Zekeriya Uykan

Analysis of input-output clustering for determining centers of RBFN

The key point in design of radial basis function networks is to specify the number and the locations of the centers. Several heuristic hybrid learning methods, which apply a clustering algorithm for locating the centers and subsequently a linear leastsquares method for the linear weights, have been previously suggested. These hybrid methods can be put into two groups, which will be called as input clustering (IC) and input-output clustering (IOC), depending on whether the output vector is also involved in the clustering process. The idea of concatenating the output vector to the input vector in the clustering process has independently been proposed by several papers in the literature although none of them presented a theoretical analysis on such procedures, but rather demonstrated their effectiveness in several applications. The main contribution of this paper is to present an approach for investigating the relationship between clustering process on input-output training samples and the mean squared output error in the context of a radial basis function netowork (RBFN). We may summarize our investigations in that matter as follows: 1) A weighted mean squared input-output quantization error, which is to be minimized by IOC, yields an upper bound to the mean squared output error. 2) This upper bound and consequently the output error can be made arbitrarily small (zero in the limit case) by decreasing the quantization error which can be accomplished through increasing the number of hidden units.

A PI-power control algorithm for cellular radio systems

Along with distributiveness, convergence speed of power control is one of the most important criteria by which we can determine the practical applicability of a given power control algorithm. A good power control algorithm should quickly and distributively converge to the state where the system supports as many users as possible. This paper proposes a fast and distributed power control algorithm based on the well-known PI-controller. As in the paper by Foschini and Miljanic (see IEEE Trans. Vehicular Technol., vol.42, no.4, p.641-6, Nov. 1993) we start with a differential equation form of the controller and analyze its convergence properties in the case of feasible systems. The actual power control algorithm is then derived by discretization of the continuous time version. Using the distributed constrained power control (DCPC) as a reference algorithm, we carried out computational experiments on a CDMA system. The results indicate that our algorithm significantly enhances the convergence speed of power control.

Joint Optimization of Transmission-Order Selection and Channel Allocation for Bidirectional Wireless Links—Part I: Game Theoretic Analysis

In this two-part paper, we consider a system consisting of bidirectional wireless links that interfere with each other, which has been the of focus of intensive research recently in emerging wireless systems like Device-to-Device (D2D) communications underlaying cellular networks, heterogeneous networks, and small-cell networks. The problem is allocating the time resources (transmission orders) and frequency resources (channels) among the transmitters such that the overall network interference is minimized. Here, transmission order (TO) is a novel dimension for optimization. In Part I, we analyze the TO optimization problem in the presence of channel allocation (CA), i.e., joint CA and the TO optimization problem from a game theoretic perspective, and prove that the joint optimization problem can be formulated as an exact potential game, which has at least one “pure strategy Nash Equilibrium” for any subset of the complete CA-TO action set and for any initial CA and TO conditions. We also show that the proposed joint CA and TO game is equal to the max-cut of a novel TO-dependent holistic system interference graph. In Part II, we present novel joint CA-TO algorithms and their performance analysis in D2D communications underlays.

Clustering-based algorithms for single-hidden-layer sigmoid perceptron

Gradient-descent type supervised learning is the most commonly used algorithm for design of the standard sigmoid perceptron (SP). However, it is computationally expensive (slow) and has the local-minima problem. Moody and Darken (1989) proposed an input-clustering based hierarchical algorithm for fast learning in networks of locally tuned neurons in the context of radial basis function networks. We propose and analyze input clustering (IC) and input-output clustering (IOC)-based algorithms for fast learning in networks of globally tuned neurons in the context of the SP. It is shown that localizing the input layer weights of the SP by the IC and the IOC minimizes an upper bound to the SP output error. The proposed algorithms could possibly be used also to initialize the SP weights for the conventional gradient-descent learning. Simulation results offer that the SPs designed by the IC and the IOC yield comparable performance in comparison with its radial basis function network counterparts.

Unsupervised learning of sigmoid perceptron

A previous paper has derived a clustering-based upper bound on mean squared output error of radial basis function networks that explicitly depends on the network parameters. In this study we focus on single-hidden-layer-sigmoid perceptron. Using the analysis of the previous paper, this paper (i) presents a similar upper bound on output error of the sigmoid perceptron and the upper bound can be made arbitrarily small by increasing the number of sigmoid units, and (ii) proposes unsupervised type learning of input-layer (synaptic) weights in contrast to traditional gradient-descent type supervised learning, i.e., the proposed method minimizes the upper bound by a clustering algorithm for determining the input-layer weights in contrast to the gradient-descent type algorithm minimizing the output error, which is traditionally used in the design of the perceptron. The simulation results show that (i) the proposed hierarchical method requires less time for learning when compared to gradient-descent-type supervised algorithm, (ii) it yields comparable performance in comparison with radial basis function network, and (iii) the upper bounds minimized during the clustering are quite tight to the output error function.

On the "SIR"s ("Signal"-to-"Interference"-Ratio) in Discrete-Time Autonomous Linear Networks

A Hopfield-like neural network, called SALU-SIR,whose system weight matrix is symmetric is presented withits mathematical analysis in [7]. However, what happens if the system matrix is unsymmetric? Is the system still stable in the unsymmetric case? In this paper, we address these importantquestions, whose answer is paramount especially when the system is to be implemented in practice.The underlying linear system of the proposed network is x(k+1) = Ax(k)+b where A is any real square unsymmetric matrix with linearly independent eigenvectors whose largest eigenvalue is real and its norm is larger than 1, and vector b is constant. Our investigations in this paper show that i) the unsymmetric case is also stable; ii) the unsymmetric case yields state-specific ultimate SIRs as compared to the system-specific ultimate SIR in the symmetric case [7], which allows us to design more complex systems. iii) the ultimate “SIR”s in the investigated unsymmetric matrix A case are equal to aiiλmax−aii , i = 1, 2, . . . , N, where Nis the number of states, aii is the diagonal elements of matrix A, and λmax is the (single or multiple) eigenvalue with maximum norm.Possible applications include binary associative memory systems, image restoration, etc in the area of artificial intelligence and cognition.

Upper bounds on RBFN designed by input clustering

In the design of radial basis function networks (RBFNs), several heuristic hybrid learning methods, including a clustering algorithm for locating the centers and a linear least-squares method for the linear weights, have been previously suggested. These hybrid methods can be put into two groups depending on whether the output vector is also involved in the clustering process, which is called the input clustering (IC) and input-output clustering (IOC). A recent paper by Uykan et al. (1998) presents a clustering-based upper bound on the RBFN output error designed by IOC. The main contribution of this paper is to obtain a similar upper bound for the IC case which explicitly depends on the RBFN parameters. This paper also presents some different upper bounds for l/sub 1/ and l/sub 2/ norms used for the quantisation error and the output error in both IC and IOC cases.

Clustering for determining distributed antenna locations in wireless networks

In this paper we extend the concept of the well-known input–output clustering (IOC) technique in Uykan et al. (IEEE Trans Neural Netw 11(4):851–858, 2000) to antenna location optimization problem in wireless networks and propose an input–output space clustering criterion (IOCC) to optimize the locations of the remote antenna units (RAUs) of generalized distributed antenna systems (DASs) under sum power constraint. In IOCC, the input space refers to RAU location space and output space refers to location specific ergodic capacity space for noise-limited environments. Given a location-specific arbitrary desired ergodic capacity function over a geographical area, we define the error as the difference between actual and desired ergodic capacity. Following the major steps of the well-known IOC technique in Uykan et al. (IEEE Trans Neural Netw 11(4):851–858, 2000) and Uykan (IEEE Trans Neural Netw 14(3):708–715, 2003) we show that for the DAS wireless networks: (1) the IOCC provides an upper bound to the cell averaged ergodic capacity error; and (2) the derived upper bound is equal to a weighted quantization error function in location-capacity space (input–output space) and (3) the upper bound can be made arbitrarily small by a clustering process increasing the number of RAUs for a feasible DAS. IOCC converts the RAU location problem into a codebook design problem in vector quantization in input–output space, and thus includes the Squared Distance Criterion (SDC) for DAS in Wang et al. (IEEE Commun Lett 13:315–317, 2009) (and other related papers) as a special case, which takes only the input space into account. Computer simulations confirm the theoretical findings and show that the IOCC outperforms the SDC for DAS in terms of the defined cell averaged “effective” ergodic capacity.

Converged heterogeneous networks with transmit order and base-station-to-base-station interference cancellation

Mobile Converged Heterogeneous Network (MCN) is seen as a viable solution to the exponentially increasing mobile traffic demand of near-future mobile services. Recently, a new dimension for improving the system performance of TDD based wireless systems has been introduced to the 3GPP standards: Dynamic TDD, which allows cell-specific frame configurations and cell-specific control of the Transmit Order (TO). In this paper, we propose unleashing the TO options in the context of MCNs where base stations are coordinated via a central controller for effective base-station-to-base-station interference cancellation (B2B-IC), and we investigate the corresponding performance improvements. Simulation results for an MCN including macro, micro, pico, femto and small cell networks operating in the same spectrum show that the TO with B2B-IC in MCN provide remarkable performance improvements at the expense of an increase in the signal exchange among the centralized controller and the base stations.