Researcher: Erdoğan, Alper Tunga
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Erdoğan, Alper Tunga
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Publication Open Access Correlative information maximization: a biologically plausible approach to supervised deep neural networks without weight symmetry(Neural Information Processing Systems 36, 2023) Pehlevan, Cengiz; Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Bozkurt, Barışcan; Erdoğan, Alper Tunga; Koç Üniversitesi İş Bankası Yapay Zeka Uygulama ve Araştırma Merkezi (KUIS AI)/ Koç University İş Bank Artificial Intelligence Center (KUIS AI); Graduate School of Sciences and Engineering; College of EngineeringThe backpropagation algorithm has experienced remarkable success in training large-scale artificial neural networks;however, its biological plausibility has been strongly criticized, and it remains an open question whether the brain employs supervised learning mechanisms akin to it. Here, we propose correlative information maximization between layer activations as an alternative normative approach to describe the signal propagation in biological neural networks in both forward and backward directions. This new framework addresses many concerns about the biological-plausibility of conventional artificial neural networks and the backpropagation algorithm. The coordinate descent-based optimization of the corresponding objective, combined with the mean square error loss function for fitting labeled supervision data, gives rise to a neural network structure that emulates a more biologically realistic network of multi-compartment pyramidal neurons with dendritic processing and lateral inhibitory neurons. Furthermore, our approach provides a natural resolution to the weight symmetry problem between forward and backward signal propagation paths, a significant critique against the plausibility of the conventional backpropagation algorithm. This is achieved by leveraging two alternative, yet equivalent forms of the correlative mutual information objective. These alternatives intrinsically lead to forward and backward prediction networks without weight symmetry issues, providing a compelling solution to this long-standing challenge.Publication Metadata only Comparison of convex combination and affine combination of adaptive filters(Ieee, 2009) Singer, Andrew C.; Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Kozat, Süleyman Serdar; Erdoğan, Alper Tunga; Faculty Member; Faculty Member; College of Engineering; College of Engineering; 177972; 41624In the area of combination of adaptive filters, two main approaches, namely convex and affine combinations have been introduced. In this article, the relation between these two approaches is investigated. First, the problem of obtaining optimal convex combination coefficients is formulated as the projection of the optimal affine combination weights to the unit simplex in a weighted inner product space. Based on this formulation the closed form expressions for optimal combination weights and target MSE levels are obtained for two and three branch cases.Publication Metadata only On the convergence of ICA algorithms with symmetric orthogonalization(IEEE, 2008) Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; Faculty Member; College of Engineering; 41624We study the convergence behavior of Independent Component Analysis (ICA) algorithms that are based on the contrast function maximization and that employ symmetric orthogonalization method to guarantee the orthogonality property of the search matrix. In particular, the characterization of the critical points of the corresponding optimization problem and the stationary points of the conventional gradient ascent and fixed point algorithms are obtained. As an interesting and a useful feature of the symmetrical orthogonalization method, we show that the use of symmetric orthogonalization enables the monotonic convergence for the fixed point ICA algorithms that are based on the convex contrast functions.Publication Metadata only An extended family of bounded component analysis algorithms(IEEE Computer Society, 2015) Department of Electrical and Electronics Engineering; N/A; Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; İnan, Hüseyin Atahan; Faculty Member; Master Student; College of Engineering; Graduate School of Sciences and Engineering; 41624; N/ABounded Component Analysis (BCA) is a recent concept proposed as an alternative method for Blind Source Separation problem. BCA enables the separation of dependent as well as independent sources from their mixtures under the practical assumption on source boundedness. This article extends the optimization setting of a recent BCA approach which can be used to produce a variety of BCA algorithms. The article also provides examples of objective functions and the corresponding iterative algorithms. The numerical examples illustrate the advantages of proposed BCA examples regarding the correlated source separation capability over the state of the art ICA based approaches. 1 © 2014 IEEE.Publication Metadata only On the convergence of ICA algorithms with symmetric orthogonalization(IEEE-Inst Electrical Electronics Engineers Inc, 2009) Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; Faculty Member; College of Engineering; 41624Independent component analysis (ICA) problem is often posed as the maximization/minimization of an objective/cost function under a unitary constraint, which presumes the prewhitening of the observed mixtures. The parallel adaptive algorithms corresponding to this optimization setting, where all the separators are jointly trained, are typically implemented by a gradient-based update of the separation matrix followed by the so-called symmetrical orthogonalization procedure to impose the unitary constraint. This article addresses the convergence analysis of such algorithms, which has been considered as a difficult task due to the complication caused by the minimum-(Frobenius or induced 2-norm) distance mapping step. We first provide a general characterization of the stationary points corresponding to these algorithms. Furthermore, we show that fixed point algorithms employing symmetrical orthogonalization are monotonically convergent for convex objective functions. We later generalize this convergence result for nonconvex objective functions. At the last part of the article, we concentrate on the kurtosis objective function as a special case. We provide a new set of critical points based on Householder reflection and we also provide the analysis for the minima/maxima/saddle-point classification of these critical points.Publication Metadata only Sparse bounded component analysis for convolutive mixtures(Institute of Electrical and Electronics Engineers (IEEE), 2018) N/A; Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Babataş, Eren; Erdoğan, Alper Tunga; PhD Student; Faculty Member; Graduate School of Sciences and Engineering; College of Engineering; N/A; 41624In this article, we propose a Bounded Component Analysis (BCA) approach for the separation of the convolutive mixtures of sparse sources. The corresponding algorithm is derived from a geometric objective function defined over a completely deterministic setting. Therefore, it is applicable to sources which can be independent or dependent in both space and time dimensions. We show that all global optima of the proposed objective are perfect separators. We also provide numerical examples to illustrate the performance of the algorithm.Publication Metadata only A fast blind equalization method based on subgradient projections(IEEE, 2004) N/A; N/A; Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Kızılkale, Can; Erdoğan, Alper Tunga; PhD Student; Faculty Member; Graduate School of Sciences and Engineering; College of Engineering; N/A; 41624A novel blind equalization method based on a subgradient search over a convex cost surface is proposed. This is an alternative to the existing iterative blind equalization approaches such as the Constant Modulus Algorithm (CMA) which mostly suffer from the convergence problems caused by their non-convex cost functions. The proposed method is an iterative algorithm, for both real and complex constellations, with a very simple update rule that minimizes the l(infinity) norm of the equalizer output under a linear constraint on the equalizer coefficients. The algorithm has a nice convergence behavior attributed to the convex l(infinity) cost surface. Examples are provided to illustrate the algorithm's performance.Publication Metadata only An adaptive paraunitary approach for blind equalization of all equalizable MIMO channels(IEEE, 2006) Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; Faculty Member; College of Engineering; 41624We introduce a novel adaptive paraunitary approach to be used for the blind deconvolution of all deconvolvable MIMO mixing systems with memory. The proposed adaptive approach is based on the use of alternating projections technique for the enforcement of the paraunitary constraint. The use of this approach enables extension of various instantaneous Blind Source Separation (BSS) approaches to handle the convolutive BSS case. Three such methods, namely FastICA, Multi User Kurtosis and BSS for Bounded Magnitude signals are provided to illustrate the use of this approach.Publication Metadata only Sparse bounded component analysis(IEEE Computer Society, 2016) Babatas, Eren; Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; Faculty Member; College of Engineering; 41624Bounded Component Analysis (BCA) is a recent approach which enables the separation of both dependent and independent signals from their mixtures. This article introduces a novel deterministic instantaneous BCA approach for the separation of sparse bounded sources. The separation problem is posed as a geometric maximization problem, where the objective is the volume ratio of two geometric objects related to the separator output samples, namely the principal hyperellipsoid and bounding l1 norm ball. The global maxima of the corresponding objective are proven to be perfect separators. The article also provides an iterative algorithm corresponding to this objective. The numerical experiments illustrate the potential benefit of the proposed approach relative to existing algorithms.Publication Metadata only Compressed training adaptive equalization: algorithms and analysis(IEEE-Inst Electrical Electronics Engineers Inc, 2017) Yılmaz, Baki B.; Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; Faculty Member; College of Engineering; 41624We propose "compressed training adaptive equalization" as a novel framework to reduce the quantity of training symbols in a communication packet. It is a semi-blind approach for communication systems employing time-domain/frequency-domain equalizers, and founded upon the idea of exploiting the magnitude boundedness of digital communication symbols. The corresponding algorithms are derived by combining the leasts-quares- cost-function measuring the training symbol reconstruction performance and the infinity-norm of the equalizer outputs as the cost for enforcing the special constellation boundedness property along the whole packet. In addition to providing a framework for developing effective adaptive equalization algorithms based on convex optimization, the proposed method establishes a direct link with compressed sensing by utilizing the duality of the l(1) and l(infinity) norms. This link enables the adaptation of recently emerged l(1)-norm-minimization-based algorithms and their analysis to the channel equalization problem. In particular, we show for noiseless/low noise scenarios, the required training length is on the order of the logarithm of the channel spread. Furthermore, we provide approximate performance analysis by invoking the recent MSE results from the sparsity-based data processing literature. Provided examples illustrate the significant training reductions by the proposed approach and demonstrate its potential for high bandwidth systems with fast mobility.