@phdthesis {255,
	title = {Kernel methods for nonlinear identification, equalization and separation of signals},
	year = {2010},
	note = {Software available at \url{https://github.com/steven2358/kmbox/}},
	school = {University of Cantabria},
	author = {Van Vaerenbergh, Steven}
}
@article {Trans_Neural_Networks_2006,
	title = {A spectral clustering approach to underdetermined post-nonlinear blind source separation of sparse sources},
	journal = {IEEE Transactions on Neural Networks},
	volume = {17},
	number = {3},
	year = {2006},
	month = {May},
	pages = {811{\textendash}814},
	abstract = {This letter proposes a clustering-based approach for solving the underdetermined (i.e., fewer mixtures than sources) postnonlinear blind source separation (PNL BSS) problem when the sources are sparse. Although various algorithms exist for the underdetermined BSS problem for sparse sources, as well as for the PNL BSS problem with as many mixtures as sources, the nonlinear problem in an underdetermined scenario has not been satisfactorily solved yet. The method proposed in this letter aims at inverting the different nonlinearities, thus reducing the problem to linear underdetermined BSS. To this end, first a spectral clustering technique is applied that clusters the mixture samples into different sets corresponding to the different sources. Then, the inverse nonlinearities are estimated using a set of multilayer perceptrons (MLPs) that are trained by minimizing a specifically designed cost function. Finally, transforming each mixture by its corresponding inverse nonlinearity results in a linear underdetermined BSS problem, which can be solved using any of the existing methods.},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio}
}
@article {352,
	title = {Semi-Supervised Object Recognition Based on Connected Image Transformations},
	journal = {Expert Systems with Applications},
	volume = {40},
	year = {2013},
	month = {December},
	pages = {7069--7079},
	abstract = {We present a novel semi-supervised classifier model based on paths between unlabeled and labeled data through a sequence of local pattern transformations. A reliable measure of path-length is proposed that combines a local dissimilarity measure between consecutive patters along a path with a global, connectivity-based metric. We apply this model to problems of object recognition, for which we propose a practical classification algorithm based on sequences of "Connected Image Transformations" (CIT). Experimental results on four popular image benchmarks demonstrate how the proposed CIT classifier outperforms state-of-the-art semi-supervised techniques. The results are particularly significant when only a very small number of labeled patterns is available: the proposed algorithm obtains a generalization error of 4.57\% on the MNIST data set trained on 2000 randomly chosen patterns with only 10 labeled patterns per digit class.},
	issn = {0957-4174},
	doi = {10.1016/j.eswa.2013.06.029},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and Barbano, Paolo Emilio}
}
@article {omgp_pr,
	title = {Overlapping Mixtures of Gaussian Processes for the Data Association Problem},
	journal = {Pattern Recognition},
	volume = {45},
	number = {4},
	year = {2012},
	month = {April},
	pages = {1386{\textendash}1395},
	abstract = {In this work we introduce a mixture of GPs to address the data association problem, i.e. to label a group of observations according to the sources that generated them. Unlike several previously proposed GP mixtures, the novel mixture has the distinct characteristic of using no gating function to determine the association of samples and mixture components. Instead, all the GPs in the mixture are global and samples are clustered following {\textquotedblleft}trajectories{\textquotedblright} across input space. We use a non-standard variational Bayesian algorithm to efficiently recover sample labels and learn the hyperparameters. We show how multi-object tracking problems can be disambiguated and also explore the characteristics of the model in traditional regression settings.},
	issn = {0031-3203},
	author = {L{\'a}zaro-Gredilla, Miguel and Van Vaerenbergh, Steven and Lawrence, Neil D.}
}
@article {JOC_Kernel_RLS_2007,
	title = {Nonlinear System Identification using a New Sliding-Window Kernel {RLS} Algorithm},
	journal = {Journal of Communications},
	volume = {2},
	number = {3},
	year = {2007},
	month = {May},
	pages = {1{\textendash}8},
	abstract = {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, the studied method combines a sliding-window approach (to fix the dimensions of the kernel matrix) with conventional ridge regression (to improve generalization). The resulting kernel RLS algorithm is applied to several nonlinear system identification problems. Experiments show that the proposed algorithm is able to operate in a time-varying environment and to adjust to abrupt changes in either the linear filter or the nonlinearity.},
	keywords = {kernel adaptive filtering, KRLS},
	author = {Van Vaerenbergh, Steven and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@article {568,
	title = {Multi-Channel Factor Analysis with Common and Unique Factors},
	journal = {IEEE Transactions on Signal Processing},
	volume = {68},
	year = {2020},
	pages = {113-126},
	abstract = {This work presents a generalization of classical factor analysis (FA). Each of M channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the M multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar.},
	issn = {1053-587X},
	doi = {10.1109/TSP.2019.2955829},
	author = {Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio and Louis L. Scharf and Van Vaerenbergh, Steven}
}
@article {282,
	title = {Kernel Recursive Least-Squares Tracker for Time-Varying Regression},
	journal = {IEEE Transactions on Neural Networks and Learning Systems},
	volume = {23},
	year = {2012},
	month = {August},
	pages = {1313--1326},
	abstract = {In this paper, we introduce a kernel recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose, we first derive the standard KRLS equations from a Bayesian perspective (including a sensible approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in nonstationary scenarios. The resulting method is the first kernel adaptive filtering algorithm that includes a forgetting factor in a principled and numerically stable manner. In addition to its tracking ability, it has a number of appealing properties. It is online, requires a fixed amount of memory and computation per time step, incorporates regularization in a natural manner and provides confidence intervals along with each prediction. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.},
	keywords = {kernel adaptive filtering, KRLS},
	issn = {2162-237X},
	doi = {10.1109/TNNLS.2012.2200500},
	url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6227361},
	author = {Van Vaerenbergh, Steven and L{\'a}zaro-Gredilla, Miguel and Santamar{\'\i}a, Ignacio}
}
@article {415,
	title = {Kernel Canonical Correlation Analysis for Robust Cooperative Spectrum Sensing in Cognitive Radio Networks},
	journal = {Transactions on Emerging Telecommunications Technologies},
	volume = {28},
	year = {2014},
	abstract = {Spectrum sensing is a key operation in Cognitive Radio (CR) systems, where secondary users (SUs) are able to exploit
spectrum opportunities by first detecting the presence of primary users (PUs). In a CR network composed of several
SUs, the detection accuracy can be much improved by cooperative spectrum sensing (CSS) strategies, which exploit the
spatial diversity among SUs. However, cooperative detection strategies, which are typically based on energy sensing, do
not perform satisfactorily under impairments such as non-Gaussian noise or interferences. In this paper, we propose a
scheme based on kernel canonical correlation analysis (KCCA), which is able to operate in non-ideal scenarios and in a
totally blind fashion. This technique is performed at the fusion center (FC) by exploiting the non-linear correlation among
the received signals of each SU. In this manner, statistical tests are extracted, allowing the SUs to make decisions either
autonomously at each SU or cooperatively at the FC. The performance of the KCCA-based detector is evaluated by means
of simulations and over-the-air experiments using a CR testbed composed of several Universal Radio Peripheral (USRP)
nodes. Both the simulations and the measurements show that the KCCA-based detector is able to obtain a significant
gain over a conventional energy detector, whose sensing performance is severely degraded by the presence of external
interferers.},
	keywords = {Cooperative Spectrum Sensing, Hardware Testbed, Kernel Canonical Correlation Analysis, USRP},
	issn = {2161-3915},
	doi = {10.1002/ett.2896},
	author = {Manco-V{\'a}squez, Julio and Van Vaerenbergh, Steven and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@article {533,
	title = {Kafnets: Kernel-based non-parametric activation functions for neural networks},
	journal = {Neural Networks},
	volume = {110},
	year = {2019},
	month = {February},
	pages = {19-32},
	doi = {10.1016/j.neunet.2018.11.002},
	author = {Scardapane, Simone and Van Vaerenbergh, Steven and Totaro, Simone and Uncini, Aurelio}
}
@article {342,
	title = {Gaussian Processes for Nonlinear Signal Processing: An Overview of Recent Advances},
	journal = {IEEE Signal Processing Magazine},
	volume = {30},
	year = {2013},
	month = {July},
	pages = {40-50},
	abstract = {Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as a natural nonlinear extension to optimal Wiener filtering. After establishing their basic formulation, we discuss several important aspects and extensions, including recursive and adaptive algorithms for dealing with non-stationarity, low-complexity solutions, non-Gaussian noise models and classification scenarios. Furthermore, we provide a selection of relevant applications to wireless digital communications.},
	keywords = {kernel adaptive filtering},
	issn = {1053-5888},
	doi = {10.1109/MSP.2013.2250352},
	url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6530761},
	author = {P{\'e}rez-Cruz, Fernando and Van Vaerenbergh, Steven and Murillo-Fuentes, Juan Jos{\'e} and L{\'a}zaro-Gredilla, Miguel and Santamar{\'\i}a, Ignacio}
}
@article {378,
	title = {A Gaussian Process Model for Data Association and a Semi-Definite Programming Solution},
	journal = {IEEE Transactions on Neural Networks and Learning Systems},
	volume = {25},
	year = {2014},
	month = {November},
	pages = {1967-1979},
	abstract = {In this paper we propose a Bayesian model for the data association problem, in which trajectory smoothness is enforced through the use of Gaussian process priors. This model allows to score candidate associations by using the evidence framework, thus casting the data association problem into an optimization problem. Under some additional mild assumptions, this optimization problem is shown to be equivalent to a constrained Max K-Section problem. Furthermore, for K = 2, a MaxCut formulation is obtained, to which an approximate solution can be efficiently found using an SDP relaxation. Solving this MaxCut problem is equivalent to finding the optimal association out of the combinatorially many possibilities. The obtained clustering depends only on two hyperparameters, which can also be selected by maximum evidence.},
	issn = {2162-237X},
	doi = {10.1109/TNNLS.2014.2300701},
	author = {L{\'a}zaro-Gredilla, Miguel and Van Vaerenbergh, Steven}
}
@article {530,
	title = {Complex-valued Neural Networks with Non-parametric Activation Functions},
	journal = {IEEE Transactions on Emerging Topics in Computational Intelligence},
	volume = {3},
	year = {2018},
	abstract = {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 of the complex domain (such as holomorphicity) make the design of CVNNs a more challenging task than their real counterpart. In this paper, we consider the problem of flexible activation functions (AFs) in the complex domain, i.e., AFs endowed with sufficient degrees of freedom to adapt their shape given the training data. While this problem has received considerable attention in the real case, very limited literature exists for CVNNs, where most activation functions are generally developed in a split fashion (i.e., by considering the real and imaginary parts of the activation separately) or with simple phase-amplitude techniques. Leveraging over the recently proposed kernel activation functions, and related advances in the design of complex-valued kernels, we propose the first fully complex, nonparametric activation function for CVNNs, which is based on a kernel expansion with a fixed dictionary that can be implemented efficiently on vectorized hardware. Several experiments on common use cases, including prediction and channel equalization, validate our proposal when compared to real-valued neural networks and CVNNs with fixed activation functions.},
	issn = {2471-285X},
	doi = {10.1109/TETCI.2018.2872600},
	url = {https://ieeexplore.ieee.org/document/8495012},
	author = {Scardapane, Simone and Van Vaerenbergh, Steven and Hussain, Amir and Uncini, Aurelio}
}
@article {341,
	title = {Blind Identification of SIMO Wiener Systems based on Kernel Canonical Correlation Analysis},
	journal = {IEEE Transactions on Signal Processing},
	volume = {61},
	year = {2013},
	month = {May},
	pages = {2219-2230},
	abstract = {We consider the problem of blind identification and equalization of single-input multiple-output (SIMO) nonlinear channels. Specifically, the nonlinear model consists of multiple single-channel Wiener systems that are excited by a common input signal. The proposed approach is based on a well-known blind identification technique for linear SIMO systems. By transforming the output signals into a reproducing kernel Hilbert space (RKHS), a linear identification problem is obtained, which we propose to solve through an iterative procedure that alternates between canonical correlation analysis (CCA) to estimate the linear parts, and kernel canonical correlation (KCCA) to estimate the memoryless nonlinearities. The proposed algorithm is able to operate on systems with as few as two output channels, on relatively small data sets and on colored signals. Simulations are included to demonstrate the effectiveness of the proposed technique. },
	issn = {1053-587X},
	doi = {10.1109/TSP.2013.2248004},
	author = {Van Vaerenbergh, Steven and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@article {JASP_2008_pub,
	title = {Adaptive kernel canonical correlation analysis algorithms for nonparametric identification of Wiener and Hammerstein systems},
	journal = {EURASIP Journal on Advances in Signal Processing},
	year = {2008},
	month = {April},
	abstract = {This paper treats the identification of nonlinear systems that consist of a cascade of a linear channel and a nonlinearity, such as the well-known Wiener and Hammerstein systems. In particular, we follow a supervised identification approach that simultaneously identifies both parts of the nonlinear system. Given the correct restrictions on the identification problem, we show how kernel canonical correlation analysis (KCCA) emerges as the logical solution to this problem.We then extend the proposed identification algorithm to an adaptive version allowing to deal with time-varying systems. In order to avoid overfitting problems, we discuss and compare three possible regularization techniques for both the batch and the adaptive versions of the proposed algorithm. Simulations are included to demonstrate the effectiveness of the presented algorithm.},
	author = {Van Vaerenbergh, Steven and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {473,
	title = {A Split Kernel Adaptive Filtering Architecture for Nonlinear Acoustic Echo Cancellation},
	booktitle = {24th European Signal Processing Conference (EUSIPCO 2016)},
	year = {2016},
	month = {September},
	address = {Budapest, Hungary},
	abstract = {We propose a new linear-in-the-parameters (LIP) nonlinear filter based on kernel methods to address the problem of nonlinear acoustic echo cancellation (NAEC). For this purpose we define a framework based on a parallel scheme in which any kernel-based adaptive filter (KAF) can be incorporated efficiently. This structure is composed of a classic adaptive filter on one branch, committed to estimating the linear part of the echo path, and a kernel adaptive filter on the other branch, to model the nonlinearities rebounding in the echo path. In addition, we propose a novel low-complexity least mean square (LMS) KAF with very few parameters, to be used in the parallel architecture. Finally, we demonstrate the effectiveness of the proposed scheme in real NAEC scenarios, for different choices of the KAF.},
	isbn = {978-0-9928-6265-7},
	author = {Van Vaerenbergh, Steven and Comminiello, Danilo and Azpicueta-Ruiz, Luis A.}
}
@conference {Eusipco2007_FFF_MIMO,
	title = {A Spectral Clustering Algorithm for Decoding Fast Time-Varying {BPSK} {MIMO}},
	booktitle = {15th European Signal Processing Conference (EUSIPCO 2007)},
	year = {2007},
	month = {September},
	address = {Poznan, Poland},
	author = {Van Vaerenbergh, Steven and E. Est{\'e}banez and Santamar{\'\i}a, Ignacio}
}
@conference {vanvaerenbergh2006sliding,
	title = {A Sliding-Window Kernel {RLS} Algorithm and its Application to Nonlinear Channel Identification},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2006)},
	year = {2006},
	month = {May},
	address = {Toulouse, France},
	abstract = {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, we combine a sliding-window approach (to fix the dimensions of the kernel matrix) with conventional -norm regularization (to improve generalization). The proposed kernel RLS algorithm is applied to a nonlinear channel identification problem (specifically, a linear filter followed by a memoryless nonlinearity), which typically appears in satellite communications or digital magnetic recording systems. We show that the proposed algorithm is able to operate in a time-varying environment and tracks abrupt changes in either the linear filter or the nonlinearity.},
	keywords = {kernel adaptive filtering, KRLS},
	author = {Van Vaerenbergh, Steven and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {Icassp2011_Semisupervised,
	title = {Semi-Supervised Handwritten Digit Recognition Using Very Few Labeled Data},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2011)},
	year = {2011},
	month = {May},
	address = {Prague, Czech Republic},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and Barbano, Paolo Emilio}
}
@conference {471,
	title = {On The Relationship Between Online Gaussian Process Regression And Kernel Least Mean Squares Algorithms},
	booktitle = {2016 IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2016)},
	year = {2016},
	month = {September},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Salerno, Italy},
	abstract = {We study the relationship between online Gaussian process (GP) regression and kernel least mean squares (KLMS) algorithms. While the latter have no capacity of storing the entire posterior distribution during online learning, we discover that their operation corresponds to the assumption of a fixed posterior covariance that follows a simple parametric model. Interestingly, several well-known KLMS algorithms correspond to specific cases of this model. The probabilistic perspective allows us to understand how each of them handles uncertainty, which could explain some of their performance differences.},
	keywords = {gaussian processes, kernel adaptive filtering, KLMS},
	author = {Van Vaerenbergh, Steven and Fern{\'a}ndez-Bes, Jes{\'u}s and Elvira, Victor}
}
@conference {493,
	title = {Recursive multikernel filters exploiting nonlinear temporal structure},
	booktitle = {25th European Signal Processing Conference (EUSIPCO 2017)},
	year = {2017},
	month = {August},
	address = {Kos, Greece},
	isbn = {978-0-9928626-7-1},
	author = {Van Vaerenbergh, Steven and Scardapane, Simone and Santamar{\'\i}a, Ignacio}
}
@conference {525,
	title = {Recurrent Neural Networks With Flexible Gates Using Kernel Activation Functions},
	booktitle = {IEEE International Workshop on Machine Learning for Signal Processing},
	year = {2018},
	month = {September},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Aalborg, Denmark},
	abstract = {Gated recurrent neural networks have achieved remarkable results in the analysis of sequential data. Inside these networks, gates are used to control the flow of information, allowing to model even very long-term dependencies in the data. In this paper, we investigate whether the original gate equation (a linear projection followed by an element-wise sigmoid) can be improved. In particular, we design a more flexible architecture, with a small number of adaptable parameters, which is able to model a wider range of gating functions than the classical one. To this end, we replace the sigmoid function in the standard gate with a non-parametric formulation extending the recently proposed kernel activation function (KAF), with the addition of a residual skip-connection. A set of experiments on sequential variants of the MNIST dataset shows that the adoption of this novel gate allows to improve accuracy with a negligible cost in terms of computational power and with a large speed-up in the number of training iterations.},
	author = {Scardapane, Simone and Van Vaerenbergh, Steven and Comminiello, Danilo and Totaro, Simone and Uncini, Aurelio}
}
@conference {431,
	title = {A Probabilistic Least-Mean-Squares Filter},
	booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2015},
	month = {April},
	address = {Brisbane, Queensland, Australia},
	abstract = {We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the standard LMS. Numerical results show the improved performance of the algorithm with respect to standard LMS and state-of-the-art algorithms with similar complexity. The goal of this work, therefore, is to open the door to bring some more Bayesian machine learning techniques to adaptive filtering.},
	keywords = {adaptive filtering, least-mean-squares, probabilistic models, state-space models},
	doi = {10.1109/ICASSP.2015.7178361},
	author = {Fern{\'a}ndez-Bes, Jes{\'u}s and Elvira, Victor and Van Vaerenbergh, Steven}
}
@conference {393,
	title = {Probabilistic Kernel Least Mean Squares Algorithms},
	booktitle = {2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2014},
	month = {05/2014},
	abstract = {The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm is closely related to the Kalman filtering, and thus, the KLMS can be interpreted as an approximate Bayesian filtering method. This allows us to systematically develop extensions of the KLMS by modifying the underlying state-space and observation models. The resulting extensions introduce many desirable properties such as "forgetting", and the ability to learn from discrete data, while retaining the computational simplicity and time complexity of the original algorithm.},
	keywords = {kernel adaptive filtering, KLMS, sequential Bayesian learning, state-space model},
	isbn = {978-1-4799-2892-7},
	author = {Park, Il Memming and Seth, Sohan and Van Vaerenbergh, Steven}
}
@conference {394,
	title = {Physical Layer Authentication based on Channel Response Tracking using Gaussian Processes},
	booktitle = {2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2014},
	month = {May},
	pages = {2429--2433},
	abstract = {Physical-layer authentication techniques exploit the unique properties of the wireless medium to enhance traditional higher-level authentication procedures. We propose to reduce the higher-level authentication overhead by using a state-of-the-art multi-target tracking technique based on Gaussian processes. The proposed technique has the additional advantage that it is capable of automatically learning the dynamics of the trusted user{\textquoteright}s channel response and the time-frequency fingerprint of intruders. Numerical simulations show very low intrusion rates, and an experimental validation using a wireless test bed with programmable radios demonstrates the technique{\textquoteright}s effectiveness.},
	keywords = {gaussian processes, multi-target tracking, physical-layer authentication, wireless communications},
	isbn = {978-1-4799-2892-7},
	author = {Van Vaerenbergh, Steven and Gonz{\'a}lez, {\'O}scar and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {507,
	title = {Pattern Localization in Time Series through Signal-To-Model Alignment in Latent Space},
	booktitle = {2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2018},
	month = {April},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Calgary, Alberta, Canada},
	abstract = {In this paper, we study the problem of locating a predefined sequence of patterns in a time series. In particular, the studied scenario assumes a theoretical model is available that contains the expected locations of the patterns. This problem is found in several contexts, and it is commonly solved by first synthesizing a time series from the model, and then aligning it to the true time series through dynamic time warping. We propose a technique that increases the similarity of both time series before aligning them, by mapping them into a latent correlation space. The mapping is learned from the data through a machine-learning setup. Experiments on data from non-destructive testing demonstrate that the proposed approach shows significant improvements over the state of the art.},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and Elvira, Victor and Salvatori, Matteo}
}
@conference {MLSP09_Clustering_Time_Varying_MIMO,
	title = {Path-Based Spectral Clustering for Decoding Fast Time-Varying {MIMO} Channels},
	booktitle = {2009 International Workshop on Machine Learning for Signal Processing (MLSP)},
	year = {2009},
	month = {September},
	address = {Grenoble, France},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and Barbano, Paolo Emilio and Ozertem, Umut and Erdogmus, Deniz}
}
@conference {IJCNN_2006,
	title = {Online kernel canonical correlation analysis for supervised equalization of {Wiener} systems},
	booktitle = {IEEE International Joint Conference on Neural Networks (IJCNN 2006)},
	year = {2006},
	month = {July},
	address = {Vancouver, Canada},
	author = {Van Vaerenbergh, Steven and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {523,
	title = {MoCap multichannel time series representation and relevance analysis by kernel adaptive filtering and multikernel learning oriented to action recognition tasks},
	booktitle = {International Conference on Time Series and Forecasting (ITISE 2018)},
	year = {2018},
	month = {September},
	pages = {1316-1327},
	address = {Granada, Spain},
	isbn = {978-84-17293-57-4},
	author = {Pulgarin-Giraldo, Juan Diego and Alvarez-Meza, Andres Marino and Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and Castellanos, German}
}
@conference {392,
	title = {Kernel-Based Identification of Hammerstein Systems for Nonlinear Acoustic Echo-Cancellation},
	booktitle = {2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2014},
	month = {05/2014},
	abstract = {Traditional acoustic echo cancelers use a linear model to represent the echo path. Nevertheless, many consumer devices include loudspeakers and audio power amplifiers that may generate significant nonlinear distortions, creating the need for acoustic echo cancelers to produce a nonlinear filter response. To address this issue, we propose a nonlinear acoustic echo cancellation algorithm based on the framework of kernel methods. We model the echo path as a Hammerstein system, and we propose a resource-efficient strategy to identify the nonlinear and linear parts. While the basic algorithm is presented as an iterative batch method, we show that a simple extension allows it to be used in online scenarios as well. Results for both types of scenarios show that the algorithm produces good results on a system with a clipping nonlinearity and a realistic room impulse response.},
	keywords = {acoustic echo cancellation, Hammerstein systems, kernel methods, nonlinear distortions},
	isbn = {978-1-4799-2892-7},
	author = {Van Vaerenbergh, Steven and Azpicueta-Ruiz, Luis A.}
}
@conference {MLSP_2008_pub,
	title = {A kernel canonical correlation analysis algorithm for blind equalization of oversampled Wiener systems},
	booktitle = {IEEE International Workshop on Machine Learning for Signal Processing},
	year = {2008},
	month = {October},
	address = {Cancun, Mexico},
	author = {Van Vaerenbergh, Steven and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {362,
	title = {Kernel Adaptive Filtering: Which Technique to Choose in Practice},
	booktitle = {International Workshop on Advances in  Regularization, Optimization, Kernel Methods and Support Vector Machines: theory and applications (ROKS 2013)},
	year = {2013},
	month = {July},
	pages = {101--102},
	abstract = {The field of kernel adaptive filtering has produced a myriad of techniques throughout the past decade. While each algorithm provides some advantages over others in certain scenarios, it is often not clear which technique should be used on a practical problem, in which specific restrictions are in place. We propose a set of empirical performance measures and we provide a framework that can be used to decide which algorithm to use in practice. We include results on several benchmark data sets.},
	keywords = {kernel adaptive filtering},
	isbn = {978-94-6018-700-1},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio}
}
@conference {521,
	title = {Improving Graph Convolutional Networks with Non-Parametric Activation Functions},
	booktitle = {26th European Signal Processing Conference (EUSIPCO 2018)},
	year = {2018},
	month = {September},
	publisher = {EURASIP},
	organization = {EURASIP},
	address = {Rome, Italy},
	abstract = {Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs have been proposed, they only consider simple nonlinear activation functions in their layers, such as rectifiers or squashing functions. In this paper, we investigate the use of graph convolutional networks (GCNs) when combined with more complex activation functions, able to adapt from the training data. More specifically, we extend the recently proposed kernel activation function, a non-parametric model which can be implemented easily, can be regularized with standard l?p-norms techniques, and is smooth over its entire domain. Our experimental evaluation shows that the proposed architecture can significantly improve over its baseline, while similar improvements cannot be obtained by simply increasing the depth or size of the original GCN.},
	author = {Scardapane, Simone and Van Vaerenbergh, Steven and Comminiello, Danilo and Uncini, Aurelio}
}
@conference {vanvaerenbergh2010_fbkrls,
	title = {Fixed-Budget Kernel Recursive Least-Squares},
	booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010)},
	year = {2010},
	month = {March},
	address = {Dallas, USA},
	keywords = {kernel adaptive filtering, KRLS},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and Liu, Weifeng and Pr{\'\i}ncipe, Jos{\'e} C.}
}
@conference {404,
	title = {Experimental Evaluation of a Cooperative Kernel-Based Approach for Robust Spectrum Sensing},
	booktitle = {8th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)},
	year = {2014},
	month = {June},
	address = {A Coru{\~n}a, Spain},
	isbn = {978-1-4799-1479-1},
	author = {Manco-V{\'a}squez, Julio and Van Vaerenbergh, Steven and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {314,
	title = {Estimation of the Forgetting Factor in Kernel Recursive Least Squares},
	booktitle = {2012 IEEE International Workshop On Machine Learning For Signal Processing (MLSP)},
	year = {2012},
	month = {September},
	abstract = {In a recent work we proposed a kernel recursive least-squares tracker (KRLS-T) algorithm that is capable of tracking in non-stationary environments, thanks to a forgetting mechanism built on a Bayesian framework. In order to guarantee optimal performance its parameters need to be determined, specifically its kernel parameters, regularization and, most importantly in non-stationary environments, its forgetting factor. This is a common difficulty in adaptive filtering techniques and in signal processing algorithms in general. In this paper we demonstrate the equivalence between KRLS-T{\textquoteright}s recursive tracking solution and Gaussian process (GP) regression with a specific class of spatio-temporal covariance. This result allows to use standard hyperparameter estimation techniques from the Gaussian process framework to determine the parameters of the KRLS-T algorithm. Most notably, it allows to estimate the optimal forgetting factor in a principled manner. We include results on different benchmark data sets that offer interesting new insights.},
	keywords = {kernel adaptive filtering},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and L{\'a}zaro-Gredilla, Miguel}
}
@conference {517,
	title = {Decision Support System for Plan and Crop Treatment and Protection based on Wireless Sensor Networks},
	booktitle = {41st International Spring Seminar on Electronics Technology (ISSE)},
	year = {2018},
	month = {May},
	address = {Zlatibor, Serbia},
	abstract = {A decision support system (DSS) able to control the course of agricultural production and protect healthy and treat diseased plants and crops taking into account the temporal and spatial variability of environmental parameters has been described. It is based on remote sensing and the most sophisticated machine learning techniques: Gaussian Processes (GPs) and Deep Neural Networks (DNNs). An example of knowledge extraction and actionable rule definition has been presented too. },
	author = {Stamenkovic, Z. and Randji{\'c},S and Santamar{\'\i}a, Ignacio and Markovic, D and Van Vaerenbergh, Steven and Pe{\v s}ovi{\'c}, U}
}
@conference {356,
	title = {A Comparative Study of Kernel Adaptive Filtering Algorithms},
	booktitle = {2013 IEEE Digital Signal Processing (DSP) Workshop and IEEE Signal Processing Education (SPE)},
	year = {2013},
	month = {August},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {Kernel adaptive filtering is a growing field of signal processing that is concerned with nonlinear adaptive filtering. When implemented naively, the time and memory complexities of these algorithms grow at least linearly with the amount of data processed. A large number of practical solutions have been proposed throughout the last decade, based on sparsification or pruning mechanisms. Nevertheless, there is a lack of understanding of their relative merits, which often depend on the data they operate on. We propose to study the quality of the solution as a function of either the time or the memory complexity. We empirically test six different kernel adaptive filtering algorithms on three different benchmark data sets. We make our code available through an open source toolbox that includes additional algorithms and allows to measure the complexities explicitly in number of floating point operations and bytes needed, respectively.},
	keywords = {kernel adaptive filtering},
	isbn = {978-1-4799-1616-0},
	doi = {10.1109/DSP-SPE.2013.6642587 },
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio}
}
@conference {Miguel_KRLS_MLSP2011,
	title = {A {Bayesian} Approach To Tracking With Kernel Recursive Least-Squares},
	booktitle = {IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2011)},
	year = {2011},
	month = {September},
	address = {Beijing, China},
	abstract = {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 this purpose we first derive the standard KRLS equations from a Bayesian perspective (including a principled approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in non-stationary scenarios. In addition to this tracking ability, the resulting algorithm has a number of appealing properties: It is online, requires a fixed amount of memory and computation per time step and incorporates regularization in a natural manner. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.},
	keywords = {kernel adaptive filtering, KRLS},
	author = {L{\'a}zaro-Gredilla, Miguel and Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio}
}
@conference {535,
	title = {Analysis and classification of MoCap data by Hilbert space embedding-based distance and multikernel learning},
	booktitle = {The 23rd Iberoamerican Congress on Pattern Recognition},
	year = {2018},
	month = {November},
	address = {Madrid, Spain},
	author = {Pulgarin-Giraldo, Juan Diego and Alvarez-Meza, Andres Marino and Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and Castellanos, German}
}
@conference {518,
	title = {An alternating optimization algorithm for two-channel factor analysis with common and uncommon factors},
	booktitle = {52nd Asilomar Conference on Signals, Systems and Computers},
	year = {2018},
	month = {October},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Pacific Grove (CA), USA},
	author = {Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio and Van Vaerenbergh, Steven and Louis L. Scharf}
}
@conference {345,
	title = {Adaptive Kernel Canonical Correlation Analysis Algorithms for Maximum and Minimum Variance},
	booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013)},
	year = {2013},
	month = {May},
	address = {Vancouver, Canada},
	abstract = {We describe two formulations of the kernel canonical correlation analysis (KCCA) problem for multiple data sets. The kernel-based algorithms, which allow one to measure nonlinear relationships between the data sets, are obtained as nonlinear extensions of the classical maximum variance (MAXVAR) and minimum variance (MINVAR) canonical correlation analysis (CCA) formulations. We then show how adaptive versions of these algorithms can be obtained by reformulating KCCA as a set of coupled kernel recursive least-squares algorithms. We illustrate the performance of the proposed algorithms on a nonlinear identification application and a cognitive radio detection problem.},
	author = {Van Vaerenbergh, Steven and V{\'\i}a, Javier and Manco-V{\'a}squez, Julio and Santamar{\'\i}a, Ignacio}
}
@inbook {249,
	title = {A Spectral Clustering Approach for Blind Decoding of MIMO Transmissions over Time-Correlated Fading Channels},
	booktitle = {Intelligent Systems: Techniques and Applications, Evor Hines et. al (Eds.)},
	year = {2008},
	publisher = {Shaker Publishing},
	organization = {Shaker Publishing},
	address = {The Netherlands},
	isbn = {978-90-423-0345-4},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio}
}
@inbook {423,
	title = {Online Regression with Kernels},
	booktitle = {Regularization, Optimization, Kernels, and Support Vector Machines},
	number = {Machine Learning \& Pattern Recognition Series},
	year = {2014},
	pages = {477-501},
	publisher = {Chapman and Hall/CRC},
	organization = {Chapman and Hall/CRC},
	chapter = {21},
	address = {New York},
	abstract = {Online machine learning algorithms are designed to learn from one data instance at a time. They are typically used in real-time scenarios, such as prediction or tracking problems, where data arrive sequentially and instant decisions must be made. The real-time nature of these settings implies that shortly after the decision is made, the true label will be made available, which allows the learning algorithm to adjust its solution before a new datum is received.

Online kernel methods extend the nonlinear learning capabilities of standard batch kernel methods to online environments. Especially important for these techniques is that they maintain their computational load moderate during each iteration, in order to perform fast updates in real time. Ideally, they should not only be able to learn in a stationary environment but also in non-stationary settings, where they must forget outdated information and adapt their solution to respond to changes in time. Online kernel methods also find use in batch scenarios where the amount of data is too high to fit in the machine{\textquoteright}s memory, and one or several passes over the data are to be performed.

In this chapter we focus on the problem of online regression. We will give an overview of the most important kernel-based methods for this problem, which have been developed over the span of the last decade. We start by formulating the online solution to the kernel ridge regression problem, and we point out different strategies to overcome the bottlenecks associated to using kernels in online methods. The discussed techniques are often referred to as kernel adaptive filtering algorithms, due to their close relationship with classical adaptive filters from the signal processing literature. After reviewing the most relevant algorithms in this area, we introduce an evaluation framework that allows us to compare their performance. We finish the discussion with a brief overview of the recent and future research directions.},
	keywords = {KLMS, KRLS},
	isbn = {9781482241396},
	url = {http://www.crcpress.com/product/isbn/9781482241396},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio}
}
@inbook {498,
	title = {Adaptive Kernel Learning for Signal Processing},
	booktitle = {Digital Signal Processing with Kernel Methods},
	year = {2018},
	publisher = {Wiley},
	organization = {Wiley},
	chapter = {9},
	issn = {978-1-118-61179-1},
	url = {http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1118611799.html},
	author = {Van Vaerenbergh, Steven}
}
