11,017 research outputs found
Graph Kernels
We present a unified framework to study graph kernels, special cases of which include the random
walk (GƤrtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004;
MahƩ et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time
complexity of kernel computation between unlabeled graphs with n vertices from O(n^6) to O(n^3).
We find a spectral decomposition approach even more efficient when computing entire kernel matrices.
For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn^3)
time per iteration, where d is the size of the label set. By extending the necessary linear algebra to
Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels,
and O(n^4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n^2)
time per iteration in all cases. Experiments on graphs from bioinformatics and other application
domains show that these techniques can speed up computation of the kernel by an order of magnitude
or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when
specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to
R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment
kernel of Frƶhlich et al. (2006) yet provably positive semi-definite
Use of Weighted Finite State Transducers in Part of Speech Tagging
This paper addresses issues in part of speech disambiguation using
finite-state transducers and presents two main contributions to the field. One
of them is the use of finite-state machines for part of speech tagging.
Linguistic and statistical information is represented in terms of weights on
transitions in weighted finite-state transducers. Another contribution is the
successful combination of techniques -- linguistic and statistical -- for word
disambiguation, compounded with the notion of word classes.Comment: uses psfig, ipamac
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