The goal of this paper is to show that generalizing the notion of frequent patterns can be useful in extending association analysis to more complex higher order patterns. To that end, we describe a general framework for modeling a complex pattern based on evaluating the interestingness of its sub-patterns. A key goal of any framework is to allow people to more easily express, explore, and communicate ideas, and hence, we illustrate how our framework can be used to describe a variety of commonly used patterns, such as frequent patterns, frequent closed patterns, indirect association patterns, hub patterns and authority patterns. To further illustrate the usefulness of the framework, we also present two new kinds of patterns that derived from the framework: clique pattern and bi-clique pattern and illustrate their practical use.