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Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters).

Source: Wikipedia

Association rule learning is a method for discovering interesting relations between variables in large databases.

Source: Wikipedia

So both, clustering and association rule mining (ARM), are in the field of unsupervised machine learning. Clustering is about the data points, ARM is about finding relationships between the attributes of those datapoints.

However, I wonder if there are more relationships. For example, given a clustering, can this enhance / simplify ARM or vice versa?

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First of all, the problem of finding frequent itemsets (ARM) differs from the similarity search (clustering).

If you think about market baskets, clustering tries to find objects that have a large fraction of their baskets in common, the absolute number of those objects (basket occurences) is not of interest. With ARM we are interested in the absolute number of baskets that contain a particular set of items.

CLustering: Allocates objects in such a way that objects in the same group (called a cluster) are more similar (given a distance metric) to each other than to those in other groups (clusters).

ARM: Given many baskets (could be actual supermarket baskets) find which items inside a basket predict another item in the basket.

Sources

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The paper

Marie Plasse et al: Combined use of association rules mining and clustering methods to find relevant links between binary rare attributes in a large data set. Link

combines both, clustering and association rule mining. They could improve ARM by association rule mining. From the abstract:

A method to analyse links between binary attributes in a large sparse data set is proposed. Initially the variables are clustered to obtain homogeneous clusters of attributes. Association rules are then mined in each cluster. A graphical comparison of some rule relevancy indexes is presented. It is used to extract best rules depending on the application concerned. The proposed methodology is illustrated by an industrial application from the automotive industry with more than 80 000 vehicles each described by more than 3000 rare attributes.

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