The K-means algorithm is a popular unsupervised machine learning technique used for clustering data into groups or clusters based on similarities in the feature space. It aims to partition the data into K clusters where each data point belongs to the cluster with the nearest mean, serving as the prototype of the cluster.
Here's how the K-means algorithm works :
* Initialization : The algorithm begins by randomly initializing K cluster centroids in the feature space. These centroids represent the initial guess for the centers of the clusters.
* Assignment Step : In this step, each data point is assigned to the nearest centroid based on a distance metric, typically Euclidean distance. The data points are then grouped into K clusters based on their assignments to centroids.
* Update Step : After assigning data points to clusters, the centroids of the clusters are recalculated as the mean of all data points assigned to each cluster. These recalculated centroids become the new centroids for the next iteration.
* Iteration : Steps 2 and 3 are repeated iteratively until convergence, which occurs when the centroids no longer change significantly between iterations or when a maximum number of iterations is reached.
* Convergence : Once the algorithm converges, each data point is assigned to the cluster with the nearest centroid, and the final cluster centroids represent the centers of the clusters.
The K-means algorithm aims to minimize the within-cluster sum of squared distances, also known as inertia or distortion. It does this by iteratively optimizing the cluster centroids to minimize the distance between data points and their assigned centroids.
Key considerations and limitations of the K-means algorithm include :* The algorithm is sensitive to the initial placement of centroids, which can affect the final clustering results. Different initializations may lead to different clustering outcomes.
* K-means assumes clusters of approximately equal size and density, spherical shapes, and similar variance within clusters. It may not perform well on non-linear or irregularly shaped clusters.
* The choice of the number of clusters (K) is critical and often requires domain knowledge or heuristic approaches such as the elbow method or silhouette analysis.
* K-means is computationally efficient and scalable to large datasets but may struggle with high-dimensional data or data with varying cluster densities.
