Many clustering models define good clusters as extrema of objective functions. Optimization of these models is often done using an alternating optimization (AO) algorithm driven by necessary conditions for local extrema. We abandon the objective function model in favor of a generalized model called alternating cluster estimation (ACE). ACE uses an alternating iteration architecture, but membership and prototype functions are selected directly by the user. Virtually every clustering model can be realized as an instance of ACE. Out of a large variety of possible instances of non-AO models, we present two examples: 1) an algorithm with a dynamically changing prototype function that extracts representative data and 2) a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions. We illustrate these non-AO instances on three problems: a) simple clustering of plane data where we show that creating an unmatched ACE algorithm overcomes some problems of fuzzy c-means (FCM-AO) and possibilistic c-means (PCM-AO); b) functional approximation by clustering on a simple artificial data set; and c) functional approximation on a 12 input 1 output real world data set. ACE models work pretty well in all three cases.
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