Tree 2 – Decision Trees for Tree Structured Data

Abstract

Abstract. We present Tree 2 , a new approach to structural classification. This integrated approach induces decision trees that test for pattern occurrence in the inner nodes. It combines state-of-the-art tree mining with sophisticated pruning techniques to find the most discriminative pattern in each node. In contrast to existing methods, Tree 2 uses no heuristics and only a single, statistically well founded parameter has to be chosen by the user. The experiments show that Tree 2 classifiers achieve good accuracies while the induced models are smaller than those of existing approaches, facilitating better comprehensibility.

Cluster-grouping: from subgroup discovery to clustering

“…We have already employed the basic principles of CG in a different domain, tree-structured data (Bringmann and Zimmermann 2005) and the cluster-grouping paradigm could also be extended into the area of logical and relational learning (De Raedt 2008).…”

“…These findings suggest (1) that the robustness of sequential covering algorithms such as RIPPER or CN2 that use beam search, a heuristic technique, may be improved by using CG (2) that it may be advantageous to replace the use of support and confidence in associative classification techniques such as CBA (Liu et al 1998) and CMAR (Li et al 2001) by using correlation measures grounded in statistical theory, (3) that also decision tree approaches, who choose an optimal pattern based on a single attribute, may profit from using CG instead, cf. also our approach to clustering below and the Tree 2 approach of Bringmann and Zimmermann (2005).…”

The Chosen Few: On Identifying Valuable Patterns

“…Due to a less than efficient implementation, the subset selection for the 10% setting on the mushroom data set, which produced 16000+ closed patterns, didn't finish in time and is not reported here. As Table 1 shows even setting σ to quite large values 3 and restricting the result to closed patterns, removing quite some redundancy, the size of the pattern sets are still too large for use by a human expert. It can be observed that reducing the set 2 The JRip implementation of WEKA 3 Other work often reports values of only 1% 191 951 694 1018 6358 2063 15433 4873 17384 ΦQ 5 6 3 3 3 5 2 3 3 ΦI 3 3 3 4 4 3 3 2 6 ΦC 2 2 2 2 2 2 2 2 2 max number blocks 958 1180 266 337 342 258 275 min number patterns 17 21 23 26 19 max number patterns 160 78 71 133 231 161 229 88 141 Table 1.…”

“…As Table 1 shows even setting σ to quite large values 3 and restricting the result to closed patterns, removing quite some redundancy, the size of the pattern sets are still too large for use by a human expert. It can be observed that reducing the set 2 The JRip implementation of WEKA 3 Other work often reports values of only 1% 191 951 694 1018 6358 2063 15433 4873 17384 ΦQ 5 6 3 3 3 5 2 3 3 ΦI 3 3 3 4 4 3 3 2 6 ΦC 2 2 2 2 2 2 2 2 2 max number blocks 958 1180 266 337 342 258 275 min number patterns 17 21 23 26 19 max number patterns 160 78 71 133 231 161 229 88 141 Table 1. Data sets and the size of the according closed pattern sets, the smallest reduced sets for each measure, and the minimum and maximum number patterns for the maximal partition as well as its cardinality.…”

“…A somewhat similar approach to this work is embodied by the KFOIL [7] system, as well as by TREE 2 [3]. The main principle of these approaches is that patterns are constructed while a classifier is built.…”