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The goal of this paper is to show that generalizing the notion of support can be useful in extending association analysis to non-traditional types of patterns and non-binary data. To that end, we describe a framework for generalizing support that is based on the simple, but useful observation that support can be viewed as the composition of two functions: a function that evaluates the strength or presence of a pattern in each object (transaction) and a function that summarizes these evaluations with a single number. A key goal of any framework is to allow people to more easily express, explore, and communicate ideas, and hence, we illustrate how our support framework can be used to describe support for a variety of commonly used association patterns, such as frequent itemsets, general Boolean patterns, and error-tolerant itemsets. We also present two examples of the practical usefulness of generalized support. One example shows the usefulness of support functions for continuous data. Another example shows how the hyperclique pattern---an association pattern originally defined for binary data---can be extended to continuous data by generalizing a support function.