Two CIA agents, Tuck and Frank who are also best friends, have been benched because someone's after them. Tuck is divorced with a son whom he's not close to and Frank is a ladies man. Tuck decides to try and find someone so he places his profile on a dating website. Lauren, a woman also looking for a guy sees Tuck's profile and goes with him. She later bumps into Frank and he hits on her and she goes out with him. She's intrigued by both of them. When they learn that they're dating the same girl, they agree to let her choose. But both can't help but use their skills to keep tabs on her and each other. And also sabotage each other's dates with her. Written by rcs0411@
It was proven   that the relaxed solution of k -means clustering, specified by the cluster indicators, is given by principal component analysis (PCA), and the PCA subspace spanned by the principal directions is identical to the cluster centroid subspace. The intuition is that k-means describe spherically shaped (ball-like) clusters. If the data has 2 clusters, the line connecting the two centroids is the best 1-dimensional projection direction, which is also the first PCA direction. Cutting the line at the center of mass separates the clusters (this is the continuous relaxation of the discrete cluster indicator). If the data have three clusters, the 2-dimensional plane spanned by three cluster centroids is the best 2-D projection. This plane is also defined by the first two PCA dimensions. Well-separated clusters are effectively modeled by ball-shaped clusters and thus discovered by K-means. Non-ball-shaped clusters are hard to separate when they are close. For example, two half-moon shaped clusters intertwined in space do not separate well when projected onto PCA subspace. But k-means should not be expected to do well on this data. However, PCA's being a useful relaxation of k-means clustering was not a new result,  and it is straightforward to produce counterexamples to the statement that the cluster centroid subspace is spanned by the principal directions.