In this paper, we introduce a kernel recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To purpose, first derive the standard KRLS equations from Bayesian perspective (including sensible approach pruning) and then take advantage of framework incorporate forgetting consistent way, thus enabling perform tracking nonstationary scenarios. The resulting method adaptive filtering includes factor principled numerically stable manner....

Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but rarely used signal processing. In this tutorial, we present GPs for regression as a natural extension optimal Wiener filtering. After establishing their basic formulation, discuss several important aspects and extensions, including recursive adaptive algorithms dealing with non-stationarity, low-complexity solutions, non-Gaussian noise models...

Complex-valued neural networks (CVNNs) are a powerful modeling tool for domains where data can be naturally interpreted in terms of complex numbers. However, several analytical properties the domain (such as holomorphicity) make design CVNNs more challenging task than their real counterpart. In this paper, we consider problem flexible activation functions (AFs) domain, i.e., AFs endowed with sufficient degrees freedom to adapt shape given training data. While has received considerable...

In this paper we propose a new kernel-based version of the recursive least-squares (RLS) algorithm for fast adaptive nonlinear filtering. Unlike other previous approaches, combine sliding-window approach (to fix dimensions kernel matrix) with conventional L2-norm regularization improve generalization). The proposed RLS is applied to channel identification problem (specifically, linear filter followed by memoryless nonlinearity), which typically appears in satellite communications or digital...

We present a kernel-based recursive least-squares (KRLS) algorithm on fixed memory budget, capable of recursively learning nonlinear mapping and tracking changes over time. In order to deal with the growing support inherent online kernel methods, proposed method uses combined strategy pruning support. contrast previous sliding-window based technique, presented does not prune oldest data point in every time instant but it instead aims least significant point. also introduce label update...

We consider the problem of blind identification and equalization single-input multiple-output (SIMO) nonlinear channels. Specifically, model consists multiple single-channel Wiener systems that are excited by a common input signal. The proposed approach is based on well-known technique for linear SIMO systems. By transforming output signals into reproducing kernel Hilbert space (RKHS), obtained, which we propose to solve through an iterative procedure alternates between canonical correlation...

This study, which is part of a broader research project, aims to investigate the impact initial training received by students in Master’s Degree Secondary Education and Baccalaureate, Vocational Training, Language Teaching (MDSE) on their future teaching development current educational social framework. The main goal understand concerns, attitudes, level acquired competencies knowledge for professional as inclusive teachers. Additionally, study explore relationship between assessments...

Kernel adaptive filtering is a growing field of signal processing that concerned with nonlinear filtering. When implemented naïvely, the time and memory complexities these algorithms grow at least linearly amount data processed. A large number practical solutions have been proposed throughout last decade, based on sparsification or pruning mechanisms. Nevertheless, there lack understanding their relative merits, which often depend they operate on. We propose to study quality solution as...

In this paper we discuss in detail a recently proposed kernel-based version of the recursive least-squares (RLS) algorithm for fast adaptive nonlinear filtering. Unlike other previous approaches, studied method combines sliding-window approach (to fix dimensions kernel matrix) with conventional ridge regression improve generalization). The resulting RLS is applied to several system identification problems. Experiments show that able operate time-varying environment and adjust abrupt changes...

We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this provides adaptable step-size algorithm together with measure uncertainty about estimation. In addition, proposed approximation preserves linear complexity standard LMS. Numerical results show improved performance respect and state-of-the-art algorithms similar complexity. The goal work, therefore, is open door bring some more Bayesian machine learning techniques adaptive filtering.

In a recent work we proposed kernel recursive least-squares tracker (KRLS-T) algorithm that is capable of tracking in non-stationary environments, thanks to forgetting mechanism built on Bayesian framework. order guarantee optimal performance its parameters need be determined, specifically parameters, regularization and, most importantly factor. This common difficulty adaptive filtering techniques and signal processing algorithms general. this paper demonstrate the equivalence between...

In this study, we explore automated reasoning tools (ART) in geometry education and argue that these are part of a wider, nascent ecosystem for computer-supported geometric reasoning. To provide some context, set out to summarize the capabilities ART GeoGebra (GGb), discuss first research proposals its use classroom. While design development have been embraced already by several teams mathematics researchers developers, educational community, which is an essential actor ecosystem, has not...

In this paper we introduce a kernel-based recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To purpose first derive the standard KRLS equations from Bayesian perspective (including principled approach pruning) and then take advantage of framework incorporate forgetting consistent way, thus enabling perform tracking non-stationary scenarios. addition ability, resulting has number appealing properties: It online, requires fixed amount...

Traditional acoustic echo cancelers use a linear model to represent the path. Nevertheless, many consumer devices include loudspeakers and audio power amplifiers that may generate significant nonlinear distortions, creating need for produce filter response. To address this issue, we propose cancellation algorithm based on framework of kernel methods. We path as Hammerstein system, resource-efficient strategy identify parts. While basic is presented an iterative batch method, show simple...

We propose a new linear-in-the-parameters (LIP) nonlinear filter based on kernel methods to address the problem of acoustic echo cancellation (NAEC). For this purpose we define framework parallel scheme in which any kernel-based adaptive (KAF) can be incorporated efficiently. This structure is composed classic one branch, committed estimating linear part path, and other model nonlinearities rebounding path. In addition, novel low-complexity least mean square (LMS) KAF with very few...

This work presents a generalization of classical factor analysis (FA). Each M channels carries measurements that share factors with all other channels, but also contains are unique to the channel. Furthermore, each channel an additive noise whose covariance is diagonal, as usual in analysis, otherwise unknown. leads problem multi-channel specially structured model consisting shared low-rank components, and diagonal components. Under multivariate normal for noises, maximum likelihood (ML)...

Physical-layer authentication techniques exploit the unique properties of wireless medium to enhance traditional higher-level procedures. We propose reduce overhead by using a state-of-the-art multi-target tracking technique based on Gaussian processes. The proposed has additional advantage that it is capable automatically learning dynamics trusted user's channel response and time-frequency fingerprint intruders. Numerical simulations show very low intrusion rates, an experimental validation...

This paper treats the identification of nonlinear systems that consist a cascade linear channel and nonlinearity, such as well-known Wiener Hammerstein systems. In particular, we follow supervised approach simultaneously identifies both parts system. Given correct restrictions on problem, show how kernel canonical correlation analysis (KCCA) emerges logical solution to this problem. We then extend proposed algorithm an adaptive version allowing deal with time-varying order avoid overfitting...