K-means clustering

Definition

k-means clustering is an unsupervised machine learning algorithm used to partition a dataset into k distinct, non-overlapping groups or clusters based on feature similarities. The algorithm works by iteratively assigning data points to clusters and updating the cluster centroids, aiming to minimize the variance within each cluster and maximize the variance between clusters. This method is widely applied in data analysis, pattern recognition, and market segmentation.

5 Must Know Facts For Your Next Test

1. The k-means algorithm requires the user to specify the number of clusters (k) beforehand, which can significantly influence the outcome.
2. The algorithm initializes with random centroids, which can lead to different results on different runs; this is why multiple iterations are often run.
3. k-means is sensitive to outliers because they can skew the position of the centroids, leading to less accurate clustering.
4. The convergence of k-means occurs when the assignments of data points to clusters no longer change between iterations.
5. A common method for determining the optimal number of clusters (k) is the 'Elbow Method,' where you plot the explained variance as a function of k and look for a point where the increase rate slows down.

Review Questions

• How does the k-means algorithm determine the optimal assignment of data points to clusters?
  • The k-means algorithm determines optimal assignments by calculating the distance from each data point to the centroids of each cluster. Data points are assigned to the cluster whose centroid is closest, minimizing within-cluster variance. The algorithm iteratively updates both the assignments and the centroids until there are no further changes in assignments, indicating convergence.
• Discuss how the choice of k impacts the results of k-means clustering and how it can be effectively determined.
  • The choice of k directly affects how well data points are grouped into meaningful clusters. If k is too low, distinct patterns may be lost; if too high, noise may be introduced as separate clusters. The Elbow Method is commonly used to find an optimal k by plotting explained variance against different values of k and identifying the point where adding more clusters yields diminishing returns in variance explained.
• Evaluate the strengths and limitations of using k-means clustering in data analysis compared to other clustering methods.
  • K-means clustering is efficient and easy to implement, making it a popular choice for large datasets. However, its reliance on Euclidean distance can be limiting when dealing with non-spherical clusters or varying cluster sizes. Unlike hierarchical clustering, which creates a full dendrogram representation, k-means provides a fixed number of clusters without insight into their relationships. Additionally, sensitivity to outliers poses challenges in datasets with extreme values or noise.

Related terms

Centroid: The central point of a cluster, representing the average position of all the points within that cluster.

Euclidean Distance: A measure used to determine the distance between two points in a multi-dimensional space, commonly used in clustering algorithms.

Hierarchical Clustering: An alternative clustering method that builds a hierarchy of clusters either by progressively merging smaller clusters or splitting larger ones.