Table 1: Classification Accuracy with k-NN.
Dataset K=1 K=3 K=5 K=7 K=10 ms
Letter L 98.80 98.40 97.73 98.93 98.80 0.103
Letter M 80.53 79.60 79.86 81.86 82.93 0.105
Letter H 74.00 71.86 75.60 75.87 78.40 0.153
AIDS 96.06 94.40 93.53 93.00 89.94 2.338
Fingerprints 39.67 37.38 38.95 39.15 38.24 0.573
COIL-D 37.50 12.50 12.50 12.50 12.50 32.94
using heuristic information. The algorithm named
Beams(10) is one of its approximated variation pro-
posed in (Neuhaus et al., 2006). Note that 10 is the
value of the parameter s chosen for the algorithm ex-
ecution. The algorithm named BP is a fast bipartite
graph matching procedure proposed in (Riesen and
Bunke, 2009). Finally, GC stands for the Graph Cov-
erage algorithm. Note that in Table 2 the Heuristic-
A
∗
algorithm is unable to achieve any result for some
dataset, due to its computational limit.
The achieved results, using the k-NN rule over the
IAM datasets, clearly show the validity of the pro-
posed method, with respect to some of the state of
the art methodologies.
Table 2: Classification Results over the Letter LOW (L-L),
Letter MED (L-M), Letter HIGH (L-H), AIDS, Fingerprints
(F) and COIL (C) Datasets.
Algorithm Datasets
L-L L-M L-H AIDS F C
Heuristic-A
∗
91.0 77.9 63.0 - - 93.3
Beam(10) 91.1 78.5 63.9 96.2 84.6 93.3
BP 91.1 77.6 61.6 97.0 78.7 93.3
GC 98.9 83.2 78.4 96.0 39.6 37.5
4 CONCLUSIONS AND FUTURE
DIRECTIONS
In this paper we have proposed a novel inexact graph
matching procedure. It is simple in its formulation
and at the same time effective, relatively fast and
flexible. This is, indeed, the real interesting contri-
bution introduced by the proposed method, consid-
ering the other available graph kernels. In fact, it
is worth to stress that the graph coverage is able to
deal also with fully-labeled graphs, where vertices
and edges labels can be even complex data struc-
tures, once valid kernel functions defined in these do-
mains, to be used as similarity measures, are pro-
vided. The proposed procedure shows interesting pre-
liminary results, considering both classification accu-
racy and computational performance. We are plan-
ning to test this algorithm over more shared bench-
marking graph-based datasets. Moreover, the pro-
posed inexact graph matching procedure is based on
tensor product between graphs. This product is a
mathematically solid and properties-rich operation,
that is basically founded on multiple product between
matrices and scalars. Therefore, the procedure is well
suited to be implemented in relatively inexpensive
parallel computing devices, such as Graphic Process-
ing Units (GPUs) or Field Programmable Gate Array
(FPGA). Taking advantage of these technologies, our
effort will be focused on the formulation of a more
efficient graph coverage procedure, able to deal with
graphs of order of 200 and beyond in a reasonable
computing time.
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