Handling of Numeric Ranges for Graph-Based Knowledge Discovery

Nowadays, graph-based knowledge discovery algorithms do not consider numeric attributes (they are discarded in the preprocessing step, or they are treated as alphanumeric values with an exact matching criterion), with the limitation to work with domains that do not have this type of attribute or finding patterns without numeric attributes. In this work, we propose a new approach for the numerical attributes handling for graphbased learning algorithms. Our approach shows how graph-based learning approaches increase their accuracy for the classification task and its descriptive power when they are able to use both nominal and numerical attributes. This new approach was tested with the Subdue system in the mutagenesis and PTC domains showing an accuracy increase around 16% compared to Subdue when it does not use our numerical attributes handling algorithm. In some research areas such as data mining and machine learning, the domain data representation is a fundamental aspect that determines in great measure the quality of the results of the discovery process. Depending on the domain, the Data Mining process analyzes a data collection (such as flat files, log files, relational databases, etc.) to discover patterns, relationships, rules, associations, or useful exceptions to be used for decision making processes and for the prediction of events and/or concept discovery. Graph based algorithms have been used for years to describe (in a natural way) flat, sequential, and structural domains with acceptable results (Gonzalez, Holder, and Cook 2002), (Ketkar, Holder, and Cook 2005). Some of these domains contain important numeric attributes (attributes with continuous values). Domains with continuous values are not appropriately manipulated by graph based knowledge discovery systems, although they can be appropriately represented. To the best of our knowledge there does not exist a graph based knowledge discovery algorithm that deals with continuous valued attributes. A solution proposed in the literature to approach this problem is the use of discretization techniques as a preprocessing or post-processing step but not at the knowledge discovery phase. However, we think that these techniques do not use all the available knowledge that can be taken adCopyright c © 2010, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. vantage of during the processing phase. Adding this capacity to graph-based algorithms will allow us improving the work with numeric attributes and in this way we will be able to improve the classification accuracy for the classification task and the patterns descriptive power. We will then be able to enhance our results for structural domains containing numerical attributes. Handling of Numerical Ranges In this section, we describe the numerical ranges generation algorithm (based on frequency histograms), which calculates distances using any of seven measures (the distance between the values is calculated by any of seven methods). The distances are: a modification to the Tanimoto distance, a modification of the Euclidean distance, a modification to the Manhattan distance, a modification to the Correlation distance, a modification to the Canberra distance, and two new distance measures that we propose. Our algorithm can be seen in figure 1. The algorithm shown in figure 1 works as Figure 1: Numerical Ranges Generation Algorithm follows. The general function (GenerateRange) receives the data set and the number of examples in it. In the first step we sort the numerical attribute in ascending way (Sort function). Next, we create a frequency histogram of the ordered data. Then, we create an initial table of ranges with four fields corresponding to the center of the range, its frequency, and its low and high limits. In this initial ranges table, the center, the low and high limits contain the same value take from the frequencies histogram (GenerateHistogram function). After 156 Proceedings of the Twenty-Third International Florida Artificial Intelligence Research Society Conference (FLAIRS 2010)