A nonstationary multiresolution of L 2 (R s) is generated by a sequence of scaling functions k 2 L 2 (R s); k 2 Z: We consider (k) that is the solution of the nonstationary reenement equations k = jMj P j h k+1 (j) k+1 (M ?j); k 2 Z; where h k is nitely supported for each k and M is a dilation matrix. We study various forms of convergence in L 2 (R s) of the corresponding nonstationary cascade ...

In this paper, we present classes of kernels for machine learning from a statistics perspective. Indeed, kernels are positive definite functions and thus also covariances. After discussing key properties of kernels, as well as a new formula to construct kernels, we present several important classes of kernels: anisotropic stationary kernels, isotropic stationary kernels, compactly supported ker...

We introduce a class of nonstationary covariance functions for Gaussian process (GP) regression. Nonstationary covariance functions allow the model to adapt to functions whose smoothness varies with the inputs. The class includes a nonstationary version of the Matérn stationary covariance, in which the differentiability of the regression function is controlled by a parameter, freeing one from f...

This paper demonstrates and exploits some interesting frequency-domain properties of nonstationary signals. Considering these properties, two new methods for blind separation of linear instantaneous mixtures of mutually uncorrelated, nonstationary sources are proposed. These methods are based on spectral decorrelation of the sources. The second method is particularly important because it allows...

The performance of multihop wireless networks (MWN) is normally studied via discrete event simulation over a fixed time horizon using a steady-state type of statistical analysis procedure. However, due to the dynamic nature of network connectivity and nonstationary traffic, such an approach may be inappropriate as the network may spend most time in a transient/nonstationary state. Moreover, the...

In this article, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher-dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multidimensional scaling, group lasso, and latent variable models, a dimensionally sparse pr...

[1] In this study, we investigate two-dimensional flow through a heterogeneous, semiconfined aquifer. In the presence of leakage the mean flow varies in space and the fluctuations of the flow become nonstationary spatially. Such a situation calls for a nonstationary stochastic approach since the classical stationary stochastic approaches are no longer appropriate. We make use of a nonstationary...

This chapter introduces machine learning for nonstationary signal analysis and classification. It argues that machine learning based on the theory of reproducing kernels can be extended to nonstationary signal analysis and classification. The authors show that some specific reproducing kernels allow pattern recognition algorithm to operate in the time-frequency domain. Furthermore, the authors ...

Many algorithms for blind source separation have been introduced in the past few years, most of which assume statistically stationary sources. In many applications, such as separation of speech or fading communications signals, the sources are nonstationary. We present a new adaptive algorithm for blind source separation of nonstationary signals which relies only on the nonstationary nature of ...

Quadratic time-frequency representations (TFRs) and time-scale representations (TSRs) have been shown to be very useful for detecting nonstationary signals in the presence of nonstationary noise. The theory developed thus far is only for the single observation case; however, in many situations involving signal detection, there are advantages in using an array of receiving sensors. Sensor arrays...