Minimizing size of decision trees for multi-label decision tables

We used decision tree as a model to discover the knowledge from multi-label decision tables where each row has a set of decisions attached to it and our goal is to find out one arbitrary decision from the set of decisions attached to a row. The size of the decision tree can be small as well as very large. We study here different greedy as well as dynamic programming algorithms to minimize the size of the decision trees. When we compare the optimal result from dynamic programming algorithm, we found some greedy algorithms produce results which are close to the optimal result for the minimization of number of nodes (at most 18.92% difference), number of nonterminal nodes (at most 20.76% difference), and number of terminal nodes (at most 18.71% difference).

I. Introduction

NOW a days, multi-label decision tables have gained attention in problem of semantic annotation of images [1], music categorization into emotions [2], functional genomics [3], and text categorization [4]. Furthermore, it is natural to have such data sets in optimization problems such as finding a Hamiltonian circuit with the minimum length in the traveling salesman problem [5], finding nearest post office in the post office problem [5]; in this case we give input with more than one optimal solutions.