A 2D dataset has two clusters: one circular and one elongated (high variance in x, low variance in y). K-Means performs poorly. Why would EM/GMM with full covariances handle this better?

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K-Means fails because it cannot handle 2D data; it is designed only for 1D datasets.

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K-Means assumes isotropic (spherical) clusters via Euclidean distance; GMM with full covariance matrices can model elongated, diagonal, or correlated cluster shapes by estimating a full covariance matrix per component.

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GMM automatically determines the optimal K, while K-Means requires K to be specified.

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EM uses more data through bootstrapping, giving it an advantage on small elongated clusters.

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A 2D dataset has two clusters: one circular and one elongated (high variance in ...

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