I am a little confused about the statement on lecture10c_kmeans_annotated page 8: Clusters are forced to be spherical. What's the meaning of spherical and elliptical here? and why clusters are forced to be spherical?
Spherical means the shape if the cluster is a sphere i.e. all points in a given cluster lie inside a sphere, in other words if a point with a given distance d is in some cluster, all points with distance smaller than d (wrt the center of the cluster) will be in the same cluster (this is a huge limitation of k-means and is a direct consequence of its definition ). With GMMs the clusters are elliptical, as a consequence of multivariate gaussian random variables having the essential of their mass in an ellipse centred around the mean with radiuses and directions defined by the eigenvalues and eigenvectors of the covariance matrix.
Lecture 10c Clusters
Hi,
I am a little confused about the statement on lecture10c_kmeans_annotated page 8: Clusters are forced to be spherical. What's the meaning of spherical and elliptical here? and why clusters are forced to be spherical?
Best,
Spherical means the shape if the cluster is a sphere i.e. all points in a given cluster lie inside a sphere, in other words if a point with a given distance d is in some cluster, all points with distance smaller than d (wrt the center of the cluster) will be in the same cluster (this is a huge limitation of k-means and is a direct consequence of its definition ). With GMMs the clusters are elliptical, as a consequence of multivariate gaussian random variables having the essential of their mass in an ellipse centred around the mean with radiuses and directions defined by the eigenvalues and eigenvectors of the covariance matrix.
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