![](bg6.png)
EC1 EC2 EC3 EC4 EC5 EC6
0
2.5
5
7.5
10
12.5
15
EC Class
Test error (%)
Walks
Shortest paths
RGK
Core paths
All paths
Figure 4: Prediction results for the six main EC classes. The
first EC class (oxidoreductases) is most difficult, while the
last (ligases) is well predicted with any method.
5 DISCUSSION AND
CONCLUSIONS
The path index can also be used for on-line path fre-
quency queries: given any path P of length m ≤ h,
where h is the maximum path length enumerated, we
can output the frequency of the path P in all graphs
in just O(m log σ + output) time, where output is the
size of the output, i.e. the number of distinct graphs
having frequency that is greater than zero. Details are
out of the scope of this paper, but this type of on-line
feature query might be interesting when computing
kernels in iterative manner. Another interesting di-
rection would be to implement feature selection or `
1
regularized learning methods for graph data making
use of the efficient access to features.
We presented a method for efficiently computing
all-paths kernels for graph data. Our approach relies
on computing and storing a single compressed path
index of all graphs, which can subsequently be effi-
ciently queried for the purposes for graph kernel or
feature vector computation. We demonstrate the com-
putational feasibility of the approach by computing a
path index for graph representations of KEGG reac-
tions. Our experiments show that path kernels give
significant improvements over walk kernels in the re-
action mechanism prediction task.
ACKNOWLEDGEMENTS
We are grateful to Petteri Kaski, Mikko Koivisto
and Craig Saunders for insightful discussions. This
work was funded by the Academy of Finland grants
1140727 and 118653, the Graduate School Hecse and
by the PASCAL2 (IST grant-2007-216886).
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