Clustering-Based Energy-Efficient Broadcast Tree in Wireless Networks The characteristics of wireless networks present formidable challenges to the study of broadcasting problem. A crucial issue in wireless networks is the energy consumption, because of the nonlinear attenuation properties of radio signals. Another crucial issue is the trade-off between reaching more nodes in a single hop by using higher power versus reaching fewer nodes in that single hop by using lower power. Given a wireless network with a specified source node that broadcasts messages to all other nodes in the network, the minimum energy broadcast (MEB) problem is NP-hard. In this paper, we propose a hybrid approach CBEEB(clustering-based energy-efficient broadcast) for the MEB problem based on clustering. Theoretical analysis indicates the efficiency and effectiveness of CBEEB. Simulation results show that CBEEB has better performance compared with the existing heuristic approaches. Nodes in wireless networks are usually powered by batteries with limited capacity. Therefore, energy efficiency is one of the most important design issues for wireless networks. The energy consumption in transmission can be further reduced by using one or more intermediate nodes instead of transmitting directly.. Broadcasting in wireless networks is different from that in wired networks, since all nodes that are within the transmission range of the sender can receive the transmission without any additional cost at the sender. This characteristic of wireless transmission is known as wireless multicast advantage (WMA) [1] . This allows us to seek power optimal range assignment for the energy-efficient broadcast problem. The minimum energy broadcast (MEB) problem is to find a broadcast scheme with minimum energy consumption. The problem is also known as minimum power broadcast (MPB) problem or minimum energy consumption broadcast subgraph (MECBS) problem [2] . We use energy and power alternatively throughout this paper.. In this paper, we study the problem of broadcasting in wireless networks, where every node is equipped with omni directional antennas. We propose a hybrid algorithm based on clustering and prove its correctness. Theoretical analysis shows the effectiveness of our approach. We compare it with the Broadcast Incremental Power (BIP) [1] algorithm and the best heuristic approaches known in [2] [3] [4] by simulation. In this paper, we propose a hybrid approach for the MEB problem in wireless networks. Compared with existing approaches, theoretical and experimental results show the superiority. As further work, we will develop fully distributed algorithms for MEB problem. Most previously developed models for broadcasting and multicasting problems were linkbased models, which does not properly reflect the properties of the all-wireless network environment. To solve the MPB problem, Wieselthier et al. first proposed the node-based approach (BIP)which is more suitable for wireless environment than the link-based algorithms [1] . It was subsequently shown in [5] that the BIP algorithm has an approximation ratio between 13/3 and 12. Das et al. gave an improvement procedure called r-shrink for MEB problem [6] . Cagalj et al. [7] proposed another improvement procedure called embedded wireless multicast advantage (EWMA). Kang et al. [8] generalized the EWMA into another heuristic called largest expanding sweep search(LESS). In [9] , an ant-colony based approach for the problem was presented. An algorithm called CM using ant colony optimization approach was also presented in [3] . Furthermore, in [4] a simple simulated annealing algorithm with Metropolis chains of dynamic length was presented. The algorithm is in fact a probabilistic version of the 1-shrink tree-improvement algorithm described in [9] . Kang et al. [10] gave a perturbation based iterated local optimization method that uses LESS as local search. In [11] , Montemanni et al. presented a simulated annealing approach based on r-shrink. They used sweep procedure to improve the solution obtained through simulated annealing. Al-Shihabi et al. [12] developed a hybrid approach combining nested partitioning with LP relaxation and r-shrink method. In [13] , Wolf et al. proposed an evolutionary local search, which uses modified r-shrink as local search and random increase in transmission power of some nodes as mutation operator. Recently, Wu et al. [14] developed a generational genetic algorithm that uses permutation encoding to represent a broadcast scheme. Hashemi et al. presented a simulated annealing algorithm using a special node selection mechanism in its neighborhood structure [2] . In [15] , Singh et al. proposed a hybrid approach to the MEB problem combining a genetic algorithm with a local search heuristic, which is a modified version of r-shrink improvement procedure [6] .

O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O B O O O O O O B O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Finite-Length Scaling for Iteratively Decoded LDPC Ensembles We investigate the behavior of iteratively decoded low-density parity-check (LDPC) codes over the binary erasure channel in the so-called "waterfall region." We show that the performance curves in this region follow a simple scaling law. We conjecture that essentially the same scaling behavior applies in a much more general setting and we provide some empirical evidence to support this conjecture. The scaling law, together with the error floor expressions developed previously, can be used for a fast finite-length optimization.Index Terms-Binary erasure channel, density evolution, error probability curve, finite-length analysis, iterative decoding, lowdensity parity-check (LDPC) codes. I T IS probably fair to say that the asymptotic behavior (as the block length tends to infinity) of iterative coding systems is reasonably well understood to date. Much less is known about the finite-length behavior though.. As usual, the situation is clearest for the binary erasure channel . In this case, the finite-length analysis of the average performance of an ensemble boils down to a combinatorial problem. In [10] , recursions were given to solve this combinatorial problem for some simple regular ensembles. These recursions were generalized in [26] , [32] to deal with irregular ensembles, expurgation, and to compute block as well as bit erasure probabilities. In principle, these recursions allow to determine the average finite-length performance for any desired ensemble. In practice though this approach runs into computational limitations. Roughly, the computational complexity of the recursions grows by a factor (the block length) for each degree of freedom of the ensemble. For reasonable lengths only very simple ensembles can currently be analyzed in this way.. Given the computational complexity of an exact finite-length analysis, it is of interest to find good approximations. Let us Manuscript received June 17, 2004; revised September 17, 2008 . Current version published February 04, 2009. The material in this paper was presented in part at the Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, October 2003.. A. Amraoui and R. Urbanke are with the Swiss Federal Institute of Technology (EPFL) , Lausanne, CH-1015 Switzerland (e-mail: abdelaziz.amraoui @epfl.ch; ruediger.urbanke@epfl.ch).. A. Montanari is with the Department of Electrical Engineering and Statistics, Stanford University, Stanford, CA 94305 USA and with Laboratoire de Physique Théorique de l'ENS, Paris, France (e-mail: montanari@stanford.edu).. T. Richardson is with Flarion Technologies, Bedminster, NJ 07921 USA (e-mail: richardson@flarion.com).. Communicated by G. Zémor consider ensembles whose threshold is not determined by the stability condition, see [20] . In this case, the finite-length performance curve can be divided into two regions, [25] . The waterfall region and the error floor region. In the waterfall region, the performance is determined by "large" (linear sized) failures and it improves quickly for decreasing erasure probabilities. In the error floor region, on the other hand, the performance is determined by "small" (sublinear sized) weaknesses in the graph. Fortunately, this second region is relatively easy to handle as was demonstrated in [25] .. In this paper, we address the issue of modeling the behavior of large error events. Our approach is motivated by a general conjecture stemming from statistical physics [14] , [24] . If a system goes through a phase transition as a control parameter crosses a critical value , then around this point the system behavior obeys a very specific scaling law. This phenomenon has been repeatedly observed in a number of statistical physics models and rigorously proved in a few of them. To be concrete, consider the block error probability , as a function of the block length and the channel parameter . As , this quantity exhibits a phase transition at the iterative decoding threshold . Indeed for and for (we assume here that the ensemble is such that it has no error floor; the more general case is discussed at length in later sections). The scaling law refines this description by postulating the existence of a nonnegative constant and some nonnegative function so that (1) The same statement can be written in a slightly different (but equivalent) form as follows:. In other words, if one plots as a function of then, for increasing , the finite-length curves are expected to converge to some function . The function decreases smoothly from to as its argument changes from to . All finite-length performance curves are therefore, to first order, scaled versions of some mother curve . It might be helpful to think of the threshold as the zeroth order in a sequence of approximations (analogous to a Taylor series). Then the above scaling, if it holds, represents the first-order approximation. In fact, one can further refine the analysis to include higher order terms and write (3) where is some positive real number and is the secondorder correction term. 0018-9448/$25.00 © 2009 IEEE Such scaling laws are expected to apply in a wide array of situations in communications. The following is probably the simplest case in which a scaling law can be proved rigorously. Recall that Shannon's random parity-check ensemble of length and rate is defined by the ensemble of parity-check matrices with rows and columns, endowed with the uniform probability distribution. Consider transmission over the using a random element of Shannon's ensemble and maximum-likelihood (ML) decoding. If is the set of erased positions, let be the submatrix of consisting of the columns of indexed by . The ML block decoder will succeed if and only if has rank equal to . By definition, is itself a uniformly random binary matrix of dimension , where . Some thought shows that , .. Let denote the block error probability for communication over the channel using a code with parity-check matrix . A quick calculation reveals that (4) where in the last line we used the fact that and we defined the -function as usual by. In words, since the conditional probability of block erasure falls off steeply away from the threshold, the scaling law is dominated by the probability that the channel behaves atypically and that the number of erasures exceeds . In this paper, we prove a scaling law for iteratively decoded regular low-density parity-check (LDPC) ensembles and Poisson ensembles when transmission takes place over the . Further, we provide explicit values for the scaling parameters appearing in this scaling law for the regular case l , r . In the sequel, we give a leisurely overview regarding the main results.. Assume first that (the variable node degree) is at least . Let be a random element of the ensemble , and let be its block error probability when used over the channel . Then, as will be stated more precisely in Section III (5) where is a parameter which depends on the ensemble and can be determined through a procedure similar to density evolution, which we shall call covariance evolution. In the case of regular ensembles l r , this parameter admits a particularly elegant expression (6) where , denote the largest density evolution fixed point (i.e., solve the equations l , r ). Notice that this scaling law has a form similar to the one holding for the Shannon ensemble, cf. (4). However, strictly: the threshold width is only partially explained by the fluctuations in the number of erased bits.. We conjecture that in fact the following refined scaling law is valid: (7) Notice that the term represents a shift of the threshold due to the finite block length. More explicitly, if we define a finite-length threshold as the smallest erasure probability such that the block error rate crosses , then we have (8) In other words, density evolution overestimates the threshold by a quantity of order . Again, this constant depends on the ensemble and we will show how it can be computed through covariance evolution. Once more, for regular ensembles l r , a particularly simple formula is obtained (9) where is a universal (ensemble-independent) constant that can be expressed in terms of Airy functions (see below). In the following, we shall sometimes refer to and as to the slope and shift scaling parameters. Fig. 1 shows this scaling applied to the ensemble which will serve as our running example. It is important to stress that the above scaling law models the behavior of large error events. A better comparison with (7) is therefore obtained by considering expurgated ensembles, see [25] . For the scaling (7) holds true asymptotically regardless of the expurgation scheme. This follows since, as shown in [32] , the contribution to the block error probability stemming from sublinear-sized weaknesses in the graph decreases like 1 l . However, for expurgated ensembles, the waterfall regime emerges more crisply, and a more accurate verification of the scaling law is possible.. The situation is somewhat more complicated if the Tanner graph contains a positive fraction of degree-variable nodes, see Table I . The block lengths/expurgation parameters are n=s = 1024=24; 2048=43; 4096=82; and 8192=147 , respectively. (More precisely, we assume that the ensembles have been expurgated so that graphs in this ensemble do not contain stopping sets of size s or smaller.) The solid curves represent the exact ensemble averages. The dashed curves are computed according to the refined scaling law stated in Conjecture III-A with scaling parameters = 0:262633 + " (1 0 " ) and = 0:616045, see Table I . see Table I . The block lengths/expurgation parameters are n=s = 1024=24; 2048=43; and 4096=82, respectively. The solid curves represent the exact ensemble averages. The dashed curves are computed according to the refined scaling law stated in Conjecture III-A with scaling parameters = 0:262633 + " (1 0 " ) and = 0:616045, see Table I. i.e., if . As long as the threshold is not given by the stability condition, i.e., if , one can still distinguish two types of error events: linear-sized error events, whose contribution scales like (7) and a contribution which stems from sublinear sized weaknesses in the graph. The contribution from the latter part depends crucially on the expurgation scheme employed and does not necessarily vanish as . In the preceding discussion, we focused on the block erasure probability. The equivalent scaling law for the bit erasure probability is an adaptation: If the decoder fails at the critical 2 point then, asymptotically, it incurs a fixed bit erasure probability, call it (the fractional size of the residual graph). Therefore, if we 2 See Section II for a discussion of this notion. multiply the above expressions by we get the corresponding scaling law for the bit erasure probability. Fig. 2 shows the resulting approximation of . The scaling laws (5), (7) apply to regular as well as to irregular ensembles under mild conditions on the degree distribution. More precisely, the threshold should not be determined by the stability condition (i.e., ), and must correspond to a unique critical point (i.e., the equation admits a unique nonvanishing solution), see Sections II and III. The computation of the scaling parameters though becomes significantly more involved in the irregular case and therefore we limit ourselves in this paper to providing the detailed calculations only for regular ensembles. Fig. 3 demonstrates the scaling law for the block erasure probability applied [P (G; ")] for transmission over the BEC(") and belief propagation decoding. The (bit) threshold for this combination is " = . The solid curves are the exact ensemble averages for block lengths equal to n = 256; 1024; 4096; and 16384. The bold curve is the limiting (in n) block erasure curve. The dashed curves are the finite-length approximations computed according to (10) . to the irregular ensemble . In this case, the scaling parameters were simply fitted to the data.. The performance of ensembles whose threshold is determined by the stability condition scales in a fundamentally different way. The simplest such ensembles are cycle codes, i.e., ensembles of the type . We will discuss cycle codes in some detail since we conjecture that the same scaling behavior applies to all ensembles for which the stability condition determines the threshold. Fig. 4 shows block erasure curves for the cycle Poisson ensemble with expurgation parameter for , , , . Also shown is the asymptotic block erasure probability and our approximation for the finite-block-length erasure probability around the threshold.. These curves are qualitatively different from the ones discussed above. As investigated in more detail in Section III, the block erasure probability does not show a threshold effect: instead, it converges to a continuous function of , with discontinuous first derivative at . At finite block length , this singularity is smoothed according to the following scaling law: (10) where , , and is a constant which depends on the expurgation scheme used. This form corresponds to the approximate finite-block-length curves in Fig. 4 . The form of the mother curve is given in Lemma 2 below. The solid curves represent the simulated ensemble averages. The dashed curves are computed according to the refined scaling law (7) with scaling parameters = 0:8694 and = 5:884. These parameters were fitted to the empirical data. The block lengths/expurgation parameters are n=s = 1024=19; 2048=39; 4096=79; and 8192=79; respectively. The solid curves represent the ensemble averages obtained via simulation. The dashed curves are computed according to the refined scaling law stated in (7) with scaling parameters = 1:156 and = 0:1.

O O O O O O O O O O O O O O B I I I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B I I B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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Support Vector Machines versus Multi-Layer Perceptrons for Efficient Off-Line Signature Recognition Abstract. -The problem of automatic signature recognition has received little attention in comparison with the problem of signature verification despite its potential applications for accessing security-sensitive facilities and for processing certain legal and historical documents. This paper presents an efficient off-line human signature recognition system based on Support Vector Machines (SVM) and compares its performance with a traditional classification technique, Multi-Layer Perceptrons (MLP). In both cases we propose two approaches to the problem: (1) construct each feature vector using a set of global geometric and moment-based characteristics from each signature and (2) construct the feature vector using the bitmap of the corresponding signature. We also present a mechanism to capture the intrapersonal variability of each user using just one original signature. Our results empirically show that SVM, which achieves up to 71% correct recognition rate, outperforms MLP. Automatic human signature processing is a complex and specific area of automatic handwriting analysis [36] [19] [31] with a high scientific and technical interest. Two are the main research fields in this area: signature verification and signature recognition (or identification). The amount of interest and research efforts in these two fields is increasing due to the ability of human signatures to provide a secure process for authentication in many legal documents. The signature recognition problem consists on identifying the author of a signature. In this problem a signature database is searched to establish the identity of a given signer [28] [4] . This task is different from signature verification. Verification defines the process in which a signature is tested to decide whether a particular signature truly belongs to a person [4] [23] . The output in this case is either accepting the signature as valid or rejecting it as a forgery. Automatic signature verification is an established and very active research field [27] [35] [7] with important applications to the validation of checks and other financial documents. Due to the demonstrated practical applications of signature verification, different techniques have already been applied: fuzzy logic [21] , geometric features [15] [20] , global characteristics [38] , genetic algorithms [41] , neural networks [4] [5] [45] , Hidden Markov Models [10] , etc. In comparison, automatic signature recognition has received less attention, despite the potential applications that could use the signature as an identification tool [32] [33] . For example, an automated signature recognition system could provide a company with a unique technique for validating the identity of each individual accessing to certain securitysensitive facilities [28] . Other potential signature recognition applications are in law-enforcement applications, where the identification of perpetrators is a fundamental requirement of the solution, and in the analysis of some historical documents [21] . Some previous works in the area of automatic signature recognition are: Ammar et al [2] that uses a hierarchical scheme of signature descriptors to identify a test signature; Han and Sethi [19] , which considers a set of geometric and topologic features to map a signature image into two string of finite symbols; Pavlidis et al [34] , which proposes the application of active deformable models for approximating the external shape of a signature; and Riba et al [39] , that compares different statistical methods, using a feature extraction preprocessing, to carry out the recognition of signatures. From a theoretical point of view, signature recognition and verification are different and independent problems, recognition is a 1:N matching problem while identification is 1:1. Apparently, the signature recognition problem looks more complex than the signature verification problem, and relatively little research effort has been focused on automatic signature recognition. In Ismail and Gad's work [21] , signature recognition and verification are treated as two separate and consecutive stages, where successful verification is highly dependent on successful recognition. Pavlidis et al [34] state that it would be of great value an intelligent signature identification system, which should be capable of arriving at a decision (recognition and verification) based only on the signature of the user. In this context, signature recognition is applied as an efficient preprocessing stage for signature verification. This approach and the potential applications of signature recognition, justify from our point of view the interest in finding effective automatic solutions for the recognition problem.. Signature recognition can be solved using off-line or on-line techniques. In the on-line approach the system uses not only the signature but also the data obtained during the signing process (dynamic information). The off-line approach only uses the digitalized image of a signature extracted from a document (static information). In this paper we focus on the off-line signature recognition problem, which is the most common situation in many real applications (i.e. bank documents). A signature recognition system is characterized by two factors: (1) representation, which refers to the internal description that the system extracts from each signature of the data base and (2) match scheme, which involves the method that is used to select the best match from the set of identities of the signature data base. Ref. [19] uses a similar terminology to describe the components of a signature recognition system. Off-line signature recognition, and in general, image processing applications, face the problem of high dimensionality of the feature vectors. Because of that, a straightforward approach to the problem is to use pattern recognition techniques, like Multi-Layer Perceptrons (MLP) with standard back-propagation learning or Support Vector Machines (SVM), that have produced very good results in high dimensional classification problems [29] [13] . Neural networks, in general, and MLP networks in particular, are widely used in handwritten recognition systems because they are very easy to train, very fast to use in classification decision process and generally achieve good performances in terms of correct recognition rate [36] . This popularity is related to the use of a back-propagation algorithm for the training process. The two main limits when using MLP in classification tasks are: (1) there is no theoretic relationship between the MLP structure and the classification task and (2) MLP derive hyperplanes separation surfaces, in feature representation space, which are not optimal in terms of margin between the examples of two different classes. Different neural networks architectures, including MLP, have already been used mainly for signature verification [4] [42] [1] . The two main limitations that MLP face are solved by SVM: (1) by construction, SVM have a relationship between the structure (the support vectors) and the classification tasks and (2) SVM optimize the separation surfaces between two classes. SVM have been used very effectively for recognition applications like digit recognition [16] , face recognition [17] and 3D object recognition [37] . Ref. [9] presents an extensive review of SVM pattern recognition applications. Recently they have been applied to on-line [24] and off-line [23] signature verification problems. Nevertheless, to the best of our knowledge, SVM have not been applied to automatic human signature recognition. SVM differ radically from MLP in that SVM training always finds a global minimum. The main difference between MLP and SVM is the principle of risk minimization. In case of SVM, structural risk minimization principle is applied by minimizing an upper bound on the expected risk whereas in MLP, traditional empirical risk minimization is used minimizing the error on the training data. The difference in risk minimization is to improve the generalization performance of SVM compared to MLP [40] . This paper presents an off-line signature recognition system implemented with SVM as matching scheme and compares its performance with a more traditional MLP-solution in terms of correct classification rate. The approach to the problem, in both cases, is using two different representations: (1) using a feature vector constructed with global geometric and moment-based characteristics, and (2) using the bitmap of the normalized image of each signature as the feature vector. The second approach is possible due to the ability of both SVM and MLP to work with high dimensional problems. The paper also describes the construction of a human signature database using synthetic techniques. The main goal of this process is to create a representative training set which captures the intrapersonal variability of each writer without asking the user to provide his/her signature more that one time. The reason for that is caused by the fact that in many real applications it is not viable to get more than one signature from each system user for training purposes. The intrapersonal variability of the signature of each subject is captured by applying a combination of geometric transformations on the only original training signature. The process produces a relevant set of synthetic signatures for each writer that are used to train the two recognition systems. This is one of the main contributions of the paper, compared for example with [5] where the training of the recognition system needs between 15-25 original signatures for each individual. The rest of the paper is organized as follows. Section 2 presents an introduction to Support Vector Machines. Section 3 describes the basic characteristics of Multi-Layer Perceptrons. Section 4 gives a state of the art of SVM and MLP in signature recognition. Section 5 justifies and describes the creation and preprocessing of the signature database used. Section 6 presents a signature recognition system constructed using SVM. Section 7 presents the proposed MLP-based signature recognition system and Section 8 compares the SVM and the MLP approach among themselves and with other references. Finally, in Section 9 conclusive remarks and future work are resumed. Despite the potential applications for accessing securitysensitive facilities and for processing legal and historical documents of the signature recognition problem, it has received very little attention when compared with signature verification. The relevance of signature recognition, apart from its applications, also comes from the fact that it can be considered a fundamental preprocessing stage for signature verification. In other words, a correct signature verification depends on a correct signature recognition. This paper has presented an efficient off-line signature recognition system constructed using SVM. To the best of our knowledge this is the first application of SVM for signature recognition. MLP and SVM have been applied to many classification problems, generally yielding good performance. In this paper we also compare these two machine learning algorithms on signature recognition. From the results obtained we empirically conclude that SVM work better than MLP, with standard backpropagation learning, for off-line signature recognition (within our signature database), both for the identification rate obtained (there is an increment of 20% in the recognition rate when using SVM) and for the training time needed. This superior SVM performance is due to the superior generalization ability of Support Vector Machines in high dimensional spaces. We have also presented an original technique for the synthetic generation of a training signature database, thus avoiding the inconvenience that each user has to sign more that one time in order to be correctly recognized by the system. The system generates a significant set of synthetic signatures for training purposes using just one original signature as seed. This is a very important characteristic in order to create practical applications, because in a real environment a user will be willing to provide one original signature, but in general, no more than that. The recognition results presented in the paper prove that, when combined with SVM, this mechanism is able to capture, to a large extent, the intrapersonal variability. Regarding future research lines, first we plan to develop a more complete off-line signature database freely available to the research community in order to provide the means to compare different signature recognition techniques. With respect to the signature recognition system, regarding the good results provided by the synthetic generation of signatures, we plan to introduce also non-linear modifications in order to optimize the capture of intrapersonal variability. Another future research line is to investigate on the design of an ad-hoc kernel for the process of signature identification in order to improve the efficiency of the SVM approach.

B I I O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Automated graph-based analysis and correction of cortical volume topology Abstract-The human cerebral cortex is topologically equivalent to a sheet and can be considered topologically spherical if it is closed at the brain stem. Low-level segmentation of magnetic resonance (MR) imagery typically produces cerebral volumes whose tessellations are not topologically spherical. We present a novel algorithm that analyzes and constrains the topology of a volumetric object. Graphs are formed that represent the connectivity of voxel segments in the foreground and background of the image. These graphs are analyzed and minimal corrections to the volume are made prior to tessellation. We apply the algorithm to a simple test object and to cerebral white matter masks generated by a low-level tissue identification sequence. We tessellate the resulting objects using the marching cubes algorithm and verify their topology by computing their Euler characteristics. A key benefit of the algorithm is that it localizes the change to a volume to the specific areas of its topological defects. G EOMETRIC information about the cerebral cortex is important in various neuroimaging applications including intersubject registration and comparison, image reconstruction, and visualization techniques. The field of brain mapping has focused much attention on producing flat and other two-dimensional (2-D) representations of the cerebral cortical surface in order to produce coordinate systems in which brain geometries and other properties may be compared [1] - [9] . These methods inherently rely on an important topological property of the cerebral cortex-that it is a single sheet of connected tissue enclosing the telencephalon. By closing the cortical surface at the brainstem we can describe the cerebral cortex as having the topology of a sphere. This topology provides us with an important ability-it guarantees the existence of invertible one-to-one maps between cortical surfaces of different subjects and each other, or between these surfaces and a geometric primitive such as the sphere. With such maps, intersubject studies Publisher Item Identifier S 0278-0062(01)10001-7.. of cortical surface variation are possible using surface warping methods [3] , [5] - [9] . Two-dimensional brain surface topology is frequently assumed for cortical flattening approaches, such as those described in [1] , [2] , [4] , and [5] . The cortical mapping methods presented by Drury et al. and Fischl et al . require 2-D surfaces for flattening; such surfaces can be obtained by cutting a spherical surface [2] , [5] . Topologically correct brain surfaces can also be used to constrain the location of neural current sources to the cerebral cortex when solving inverse problems in magnetoencephalography (MEG) and electroencephalography (EEG) [1] , [10] . Applications such as these motivate the development of automated methods for generating cerebral cortex surface representations that have the appropriate topology. Magnetic resonance (MR) imaging is the typical modality from which neuroanatomical surfaces are obtained because of its ability to provide high resolution, high contrast images of the soft tissues of the human brain. The task of identifying structures in MR imagery is typically approached from one of a few directions. Registration techniques can be used to deform a labeled atlas to a subject to identify neuroanatomy [11] - [13] . These methods typically perform well in subcortical structures such as the basal ganglia but have difficulty matching the cortex due to the variability found among different subjects. For this reason, Collins et al. incorporated a low-level tissue classification scheme with a deformable atlas in order to label regions of the cortex [13] .. Another technique for identifying anatomical structures is the use of deformable surface methods, several of which have been surveyed by McInerney and Terzopoulous [14] . These methods can be implemented such that the topology of the final surface matches that of an initial template. However, this can be computationally intensive compared to low-level processing, and the deforming surface must be prevented from intersecting itself. Also, these methods do not always deform well into cortical structures due to other attractors in the image. Accurate segmentation using deformable surfaces often depends upon a reasonably accurate initialization [15] .. Low-level tissue classification approaches, in which individual voxels in the MR image are labeled according to tissue types, can provide high-resolution detail of the cortical surface and are often used to initialize active contour models. These techniques are susceptible to inhomogeneity artifacts, partial voluming, and other noise, which will result in mislabeled voxels. Additionally, the low resolution of the scanning system, as compared to the true fine scale of the neuroanatomy, will often obscure the boundaries between neighboring gyri. For these reasons, tessellations made from low-level labelings of the cerebral cortex typically exhibit numerous topological defects in the form of small handles or tunnels on the surface or even false connections between the hemispheres, as seen in Fig. 1 .. The method presented by Teo et al. provides for identification of potential topological defects which can then be corrected by hand; verification of the Euler characteristic on the volume ensures that the corrected volume will have the appropriate topology [16] . The cortical surface-based analysis methods presented by Dale, Fischl, and Sereno [4] , [5] addressed this problem using hand editing for larger topological defects while ignoring smaller ones that do not impact their flattening methods. Identification of the topological errors was performed by viewing an inflating cortical surface, and correction was achieved by editing the surface or the data. Interactive correction of surface meshes, or the volumes from which they are generated, can be difficult and time consuming, particularly for errors involving only a few voxels. More recently, Fischl et al. presented a method to perform automated topological surgery on the initial cortical surface [17] . This method inflates the cortex to a sphere and identifies overlapping triangles in the spherical surface. These areas occur due to topological handles, and are retessellated to correct the topological defects.. The cortical identification method presented by Xu et al. also addresses the issue of automatically correcting surface topology [18] , [19] . Their method makes use of fuzzy classification to produce an initial isocontour representing the boundary between white matter and grey matter. If this surface is not homeomorphic to a sphere the fuzzy membership set is median-filtered spatially and the isocontour surface is recomputed. This procedure is iterated until a surface with the appropriate topology is found. The topologically correct isocontour surface is then used as an initial condition for an active contour model that finds the medial grey matter cortical surface using a gradient vector flow method [20] . While this approach has been shown to produce topologically spherical surfaces, the use of median filtering on the membership set affects the entire volume and can smooth certain aspects of the cortex. A second drawback to this approach is that the use of a 3 3 3 median filter does not guarantee a topologically spherical result. An example of this is a configuration of voxels with two-voxel-thick sheets connected by a number of 2 2 bridges. The structure will not have spherical topology, but will be invariant under the median filter.. In this paper, we present a method designed to take a binary volumetric object with an arbitrary topology and automatically edit its membership such that a marching cubes [21] tessellation of the edited object will be homeomorphic to a sphere. The method identifies topological problems in the volume prior to tessellation and makes minimal changes in the volume. This method is suitable for use in cortical surface identification because of its ability to find and then break or fill the small topological defects that occur during classification. Most significantly, the method identifies specific locations within the volume where topological defects form and can be corrected with changes to the membership set that are local to the area of the proposed defect. In most cases, these changes are on the order of one or two voxels. In this way, the algorithm respects the geometry of the cerebral cortex when making its changes to the volume. We demonstrate the method on a simple test object and on several white matter volumes generated from MR brain images. In this paper, we have presented a new method that analyzes and alters the topology of a binary volumetric object so that its tessellation will be homeomorphic to a sphere. The method is appropriate for forcing the topology of cerebral white matter volumes to be spherical. It operates on the voxel membership set of the volume, and makes minimal changes to force it to have the topology of a sphere. The method has correctly altered the topology of every volume tested.. This method provides a completely automated way to quickly correct the topology of cortical volume segmentations. When used in combination with largely automated segmentation procedures, the burden on human operators to produce topologically correct cortical surface models is significantly reduced. This increases the scale on which surface-based intersubject population studies can realistically be performed. We implemented the topological constraint algorithm in C++ and successfully applied it to volumetric objects. We present the results of the algorithm on a small test object and demonstrate the graph formation and correction process. We then present the results of using the algorithm on several cerebral cortex masks generated from MR images of several subjects. Fig. 7 shows two renderings of a small hand-created object composed of 65 connected voxels. The voxels are contained within four slices of a 20 20 6 volume. Computation of the Euler-Poincaré formula on the marching cubes [21] tessellation shows that the object has a genus of five. The handles or holes of the object are clearly visible; we see three holes aligned with the vertical axis and two aligned horizontally. The interslice connectivity graphs for this object are also shown in Fig. 7 . Each of the three vertical holes are captured as cycles in the foreground graph, while the two horizontal holes are captured in the background graph.

O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Optimization of cooperative spectrum sensing with sensing user selection in cognitive radio networks Cooperative spectrum sensing (CSS) can improve the spectrum sensing performance by introducing spatial diversity in cognitive radio networks (CRNs). However, such cooperation also introduces the delay for reporting sensing data. Conventional cooperation scheme assumes that the cooperative secondary users (SUs) report their local sensing data to the fusion center sequentially. This causes the reporting delay to increase with the number of the cooperative SUs, and ultimately affects the performance of CSS. In this article, we consider the reporting delay and formulate the optimization problem of CSS with sensing user selection to maximize the average throughput of the CRN in both the additive white Gaussian noise (AWGN) environment and the Rayleigh fading environment. It is shown that selecting all the SUs within the CRN to cooperate might not achieve the maximal average throughput. In particular, for the AWGN environment, the sensing user selection scheme is equivalent to selecting the optimal number of cooperative SUs due to all the SUs having the same instantaneous detection signal-to-noise ratio (SNR). For the Rayleigh fading environment, the maximal average throughput is achieved by selecting a certain number of cooperative SUs with the highest instantaneous detection SNRs to cooperate. Finally, computer simulations are presented to demonstrate that the average throughput of the CRN can be maximized through the optimization. Cognitive radio (CR) technology has recently been identified as a promising way to address the spectrum scarcity by exploiting opportunistic spectrum in dynamically changing environments [1, 2] . A prerequisite of CR is the ability to detect very weak primary user (PU) signals and limit the probability of interference with PU. Thus, spectrum sensing plays an essential role in CR. However, due to multipath fading, the shadow effect and time-varying natures of wireless channels, it is hard to achieve reliable spectrum sensing by a single secondary user (SU). To combat these impacts, cooperative spectrum sensing (CSS) has been proposed to improve the spectrum sensing performance by introducing spatial diversity [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] . There are mainly two fusion rules of CSS: data fusion rule and decision fusion rule. In this article, we focus on the data fusion rule. For the data fusion rule, multiple cooperative SUs individually sense the channel, and then report their local sensing data to the fusion center through a bandwidth-limited common control channel. Finally, the fusion center will combine these data and make the final decision.. The sensing time, the data fusion rule and the fusion rule's threshold at the fusion center can all affect the performance of CSS. A longer sensing time will improve the spectrum sensing performance, but decrease the data transmission time. Moreover, an optimal data fusion rule can help reduce the impact of unreliable CR. In [8] [9] [10] , the optimal linear functions of weighed data fusion rule in different cases have been obtained. In [12] , a joint optimization of the sensing time and data fusion rule is considered.. However, in order to apply CSS, local sensing data have to be reported to the fusion center through a bandwidth-limited common control channel. This adds the reporting delay to cognitive radio networks (CRNs). To address this issue, the study [15] proposed that cooperative SUs sent local sensing data concurrently. But this scheme will increase the system design complexity or cost a large portion of precious bandwidth. Therefore, given a bandwidth-limited common control channel, the conventional scheme that cooperative SUs report their local sensing data to the fusion center sequentially may be more desirable [16] . Nevertheless, in the conventional scheme, the reporting delay increases with the number of cooperative SUs, which will lead to the decrease of the time for spectrum sensing and data transmission. Thus, there is a tradeoff between the number of cooperative SUs and the average throughput of the CRN. In [17] , the authors demonstrated that selecting all SUs to cooperate in the CRN might not achieve the optimum performance. So they proposed a sensing user selection scheme based on the individual characteristics. But the sensing time was not considered in their optimization formulation.. In this article, we consider the conventional scheme that cooperative SUs report the local sensing data to the fusion center sequentially. We formulate the optimization problem of CSS with sensing user selection in both the additive white Gaussian noise (AWGN) environment and the Rayleigh fading environment. It is demonstrated that the maximal average throughput is achieved through the optimization. It is also shown that the maximal average throughput might be achieved by selecting a certain number of cooperative SUs rather than selecting all the SUs within the CRN.. The rest of the article is organized as follows: The system model is introduced in Section 2. The problem formulation based on data fusion rule is given in Section 3, and in Section 4, the solution of the optimization problem is presented. Numerical results and discussions are given in Section 5. Finally, conclusions are drawn in Section 6. In this article, we have considered the influence of the reporting delay to the CSS and investigated the average throughput problem under CSS scenario. The optimization problem of CSS with sensing user selection was formulated to maximize the average throughput of the CRN in both the AWGN environment and the Rayleigh fading environment, and the optimal solution was proposed to solve this problem. With numerical results, it is shown that the maximum average throughput can be achieved through the optimization. Moreover, it is also shown that selecting all the SUs within the CRN to cooperate might not obtain the maximal average throughput rather than selecting a certain number of SUs to cooperate.

B O B I I O B I I O B I O B I I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Designing effective visualizations of habits data to aid clinical decision making Background: Changes in daily habits can provide important information regarding the overall health status of an individual. This research aimed to determine how meaningful information may be extracted from limited sensor data and transformed to provide clear visualization for the clinicians who must use and interact with the data and make judgments on the condition of patients. We ascertained that a number of insightful features related to habits and physical condition could be determined from usage and motion sensor data.Methods: Our approach to the design of the visualization follows User Centered Design, specifically, defining requirements, designing corresponding visualizations and finally evaluating results. This cycle was iterated three times.Results: The User Centered Design method was successfully employed to converge to a design that met the main objective of this study. The resulting visualizations of relevant features that were extracted from the sensor data were considered highly effective and intuitive to the clinicians and were considered suitable for monitoring the behavior patterns of patients. Conclusions: We observed important differences in the approach and attitude of the researchers and clinicians. Whereas the researchers would prefer to have as many features and information as possible in each visualization, the clinicians would prefer clarity and simplicity, often each visualization having only a single feature, with several visualizations per page. In addition, concepts considered intuitive to the researchers were not always to the clinicians. The UCD method was successfully employed to converge to a design that met the main objective of this study. The resulting visualizations of relevant features that were extracted from limited sensor data, were considered highly effective and intuitive to the clinicians, and were considered suitable for them to be able to monitor the behavior patterns of patients.. The researchers recommend the approach to be applied to similar fields; employing the UCD method, with perhaps more clinicians participating in the evaluation, and involving them more closely in the design process.. We acknowledge that patient behavior would be studied more accurately by using a larger number of motion sensors around the home, but even the limited number of sensors was found to provide significant information. Bed usage sensors gave richer and more reliable data for nocturnal activity. Visualization development using the UCD methodology. The overall requirement of this research was to provide visualizations of habits data that were clear, simple and intuitive, and support rapid assimilation of changes from usual behavior. There were a number of further requirements for the visualizations, such as that they should show the time of any clinical event or intervention, in order to provide context and help explain events that might be evident in the sensor data.. The UCD methodology was adopted to develop visualization of sensor data for use by clinicians to assess for changes in health status. This involves undertaking several design and evaluation cycles, each intended to iterate towards an optimized solution. In our approach, we used each cycle to serve a separate purpose.. In the first design cycle we developed many different visualizations, with the intent that the most effective would be selected to be taken forward for further development. We also sought suggestions and ideas based on the visualizations to incorporate into subsequent designs.. In the second design cycle, the focus was on improving the selected visualizations and incorporating improvements based on the suggestions and feedback from the first evaluation. We produced a number of variants of each of the visualizations to explore options and elicit feedback that might be more useful in this cycle. Feedback from the second evaluation indicated that the visualizations were much improved, as evidenced from the consistent comments, specific suggestions and improved scores. We also noted that the clinicians had a clearer understanding what was expected from them and had a greater feeling for what they desired. The effectiveness scoring provided information to allow us to judge between the variants to determine the aspects that would help improve design of the visualizations.. In the third design cycle, the focus was on improving clarity and legibility of each visualization. The quantitative scoring of the third evaluation showed that significant improvement had been achieved in how effective the clinicians considered the final visualizations. Moreover, the high scores and few feedback comments indicated that no further design cycles were needed. Over the last 25 years the percentage of the population aged 65 and over has increased. By 2034 the number of people aged 85 and over is projected to account for 5% of the total population. Along with this increase comes increased clinical need. Many amongst this ageing population are living with one or more long term chronic conditions [1] .. The EU funded project inCASA (Integrated Network for Completely Assisted Senior citizen's Autonomy) [2] developed an integrated service delivery model that combined health and social care services to provide a coordinated response to the needs of frail elderly people with long term conditions. The integrated service was driven by the needs of health and social care and information about the patient and data from remote monitoring was shared and exchanged between the primary care team and social services.. One way of promoting independent living is by monitoring daily habits of the elderly. Changes in daily habits can provide important information regarding well-being, functional capability, cognitive ability, loss of autonomy/ independence, deterioration in health status, or progress of an existing illness [3] . Although there are a significant number of studies and reviews on the monitoring of chronic diseases, with themes of technology or treatment effectiveness [4] [5] [6] [7] [8] [9] , there are only a few reviews on monitoring of daily activities in elderly patients [10, 11] and, as found in [12] , there are no studies that sought to correlate activity, physiological monitoring and clinical events.. Patients enrolled into the inCasa service were provided with integrated technology to collect both health and habits monitoring data. The devices automatically transmitted the information via a home hub and data was analyzed in order to profile user behavior and to compare variations in the activity data with the variations in the physiological parameters. Clinicians carried out initial assessment of the patient data and if necessary would refer the patient for clinical intervention, social services or other community services as required. In this paper we use the term clinician to refer to general practitioners and practice nurses. The research supports independent living and responds to the combined clinical and social needs of an elderly population.. Patients were identified using a combination of health and social care registers. The level of frailty was assessed using the Edmonton Frail Scale [13] in addition to a number of other clinical measures. A total of 44 people were recruited into the service and 36 completed a minimum of 30 days of monitoring. 61% of those enrolled into the service were determined as being of average frailty and 27% as being very frail, leaving the remaining 12% as not frail.. Extensive research has been undertaken on sleep and activity patterns and their significance [14] [15] [16] . However it is desirable to obtain sleep and activity data in a way that is unobtrusive and does not rely on the active participation of the subjects, especially if this involves patients with a health problem. Although some research has been done on automatic collection of data, most systems have been established in purpose facilities rather than deployed with patients living in their own home, and not on a significant scale [12] . Clearly there are challenges. One of these is developing a platform that can be deployed at low cost, having devices for both activity and physiological monitoring, and fits well with UK health services. A cost-effective and minimally invasive solution in a real home would imply that the platform has a limited number of sensors, giving limited but adequate sensor information. The key area of research is how to determine the minimum monitoring requirements and how meaningful information may be extracted from that limited sensor data. This paper reports on the results of the development of our system, determination of data requirements, and analysis. A further important aspect of the research is how the data is transformed to enable clear and intuitive visualization for the clinicians that must use and interact with the data and make judgments on the condition of patients. This is also an area where little or no research has been undertaken.. In general, visualization has been widely used to enhance understanding and to promote insight into data and processes [17] . Effective visualization techniques are essential to allow patterns to be observed; that is, finding effective visualization to support the human ability to recognize complex patterns not easily detected otherwise [18] .. The aim of this research was to provide the clinicians with tools to enable them to observe sensor data and determine anomalies. Our approach was to create visualizations that clinicians would consider intuitive and effective, allow them to recognize issues with a patient, and that would indicate the need for intervention and facilitate effective and expeditious decision making.. A well-established process of design taking into account subjective user perception is the User Centered Design (UCD) technique [19] . UCD allows users to be part of the process within the intended context and facilitate the design to evolve. In this study the participants are the clinicians, and what is taken into account for improving the design is their perception of what they consider effective visualizations.. The visualizations in this study are based on medical sensor data. This includes processing the sensor data to extract and present significant features. The sensors that were deployed in the home of each patient were at most two motion sensors, or one motion and one bed usage sensor.

O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B I I O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O