We previously proposed a joint learning scheme of Gaussian parameters (scales and centers) and coefficients for online nonlinear estimation. The instantaneous squared error cost in terms of the Gaussian scales, however, tends to have shallow slopes when the initial guess is far from optimal, causing extremely slow convergence. In this paper, we propose steepening the cost function by adding a squared distance function from the instantaneously-optimal scale. Numerical examples show that the use of the steepened cost ameliorates the convergence behaviors of the scale parameters in inappropriate initial-scale settings.

We propose an efficient adaptive update method for the kernel parameters: the kernel coefficients, scales and centers. The mirror descent and the steepest descent method for squared error cost function are employed to update the kernel scales and centers, respectively. Although the problem considered in this paper is nonconvex, we reduce the possibility of falling into local minima by using a novel multiple initialization scheme to grow the dictionary without great increases of the dictionary size. Through computer experiments, we show that the proposed algorithm enjoys a high adaptation-capability while maintaining a small dictionary size, without detailed tuning of the initial kernel parameters.

This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It also includes stability conditions in the mean and mean-square sense. The present study is based on the analysis of the kernel normalized least mean square (KNLMS) algorithm initially proposed by Chen et al. Simulation results validate the analysis.

The existing kernel filtering algorithms are classified into two categories depending on what space the optimization is formulated in. This paper bridges the two different approaches by focusing on the isomorphism between the dictionary subspace and a Euclidean space with the inner product defined by the kernel matrix. Based on the isomorphism, we propose a novel kernel adaptive filtering algorithm which adaptively refines the dictionary and thereby achieves excellent performance with a small dictionary size. Numerical examples show the efficacy of the proposed algorithm.

We propose a novel kernel adaptive filtering algorithm, dubbed Parallel HYperslab Projection along Affine Sub-Spaces (Φ-PASS), which reuses observed data efficiently. We first derive its fully-updating version that projects the current filter onto multiple hyperslabs in parallel along the dictionary subspace. Each hyperslab accommodates one of the data observed up to the present time instant. The algorithm is derived with the adaptive projected subgradient method (APSM) based on which a convergence analysis is presented. We then generalize the algorithm so that only a few coefficients, whose associated dictionary-data are coherent to the datum of each hyperslab, can be updated selectively for low complexity. This is accomplished by performing the hyperslab projections along affine subspaces defined with the selected dictionary-data. Numerical examples show the efficacy of the proposed algorithm.

A new coding scheme for dithered halftone pictures, called `pattern length' coding, is proposed. This scheme is based on the fact that, in dithered pictures, some special horizontal bit-patterns frequently take place. Counting the pattern strings provides coding efficiency that is as good as any other scheme presented so far. In addition, this scheme is suitable for pictures which have both ordinary document areas and halftone areas, thus keeping better compatibility with standard facsimile coding schemes.