Let D = (O,I,R) be a data mining context where O and I are finite sets of objects (transactions) and items respectively. ? ? ? x ? is a binary relation between objects and items. For O ? O, and I ? I, we define: f(O): 2O ? 2If(O) = (i? I | ?o ? O, (o,i) ? R} g(I): 2I ? 2Og(I) = (o? O | ?i ? I, (o,i) ? R} f(O) associates with O the items common to all objects o ? O and g(I) associates with I the objects related to all items i ? I. The operators h = f o g in 2I and h’ = g o f in 2O are Galois closure operators. An itemset C ? I from D is a closed itemset iff h(C) = C.
Published in Chapter:
Mining Frequent Closed Itemsets for Association Rules
Anamika Gupta (University of Delhi, India), Shikha Gupta (University of Delhi, India), and Naveen Kumar (University of Delhi, India)
Copyright: © 2009
|Pages: 10
DOI: 10.4018/978-1-60566-242-8.ch057
Abstract
Association refers to correlations that exist among data. Association Rule Mining (ARM) is an important data-mining task. It refers to discovery of rules between different sets of attributes/items in very large databases (Agrawal R. & Srikant R. 1994). The discovered rules help in strategic decision making in both commercial and scientific domains. A classical application of ARM is market basket analysis, an application of data mining in retail sales where associations between the different items are discovered to analyze the customer’s buying habits in order to develop better marketing strategies. ARM has been extensively used in other applications like spatial-temporal, health care, bioinformatics, web data etc (Han J., Cheng H., Xin D., & Yan X. 2007).