K-means clustering

Definition

K-means clustering is a popular unsupervised machine learning algorithm used to partition a dataset into 'k' distinct, non-overlapping groups based on their features. The algorithm works by assigning data points to the nearest cluster center, which is calculated as the mean of all points in that cluster, and iteratively updates the clusters until convergence. This method is widely used in predictive modeling to discover inherent groupings within data, making it easier to analyze patterns and trends.

5 Must Know Facts For Your Next Test

1. K-means clustering aims to minimize the sum of squared distances between data points and their corresponding cluster centroids.
2. The choice of 'k', or the number of clusters, significantly impacts the results of k-means clustering; selecting an inappropriate 'k' can lead to poor clustering outcomes.
3. The algorithm is sensitive to outliers, which can distort the position of centroids and lead to misleading clusters.
4. K-means clustering requires a pre-defined number of clusters, which can be a limitation if prior knowledge about the data is not available.
5. The algorithm's efficiency can be improved using techniques such as initializing centroids using methods like k-means++, which helps in achieving better convergence.

Review Questions

• How does k-means clustering assign data points to clusters and what role do centroids play in this process?
  • K-means clustering assigns data points to clusters based on their proximity to the centroid of each cluster. Initially, centroids are randomly chosen from the dataset. During each iteration, data points are assigned to the nearest centroid based on a distance metric, usually Euclidean distance. After all points are assigned, the centroids are recalculated as the mean of all points in each cluster. This process continues until there are no changes in assignments, indicating that convergence has been reached.
• Discuss how the Elbow Method helps determine the optimal number of clusters in k-means clustering.
  • The Elbow Method assists in selecting the optimal number of clusters 'k' for k-means clustering by plotting the explained variance or within-cluster sum of squares against different values of 'k'. As 'k' increases, the explained variance will typically increase and level off at a certain point, forming an 'elbow' shape on the graph. The point where the curve starts to flatten indicates that adding more clusters yields diminishing returns in variance explained, suggesting that this is an appropriate choice for 'k'.
• Evaluate the impact of outliers on k-means clustering and propose strategies to mitigate these effects.
  • Outliers can significantly affect k-means clustering by skewing centroids and resulting in misleading cluster assignments. When outliers are included in a cluster, they can pull the centroid away from where most data points are located. To mitigate these effects, preprocessing steps such as outlier detection and removal can be applied before running k-means. Additionally, using robust alternatives like k-medoids or density-based clustering methods may help reduce sensitivity to outliers while providing meaningful groupings.

Related terms

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

Unsupervised Learning: A type of machine learning where models are trained on data without labeled outcomes, allowing the algorithm to identify patterns and structures within the data.

Elbow Method: A technique used to determine the optimal number of clusters 'k' in k-means clustering by plotting the explained variance against the number of clusters and identifying the 'elbow' point.