21 accepted papers
This paper studies the external division operator, an external division (an affine combination with positive and negative weights) of two proximity operators. We show that the external division operator is cocoercive under some condition, and it can be expressed as the proximity operator of a certai…
This paper presents a graph learning framework to produce sparse and accurate graphs from network data. While our formulation is inspired by the graphical lasso, a key difference is the use of a nonconvex alternative of the ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://ww…
This paper introduces a non-parametric learning framework to combat outliers in online, multi-output, and nonlinear regression tasks. A hierarchical-optimization problem underpins the learning task: Search in a reproducing kernel Hilbert space (RKHS) for a function that minimizes a sample average ℓ…
We propose a novel problem formulation for sparsity-aware adaptive filtering based on the nonconvex minimax concave (MC) penalty, aiming to obtain a sparse solution with small estimation bias. We present two algorithms: the first algorithm uses a single firm-shrinkage operation, while the second one…
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…
This paper presents an automatic kernel weighting technique for multikernel adaptive filtering. The full potential of the multikernel adaptive filtering approach can only be achieved when the kernels are weighted appropriately. The proposed technique balances the dominance of the kernels by making t…
We present a convexly-constrained beamformer design for brain activity reconstruction from non-invasive electroencephalography (EEG) signals. An intrinsic gap between the output variance and the mean squared errors is highlighted that occurs due to the presence of interfering activities correlated w…
This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data-driven method of analysis used to describe a nonlinear dynamical system with a linear time-evolution equation. Com…
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 considere…
We propose a hybrid dictionary approach for distributed kernel-based adaptive learning of a nonlinear function by a network of nodes. The hybrid dictionary incorporates a local part to improve learning of high frequency components in the function within the local domain of each node and a global par…
We propose a novel automatic shrinkage tuning technique for the adaptive proximal forward-backward splitting (APFBS) algorithm. The shrinkage tuning aims to choose an appropriate value of the shrinkage parameter and achieve minimal system mismatch as possible. The system mismatch is approximated bas…
Motivated by the success of reinforcement learning (RL) for discrete-time tasks such as AlphaGo and Atari games, there has been a recent surge of interest in using RL for continuous-time control of physical systems (cf. many challenging tasks in OpenAI Gym and DeepMind Control Suite). Since discreti…
We present an exact analytic expression of the contributions of the kernel principal components to the relevant information in a nonlinear regression problem. A related study has been presented by Braun, Buhmann, and Müller in 2008, where an upper bound of the contributions was given for a general s…
This paper proposes an extension of multichannel non-negative matrix factorization (MNMF) that simultaneously solves source separation and dereverberation. While MNMF was originally formulated under an underdetermined problem setting where sources can outnumber microphones, a determined counterpart…
We previously introduced a framework called time-domain spectrogram factorization (TSF), which realizes nonnegative matrix factorization (NMF)-like source separation in the time domain. This framework is particularly noteworthy in that, while maintaining the ability of NMF to obtain a parts-based re…
Exploiting the sparsity in learning algorithms is a key to achieve excellent performances of adaptive filters. This can be realized by the adaptive proximal forward-backward splitting with carefully chosen parameters. In this paper, we propose an automatic parameter tuning based on a minimization pr…
We previously introduced a phase-aware variant of the non-negative matrix factorization (NMF) approach for audio source separation, which we call the “Complex NMF (CNMF).” This approach makes it possible to realize NMF-like signal decompositions in the complex time-frequency domain. One limitation o…
We present a variant of the regularized dual averaging (RDA) algorithm for stochastic sparse optimization. Our approach differs from the previous studies of RDA in two respects. First, a sparsity-promoting metric is employed, originated from the proportionate-type adaptive filtering algorithms. Seco…
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…
We investigate the use of compactly supported kernels (CSKs) for the kernel normalized least mean square (KNLMS) algorithm proposed initially by Richard et al. in 2009. The use of CSKs yields sparse kernelized input vectors, offering an opportunity for complexity reduction. We propose a simple two-s…
We propose a novel multikernel adaptive filtering algorithm based on the iterative projections in the sum space of reproducing kernel Hilbert spaces. We employ linear and Gaussian kernels, envisioning an application to partially-linear-system identification/estimation. The algorithm is derived by re…