K-means clustering

Definition

K-means clustering is an unsupervised machine learning algorithm that partitions a dataset into k distinct clusters based on feature similarity. Each cluster is represented by its centroid, which is the mean of all data points within that cluster. The algorithm iteratively assigns data points to the nearest centroid and recalculates the centroids until convergence. Normalization and standardization are essential preprocessing steps for this method, as they ensure that all features contribute equally to the distance calculations, while other clustering methods, such as density-based clustering, focus on the distribution and density of data points rather than fixed centroids.

5 Must Know Facts For Your Next Test

1. The k-means algorithm requires the user to specify the number of clusters (k) before running, which can significantly affect the results.
2. The algorithm works best when clusters are spherical and evenly sized, as it relies on calculating distances from centroids.
3. K-means can be sensitive to outliers, which can distort the position of centroids and lead to poor clustering performance.
4. Convergence occurs when no data points change their assigned cluster or when centroids no longer move significantly between iterations.
5. Elbow method is a popular technique used to determine the optimal number of clusters by plotting the explained variance against different values of k.

Review Questions

• How does data normalization and standardization impact the performance of k-means clustering?
  • Normalization and standardization are crucial for k-means clustering because they ensure that all features contribute equally to the distance calculations. If features have different scales, such as height in centimeters and weight in kilograms, those with larger ranges can disproportionately influence the placement of centroids. By normalizing or standardizing the data, you can achieve more accurate clustering results since each feature will be treated with equal importance.
• Compare k-means clustering with density-based clustering methods, highlighting their key differences and use cases.
  • K-means clustering is centered around partitioning data into fixed-size clusters based on distance from centroids, making it suitable for datasets with well-separated spherical clusters. In contrast, density-based clustering methods like DBSCAN group points based on the density of data points in a region, effectively identifying clusters of varying shapes and sizes while also detecting outliers. This makes density-based methods more versatile for real-world applications where clusters may not conform to spherical shapes.
• Evaluate the effectiveness of different techniques used to determine the optimal number of clusters (k) for k-means clustering, considering their strengths and weaknesses.
  • Determining the optimal number of clusters for k-means can be approached using several techniques like the Elbow method, Silhouette score, or Gap statistic. The Elbow method visually assesses variance explained versus different k values but may be subjective as it's based on visual inspection. The Silhouette score provides a quantitative measure of how similar an object is to its own cluster compared to others but may not always indicate a clear 'best' k. The Gap statistic compares total intra-cluster variation for different values of k against a reference null distribution. While effective, it can be computationally intensive. Each technique has its strengths and weaknesses, so it’s often beneficial to use multiple methods for validation.

Related terms

Centroid: The central point of a cluster in k-means clustering, calculated as the mean of all data points in that cluster.

Euclidean Distance:

A measure of the straight-line distance between two points in Euclidean space, commonly used to determine similarity between data points in clustering.

DBSCAN: A density-based clustering algorithm that groups together points that are closely packed together while marking points in low-density regions as outliers.