Order Preserving Data Mining

Data mining has emerged over the last decade as probably the most important application in databases. To reproduce one of the most popular but accurate definitions for data mining; “it is the process of nontrivial extraction of implicit, previously unknown and potentially useful information (such as rules, constraints and regularities) from massive databases” (Piatetsky-Shapiro & Frawley 1991). In practice data mining can be thought of as the “crystal ball” of businessmen, scientists, politicians and generally all kinds of people and professions wishing to get more insight on their field of interest and their data. Of course this “crystal ball” is based on a sound and broad scientific basis, using techniques borrowed from fields such as statistics, artificial intelligence, machine learning, mathematics and database research in general among others. Applications of data mining range from analyzing simple point of sales transactions and text documents to astronomical data and homeland security (Data Mining and Homeland Security: An Overview). Usually different applications may require different data mining techniques. The main kinds of techniques that are used in order to discover knowledge from a database are categorized into association rules mining, classification and clustering, with association rules being the most extensively and actively studied area. The problem of finding association rules can be formulated as follows: Given a large data base of item transactions, find all frequent itemsets, where a frequent itemset is one that occurs in at least a userspecified percentage of the data base. In other words find rules of the form X?Y, where X and Y are sets of items. A rule expresses the possibility that whenever we find a transaction that contains all items in X, then this transaction is likely to also contain all items in Y. Consequently X is called the body of the rule and Y the head. The validity and reliability of association rules is expressed usually by means of support and confidence. An example of such a rule is {smoking, no_workout?heart_disease (sup=50%, conf=90%)}, which means that 90% of the people that smoke and do not work out present heart problems, whereas 50% of all our people present all these together. Nevertheless the prominent model for contemplating data in almost all circumstances has been a rather simplistic and crude one, making several concessions. More specifically objects inside the data, like for example items within transactions, have been attributed a Boolean hypostasis (i.e. they appear or not) with their ordering being considered of no interest because they are considered altogether as sets. Of course similar concessions are made in many other fields in order to come to a feasible solution (e.g. in mining data streams). Certainly there is a trade off between the actual depth and precision of knowledge that we wish to uncover from a database and the amount and complexity of data that we are capable of processing to reach that target. In this work we concentrate on the possibility of taking into consideration and utilizing in some way the order of items within data. There are many areas in real world applications and systems that require data with temporal, spatial, spatiotemporal or ordered properties in general where their inherent sequential nature imposes the need for proper storage and processing. Such data include those collected from telecommunication systems, computer networks, wireless sensor networks, retail and logistics. There is a variety of interpretations that can be used to preserve data ordering in a sufficient way according to the intended system functionality.