Cyclic pattern kernels for predictive graph mining

Abstract

With applications in biology, the world-wide web, and several other areas, mining of graph-structured objects has received significant interest recently. One of the major research directions in this field is concerned with predictive data mining in graph databases where each instance is represented by a graph. Some of the proposed approaches for this task rely on the excellent classification performance of support vector machines. To control the computational cost of these approaches, the underlying kernel functions are based on frequent patterns. In contrast to these approaches, we propose a kernel function based on a natural set of cyclic and tree patterns independent of their frequency, and discuss its computational aspects. To practically demonstrate the effectiveness of our approach, we use the popular NCI-HIV molecule dataset. Our experimental results show that cyclic pattern kernels can be computed quickly and offer predictive performance superior to recent graph kernels based on frequent patterns. Keywordsgraph mining, kernel methods, computational chemistry * This work was supported in part by the DFG project (WR 40/2-1) Hybride Methoden und Systemarchitekturen für heterogene Informationsräume.

Graph kernels and Gaussian processes for relational reinforcement learning

“…However, only walks up to a given length are considered in the kernel computation. More recently, Horvath et al (2004) suggested that the computational intractability can be overcome in practical applications by observing that 'difficult structures' occur only infrequently in real-world databases. As a consequence of this assertion, Horvath et al (2004) use a cycle enumeration algorithm to decompose all graphs in a molecule database into all simple cycles occurring.…”

“…More recently, Horvath et al (2004) suggested that the computational intractability can be overcome in practical applications by observing that 'difficult structures' occur only infrequently in real-world databases. As a consequence of this assertion, Horvath et al (2004) use a cycle enumeration algorithm to decompose all graphs in a molecule database into all simple cycles occurring. In the remainder of this section we will describe a modification of walk based graph kernels (Gärtner et al, 2003b) that allows for graphs with parallel edges.…”

Molecular Graph Augmentation with Rings and Functional Groups

“…As a general remark, we note that the augmentation affects several key characteristics of the input graphs, for example on the Bursi data set we observe the following changes: the vertex and edge label alphabet is increased from 13 to 69 and from 4 to 9 respectively; the vertex degree distribution and the vertex and edge count distribution changes as shown in Table 3. For some graph kernels these differences (increased average label alphabet and degree size, and number of vertices and edges) can lead to a significant increase in the expected runtime, a negative aspect 41 instead, counts the number of cycles in a graph and can suffer from the many cycles introduced by the part-of links added by the augmentation procedure. Here, as in the PMCSK case, a possible workaround would be to eliminate such links and consider the moiety graph as a disconnected component w.r.t.…”

Shortest-Path Kernels on Graphs

“…Computing kernels based on cyclic and tree patterns [11] is a further approach to define graph kernels. Instead of counting the frequency of these cycles in two input graphs, an intersection kernel is applied that counts the number of cycles that appear in both graphs.…”

“…Generally spoken, graph kernels are based on the comparison of graph-substructures via kernels. Walks [8,13], subtrees [17] and cyclic patterns [11] have been considered for this purpose. However, kernels on these substructures are either computationally expensive, sometimes even NP-hard to determine, or limited in their expressiveness.…”