A kernel-based method for pattern extraction in random process signals

In many applications, one is interested to detect certain patterns in random process signals. We consider a class of random process signals which contain sub-similarities at random positions representing the texture of an object. Those repetitive parts may occur in speech, musical pieces and sonar signals. We suggest a warped time-resolved spectrum kernel for extracting the subsequence similarity in time series in general, and as an example in biosonar signals. Having a set of those kernels for similarity extraction in different size of subsequences, we propose a new method to find an optimal linear combination of those kernels. We formulate the optimal kernel selection via maximizing the kernel Fisher discriminant (KFD) criterion and use Mesh Adaptive Direct Search (MADS) method to solve the optimization problem. Our method is used for biosonar landmark classification with promising results.