The correct answer is D. 1, 2 and 4.
K-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells.
K-means clustering is a simple, efficient, and widely used algorithm for clustering data points. However, it has some limitations. One limitation is that it can give poor results when the data points have outliers, data points with different densities, or data points with non-convex shapes.
Outliers are data points that are very different from the other data points in the dataset. K-means clustering can be sensitive to outliers, and can often assign outliers to the wrong cluster.
Data points with different densities can also cause problems for K-means clustering. If the data points are not evenly distributed, K-means clustering can sometimes assign data points to clusters that are not very close to them.
Data points with non-convex shapes can also be problematic for K-means clustering. K-means clustering is designed to find clusters that are convex, meaning that they are made up of data points that are all on the same side of a line. However, if the data points have non-convex shapes, K-means clustering can sometimes assign data points to clusters that are not very well-defined.
In conclusion, K-means clustering is a simple and efficient algorithm for clustering data points. However, it has some limitations, and can give poor results when the data points have outliers, data points with different densities, or data points with non-convex shapes.