D () has lower space complexity than the original problem or can be minimized more efficiently.

A natural generalization is to replace this input setP of n points by a setP of n sets inX. The distance from such an input setP P to a setC of centers can then be defined as the distance between the closest point-center pair. This problem is calledk-mean for sets; see e.g.

A natural generalization is to replace this input setP of n points by a setP of n sets inX. The distance from such an input setP P to a setC of centers can then be defined as the distance between the closest point-center pair. This problem is calledk-mean for sets; see e.g.

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Several approaches have been proposed to remedy the edacious nature of archetypal analysis, proposing, e.g.,efficient active-set quadratic programming (Chen etal.,2014),

Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store.

Inparticular,weconsiderthesetting where the time series data onN entities is generated from a Gaussian mixture model with autocorrelations overk clusters inRd. Our main contribution is an algorithm to construct coresets for the maximum likelihood objective for this mixture model.