Description: The K-means algorithm is a clustering technique that aims to partition a set of n observations into k clusters, where each observation is assigned to the cluster whose mean is closest. This method is based on minimizing the variance within each cluster, meaning it tries to group the data in such a way that the elements within each group are as similar as possible to each other, while the groups themselves are as different as possible. K-means is an iterative algorithm that starts with the random selection of k centroids, which are the central points of each cluster. It then assigns each observation to the cluster whose centroid is closest, recalculates the centroids based on the new assignments, and repeats this process until the cluster assignments no longer change or a maximum number of iterations is reached. This algorithm is widely used in various fields such as computer vision, data analysis, and data mining for tasks such as image segmentation, market analysis, and document clustering. Its simplicity and efficiency make it a popular tool; however, its performance can be affected by the choice of the number of clusters and the initialization of the centroids.
History: The K-means algorithm was first proposed by statistician Hugo Steinhaus in 1956, although its popularity grew in the 1960s with the work of James MacQueen, who formalized the algorithm and made it more accessible for use in data analysis. Since then, it has been the subject of numerous research studies and improvements, including variations that address its limitations, such as sensitivity to centroid initialization and the choice of the number of clusters.
Uses: K-means is used in various applications, such as image segmentation, data compression, market analysis, and document clustering. In computer vision, it is particularly useful for identifying patterns and features in images, enabling automatic object classification and image quality enhancement.
Examples: A practical example of K-means is the segmentation of an image into different regions, such as sky, land, and vegetation, where each region is grouped based on color and texture characteristics. Another example is identifying customer groups in market analysis, where they are clustered based on their purchasing preferences.
