in this paper, a novel matched filter based on a new kernel function with cauchy distribution is introduced to improve the accuracy ofthe automatic retinal vessel detection compared with other available matched filter‑based methods, most notably, the methods builton gaussian distribution function. several experiments are conducted to pick the best values of the parameters for the new designedfi...

This paper proposes a novel Gaussian process approach to fault removal in time-series data. Fault removal does not delete the faulty signal data but, instead, massages the fault from the data. We assume that only one fault occurs at any one time and model the signal by two separate non-parametric Gaussian process models for both the physical phenomenon and the fault. In order to facilitate faul...

Gaussian processes are a state-of-the-art method for learning models from data. Data with an underlying periodic structure appears in many areas, e.g., in climatology or robotics. It is often important to predict the long-term evolution of such a time series, and to take the inherent periodicity explicitly into account. In a Gaussian process, periodicity can be accounted for by an appropriate k...

We construct the fundamental solution of ∂t + ∆x + q(t, x), for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative negligibility. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the assumption of relative negligibili...

In this paper, we propose a new method to estimate the multivariate conditional density, f(mjx), a density over the output space m conditioned on any given input x. In particular, we are interested in cases where the number of available training data points is relatively sparse within x space. We start from a priori considerations and establish certain desirable characteristics in kernel functi...