K- Means using Silhouette Method

Interpreting the K-Means Clustering Results

1. Understanding Silhouette Scores and Cluster Quality

• The Silhouette Score measures how well-separated clusters are.

• Higher scores indicate clearer, more distinct clusters, while lower scores suggest overlapping or poorly separated clusters.

• The three best k values (determined by the Silhouette Method) represent cluster numbers that maximize separation and internal consistency.

2. Interpretation of Clusters for Your Dataset

• If the dataset has features related to anxiety severity, lifestyle factors, or health indicators, then clusters may represent different groups of people with similar characteristics.

• For example, if clustering is done on PCA-reduced data, clusters might indicate:

  • Cluster 1: High stress, poor sleep, high anxiety levels.

  • Cluster 2: Moderate anxiety, average physical activity, balanced lifestyle.

  • Cluster 3: Low anxiety, good sleep patterns, active lifestyle.

• If the dataset includes medical or psychological factors, clusters may reveal risk groups for anxiety disorders or treatment effectiveness patterns.

3. Impact of Different k Values

• Lower k values (e.g., k=2 or k=3):

  • Clusters are broad and may mix individuals with different characteristics.

  • Can be useful for high-level segmentation (e.g., high anxiety vs. low anxiety groups).

• Higher k values (e.g., k=6 or k=7):

  • More granular segmentation but might lead to overfitting or artificial clusters.

  • Can be useful for detailed subgroup analysis (e.g., students with mild anxiety vs. professionals with severe anxiety).

4. Evaluating Cluster Centroids

• The red centroids in the plots represent the center of each cluster, indicating the average feature values for that group.

• Analyzing the centroids can provide insights such as:

  • If a cluster’s centroid has low sleep hours but high stress levels, it may represent a high-risk group for anxiety.

  • If a centroid shows high caffeine intake and high heart rate, it may indicate lifestyle factors affecting anxiety severity.

5. How This Helps in Your Study

• Personalized Interventions: If clusters show distinct groups with varying anxiety levels, targeted mental health interventions can be designed.

• Feature Importance Analysis: Looking at the variables that define each cluster can help identify key factors influencing anxiety.

• Predictive Analysis: If labels (e.g., anxiety severity) are reintroduced, clustering results can be validated against known anxiety levels.

Comparing Dendrogram Results to K-Means Clustering Results

1. Cluster Structure and Shape

   • K-Means assumes clusters are spherical and evenly distributed, making it suitable for well-separated and compact clusters.

   • Hierarchical Clustering (Dendrogram) does not assume cluster shapes, allowing for more flexibility in detecting clusters of arbitrary shapes.

2. Determining the Number of Clusters

   • K-Means requires specifying the number of clusters (k) beforehand, often determined using methods like the Silhouette Score or Elbow Method.

   • Hierarchical Clustering provides a dendrogram, which visually represents how clusters merge, allowing more flexibility in deciding the optimal number of clusters.

3. Interpretability

   • Dendrograms provide hierarchical relationships, allowing us to see how clusters are nested and how merging occurs at different levels.

   • K-Means does not provide hierarchical relationships and strictly partitions the dataset into k fixed clusters.

4. Scalability and Performance

   • K-Means is computationally efficient, making it suitable for large datasets as it scales linearly with the number of data points.

   • Hierarchical Clustering is computationally expensive (O(n²) complexity), making it impractical for large datasets but useful for smaller, well-structured data.

5. Handling of Outliers and Noise

   • K-Means is sensitive to outliers, as extreme values can significantly impact centroid positions.

   • Hierarchical Clustering can be affected by noise, but methods like Ward’s linkage help mitigate some of its sensitivity to extreme values.

Comparison of DBSCAN, K-Means, and Hierarchical Clustering Results

1. Cluster Shape and Structure

   • K-Means assumes spherical clusters and works well for evenly distributed clusters of similar sizes.

   • Hierarchical Clustering allows for arbitrary shapes but merges clusters based on linkage criteria, which may not always align with natural groupings.

   • DBSCAN is ideal for clusters of varying shapes and densities, as it groups together dense regions while identifying outliers as noise.

2. Determining the Number of Clusters

   • K-Means requires the number of clusters (k) to be predefined, which can be optimized using the Silhouette Score or Elbow Method.

   • Hierarchical Clustering suggests the number of clusters visually through a dendrogram, making it more flexible in determining optimal cluster counts.

   • DBSCAN automatically determines the number of clusters, depending on the density threshold parameters (eps and min_samples), removing the need to predefine k.

3. Handling Outliers and Noise

   • K-Means is highly sensitive to outliers, as extreme points can distort centroid positions.

   • Hierarchical Clustering also struggles with noise, but linkage methods (e.g., Ward’s method) can help reduce the impact.

   • DBSCAN is robust to noise and explicitly classifies outliers, as seen in the blue points in the DBSCAN plot representing noise points outside the main clusters.

4. Cluster Compactness and Overlap

   • K-Means forces all points into clusters, even if they do not belong to any natural grouping.

   • Hierarchical Clustering provides a structured view, but its cluster boundaries may not always be distinct.

   • DBSCAN forms clusters based on density, which can be seen in the plot as most points forming one large cluster, with only a few outliers detected.

5. Scalability and Computational Cost

   • K-Means is the most scalable and computationally efficient, making it suitable for large datasets.

   • Hierarchical Clustering is computationally expensive, especially for large datasets, as it has a complexity of O(n²).

   • DBSCAN performs well with large datasets but can struggle with high-dimensional data when selecting eps and min_samples.

6. Final Insights

   • K-Means provided distinct and well-separated clusters, though it required manual selection of k.

   • Hierarchical Clustering revealed hierarchical relationships, but the cluster structure was not as clear-cut as K-Means.

   • DBSCAN successfully identified noise and outliers, making it a good choice for datasets with non-spherical clusters and varying densities.

Conclusion

Key Insights from Clustering Analysis on Anxiety Data

1. Distinct Anxiety Profiles Exist

   • The K-Means clustering revealed that individuals could be grouped based on stress levels, sleep patterns, and activity levels.

   • High-stress clusters correlated with poor sleep and high caffeine intake, while low-stress clusters showed better sleep and balanced lifestyles.

2. Outlier and Noise Detection with DBSCAN

   • DBSCAN successfully identified outliers, which could represent individuals with extreme anxiety symptoms or unique lifestyle factors that do not fit typical patterns.

   • This suggests that some cases of anxiety may not fit into generalized clusters, highlighting the complexity of mental health factors.

3. Hierarchical Clustering Confirms Natural Grouping

   • The dendrogram structure showed that different levels of anxiety and lifestyle behaviors could be grouped naturally, supporting the idea that anxiety severity is influenced by multiple overlapping factors.

4. Strong Associations Between Lifestyle and Anxiety

   • The association rule mining (ARM) results indicated that specific behavioral patterns, such as caffeine intake and sleep quality, were highly associated with stress and anxiety severity.

   • For example, moderate to high caffeine intake was frequently linked to disrupted sleep and higher stress levels.

5. The Importance of Multidimensional Analysis

   • The PCA analysis revealed that only a few key features contribute most of the variance in the data, confirming that certain lifestyle factors disproportionately influence anxiety.

   • Reducing the dataset to 3D still retained over 24% of the variance, suggesting that complex anxiety patterns require more than just a few variables to fully understand.

CODE

Link to the Code