Which of the following are common clustering algorithms?

K-means is indeed a common clustering algorithm used in data analysis and machine learning. It operates by partitioning a dataset into K distinct, non-overlapping subsets (or clusters), where each data point belongs to the cluster with the nearest mean. This algorithm is popular due to its simplicity and efficiency, especially when dealing with a large number of observations.

K-means requires the user to specify the number of clusters (K) in advance, which can be a drawback. Nonetheless, it works well with spherical-shaped clusters and is widely used in various applications, such as customer segmentation and image compression.

In addition to K-means, there are other widely recognized clustering algorithms. Density-based and spectral clustering techniques also play significant roles in the field, alongside hierarchical clustering methods. Each of these algorithms brings unique strengths and weaknesses in terms of the types of data they can handle and their computational requirements.

Thus, while K-means is one of the foundational and commonly utilized clustering algorithms, it's important to recognize that it exists alongside several other key methodologies.