K-means Clustering Overview

K-means Clustering

• A centroid-based clustering algorithm that aims to divide a dataset into k clusters.
• Goal: Minimize the variance within each cluster.
• Steps:
  • Initialization: Choose k initial centroids randomly or use methods like K-means++ to enhance convergence.
  • Assignment Step: Each data point is assigned to the nearest centroid based on Euclidean distance.
  • Update Step: Recalculate the centroids by taking the mean of all data points assigned to each cluster.
  • Repeat: Iterate the assignment and update steps until the centroids stop changing significantly or a maximum number of iterations is reached.
• Pros: Simple and easy to implement, Efficient for large datasets.
• Cons: Requires the number of clusters k to be known beforehand, Sensitive to initial centroid placement, Works best with spherical clusters with equal variance.

Kernel K-means Clustering

• Extends standard K-means by applying the kernel trick, allowing for the identification of non-linear clusters in high-dimensional spaces.
• Steps:
  • Select a Kernel: Choose a kernel function (e.g., Gaussian, polynomial) to compute the similarity between data points.
  • Transform Data: The algorithm maps the original data into a higher-dimensional feature space using the kernel function.
  • Clustering: Perform standard K-means in the new feature space.
    • Assign data points to the closest cluster centroid based on kernel similarity.
    • Update centroids considering the transformed data.
  • Iterate: Repeat the assignment and update steps until convergence.
• Pros: Can identify complex shapes and non-linear clusters, More flexible than standard K-means due to the kernel choice.
• Cons: Computationally more expensive than K-means, Choice of kernel and its parameters heavily influence results, Still requires the number of clusters k to be specified.

Applications of K-means and Kernel K-means

• Market Segmentation: Grouping customers based on their purchasing behavior.
• Image Segmentation: Clustering pixels according to color and intensity.
• Genomics: Identifying patterns in genetic data.

Conclusion

• K-means is suitable for simple, well-separated, and spherical data.
• Kernel K-means offers higher flexibility for more complex data distributions at a higher computational cost.
• The choice between the two depends on the specific dataset and clustering objectives.