alternatively, although K=5 may have a slightly lower mathematical score, it may still have business value and can be kept as a strategic segmentation choice.

Scenario 1: K=4 Is the Most Reasonable Choice Based on Data

Assume the Elbow Method shows a clear turning point at K=4, and the Silhouette Score is also highest at K=4. This suggests that the data naturally forms 4 clearer groups.

The original business logic defined 5 groups:

Business Logic 5 GroupsPossible Data Result
Highly Active Loyal UsersForms an independent cluster
Medium-active Potential UsersMay overlap with Content Browsers
Deal-oriented UsersForms an independent cluster
Content BrowsersMay overlap with Medium-active Potential Users
Low-activity / Churn-risk UsersForms an independent cluster

In this case, they can be merged into 4 groups:

Final K=4 SegmentExplanation
Highly Active Loyal UsersHigh sessions, high PV, high interaction
Medium-active Content-potential UsersUse the app regularly and mainly browse content, but still have room to improve interaction
Deal-oriented UsersJetso / Reward clicks are significantly higher
Low-activity / Churn-risk UsersLow sessions and high last-visit days

This means merging the original:

Medium-active Potential Users + Content Browsers

into:

Medium-active Content-potential Users

because, in the data, they may both represent users who “have some usage behavior but have not yet developed deep interaction.”

Scenario 2: The Business Still Wants to Keep 5 Groups

If the Silhouette Score of K=5 is only slightly lower than K=4, for example:

KSilhouette ScoreBusiness Interpretation
40.56Clearest from a data perspective
50.53Still acceptable, and better aligned with operational strategy
60.45Starts to over-segment

In this case, K=5 can be selected, but there must be a clear reason.

Although K=4 is slightly better in mathematical metrics, K=5 can more clearly distinguish “Medium-active Potential Users” from “Content Browsers.” If these two user groups correspond to different product strategies, then K=5 may have greater business action value.

For example:

K=5 SegmentStrategic Difference
Medium-active Potential UsersUse missions, check-ins, and personalized recommendations to increase usage frequency
Content BrowsersUse related content, AI Search, save features, and topic follow to improve content exploration

If the two groups require different actions, then keeping K=5 is reasonable.

Decision Principles

You can decide whether to keep K=5 by asking three questions:

Decision QuestionIf the Answer Is Yes
Is the clustering clarity of K=5 still acceptable?Consider K=5
Does the 5th segment have enough user volume?It can be kept
Does the 5th segment require a different product / marketing strategy?It can be kept

If the 5th segment is only a very small technical split in the data, has too few users, and shares a similar strategy with another segment, then it is better to return to K=4.

Conclusion

If the Elbow Method and Silhouette Score show that K=4 is a more reasonable number of clusters, but the initial business logic defined 5 user types, it means the original business classification still needs to be validated by data.

The right approach is not to force the 5 groups to remain. Instead, compare the clustering results of K=4 and K=5. If K=4 produces clearer clusters, and two groups are highly similar in behavior, they should be merged. For example, “Medium-active Potential Users” and “Content Browsers” can be merged into “Medium-active Content-potential Users.”

On the other hand, if K=5 has a slightly lower mathematical score but each group has enough user volume, can be clearly named, and corresponds to different product or operational strategies, then K=5 can still be considered a reasonable choice.

The final K value should balance:

Data clarity and business actionability.

Related Article

How Clustering Supports UX and Product Design: From User Segmentation to Product Strategy

How to Define the Number and Types of Clustering (1): Using Data Methods to Find a Reasonable Number of Clusters