Breathing KMeans vs KMeans

Breathing KMeans improves upon traditional KMeans clustering by dynamically adding centroids near high-error clusters (breathe-in) and removing low-utility centroids that are too close together (breathe-out). This iterative approach eliminates the need for multiple random initializations, reducing runtime by up to 50% while producing more accurate clustering results. The algorithm is available as an open-source Python library with a scikit-learn-like API.