Graph Kernels

We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé 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 Fröhlich et al. (2006) yet provably positive semi-definite

Spectral learning of transducers over continuous sequences

In this paper we present a spectral algorithm for learning weighted nite state transducers (WFSTs) over paired input-output sequences, where the input is continuous and the output discrete. WFSTs are an important tool for modeling paired input-output sequences and have numerous applications in real-world problems. Recently, Balle et al (2011) proposed a spectral method for learning WFSTs that overcomes some of the well known limitations of gradient-based or EM optimizations which can be computationally expensive and su er from local optima issues. Their algorithm can model distributions where both inputs and outputs are sequences from a discrete alphabet. However, many real world problems require modeling paired sequences where the inputs are not discrete but continuos sequences. Modelling continuous sequences with spectral methods has been studied in the context of HMMs (Song et al 2010), where a spectral algorithm for this case was derived. In this paper we follow that line of work and propose a spectral learning algorithm for modelling paired input-output sequences where the inputs are continuous and the outputs are discrete. Our approach is based on generalizing the class of weighted nite state transducers over discrete input-output sequences to a class where transitions are linear combinations of elementary transitions and the weights of this linear combinations are determined by dynamic features of the continuous input sequence. At its core, the algorithm is simple and scalable to large data sets. We present experiments on a real task that validate the eff ectiveness of the proposed approach.Postprint (published version

Smart monitoring of aeronautical composites plates based on electromechanical impedance measurements and artificial neural networks

This paper presents a structural health monitoring (SHM) method for in situ damage detection and localization in carbon fiber reinforced plates (CFRPs). The detection is achieved using the electromechanical impedance (EMI) technique employing piezoelectric transducers as high-frequency modal sensors. Numerical simulations based on the finite element method are carried out so as to simulate more than a hundred damage scenarios. Damage metrics are then used to quantify and detect changes between the electromechanical impedance spectrum of a pristine and damaged structure. The localization process relies on artificial neural networks (ANNs) whose inputs are derived from a principal component analysis of the damage metrics. It is shown that the resulting ANN can be used as a tool to predict the in-plane position of a single damage in a laminated composite plate