Explica en detalle el algoritmo de K-Medias (K-Means) en el ambito de Machine Learning.

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K-Means is a fundamental clustering algorithm in machine learning. It groups data into K clusters, where K is chosen beforehand. The algorithm works by finding cluster centers called centroids and assigning each data point to the nearest centroid. Here we see a dataset that we want to partition into 3 clusters. The first step in K-Means is initialization. We start by choosing the number of clusters K, which in our example is 3. Then we randomly place K centroids in the data space. These centroids are the initial cluster centers, shown here as larger colored dots. The placement is random, so different initializations can lead to different final results. In the assignment step, we calculate the distance from each data point to every centroid. Each point is then assigned to the cluster of its nearest centroid. We can see the distance lines connecting points to centroids. Points are colored according to their assigned cluster - red points belong to the red centroid, blue points to the blue centroid, and green points to the green centroid. In the update step, we recalculate the position of each centroid. The new centroid position is the mean or average of all points assigned to that cluster. We can see the old centroids as faded dots and the new centroids as bright dots. The arrows show how each centroid moves to better represent its cluster. This movement minimizes the total distance from points to their centroids. The algorithm repeats the assignment and update steps until convergence. Convergence occurs when centroids stop moving significantly between iterations. The final result shows well-separated clusters with each centroid positioned at the center of its cluster. The colored circles represent the final cluster boundaries. K-Means has successfully partitioned our data into three distinct groups, minimizing the total within-cluster variance.