Capacity Control for Partially Ordered Feature Sets

Abstract. Partially ordered feature sets appear naturally in many classification settings with structured input instances, for example, when the data instances are graphs and a feature tests whether a specific substructure occurs in the instance. Since such features are partially ordered according to an “is substructure of” relation, the information in those datasets is stored in an intrinsically redundant form. We investigate how this redundancy affects the capacity control behavior of linear classification methods. From a theoretical perspective, it can be shown that the capacity of this hypothesis class does not decrease for worst case distributions. However, if the data generating distribution assigns lower probabilities to instances in the lower levels of the hierarchy induced by the partial order, the capacity of the hypothesis class can be bounded by a smaller term. For itemset, subsequence and subtree features in particular, the capacity is finite even when an infinit...

• Type: Conference
• Year: 2009
• Where: PKDD
• Authors: Ulrich Rückert
• Keywords: Capacity Control, Data Mining, Partially Ordered, PKDD 2009, Substructure