The largest nonidentifiable outlier: A comparison of multivariate simultaneous outlier identification rules The aim of detecting outliers in a multivariate sample can be pursued in different ways. We investigate here the performance of several simultaneous multivariate outlier identification rules based on robust estimators of location and scale. It has been shown that the use of estimators with high finite sample breakdown point in such procedures yields a good behaviour with respect to the prevention of breakdown by the masking effect (Becker, Gather 1999, J. Amer. Statist. Assoc. 94, 947-955). In this article, we investigate by simulation, at which distance from the center of an underlying model distribution outliers can be placed until certain simultaneous identification rules will detect them as outliers. We consider identification procedures based on the minimum volume ellipsoid, the minimum covariance determinant, and S-estimators. The use of robust estimators for detecting outliers in multivariate data simultaneously has been proposed by several authors e.g. Simono , 1987. Becker and Gather 1999 give a 1 formal justi cation for this, showing that using robust estimators with high nite-sample breakdown point leads to better prevention from the masking e ect than using classical estimators in such simultaneous outlier identi cation rules. Several multivariate location and scale estimators can therefore be taken into account, for example the MVE-and MCDestimators and reweighted versions of them Rousseeuw, 1985 , Lopuha a, Rousseeuw, 1991 , Croux, Haesbroeck, 2000 , constrained M-estimators Kent, Tyler, 1996 , various types of S-estimators Davies, 1987 , Maronna, Yohai, 1995 , Rocke, 1996 , or the Stahel-Donoho estimators Stahel, 1981 , Donoho, 1982 , Tyler, 1994 , Maronna, Yohai, 1995 , Gather, Hilker, 1997 We restrict ourselves to the case of the p-variate normal N , 2 IR p , S 2 IR pp positive de nite p.d., as model distribution. Following the idea of Davies and Gather 1993 , we then consider the aim of detecting all N outliers in a sample of size N, i.e. all observations lying in the N outlier region out N of N : out N = fx 2 IR p : x T 1 x 2 p 1 N g where N = 1 1 1=N for some given value of 2 0 1, such that P N no observation in a sample of size N lies in out N = 1 :. Taking usual choices for = 0 :05 0:1, this means that under the model distribution there is only a small probability for any observation of a sample of size N to lie in the outlier region, re ecting the intuitive idea that an outlier is an unexpected" and far out observation.. Let now m S be a pair of a ne equivariant estimators for . To nd all N outliers 2 in a given sample x N = x 1 : : : x N of size N, x i 2 IR p , we can use m S to estimate out N by a corresponding region OR x N N , called outlier identi er, OR x N N = fx 2 IR p : x m T S 1 x m cp N N g where cp N N is a suitably chosen constant, calculated according to some normalizing condition, for example P N no N outliers identi ed in a sample of size N = 1 1.1 with N = 1 1 1=N as before. This is equivalent t o k eeping a level when applying consecutive testing methods to identify outliers Davies, Gather, 1993. An observation x i lying in OR x N N is then detected as an outlier. The use of a ne equivariant estimators guarantees that the identi cation rule is a ne equivariant, too. For more details on the concept of N outliers see Davies, Gather 1993 , Gather, Becker 1997 , or Becker, Gather 1999 .. The simultaneous outlier identi cation procedure described above corresponds to calculating the Mahalanobis-type distances d 2 i = x i m T S 1 x i m, i = 1 : : : N , with respect to m S and identifying an observation with large d 2 i cp N N as an outlier see e.g. Barnett, Lewis, 1994 , pp. 306 ., Rousseeuw, van Zomeren, 1990 , for procedures of this kind.. In this paper, we compare outlier identi ers OR based on some of the above mentioned robust estimators with respect to a certain performance criterion, namely the size of the largest nonidenti able outlier. The question is how far away" an observation can be while still not being detected as an outlier.. 3 Our paper is organized as follows. In Section 2, we present the robust estimators m and S used in the identi cation rules. In Section 3, we discuss which positions of outliers represent a worst case situation for these procedures and introduce the notion of the largest nonidenti able outlier". We t h e n g i v e the results of a simulation study, comparing the behaviour of the identi ers with respect to this criterion.

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A fast Hermite transform We present algorithms for fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated with a three-term relation. Tradeoffs between approximation in bandlimit (in the Hermite sense), and size of the support region are addressed. Numerical experiments are presented that show the feasibility and utility of our approach. Generalizations to any family of orthogonal polynomials are outlined. Applications to various problems in tomographic reconstruction, including the determination of protein structure, are discussed. In this paper, we present a modification and application of an algebraic algorithm for the efficient computation of a certain class of discrete polynomial transforms. A preliminary version of this paper first appeared in [20] . In particular, we modify a theorem of Driscoll, Healy, and Rockmore [10] in order to find an efficient algorithm for the computation of a certain kind of discrete Hermite transform (see below) for the general purposes of tomography, and in particular, for accomplishing a key step in an algorithm for the efficient determination of protein structure from a so-called tilt series (cf. Section 6).. The classical two-dimensional tomography problem performs the reconstruction of a two-dimensional density from a collection of measured one-dimensional projections. Most computational approaches to the general problem use standard Fourier analysis and the Fast Fourier Transform (see e.g., [16] and the references therein). The availability of a fast algorithm, such as the FFT can drive the choice of the Fourier basis, but for some problems, it may be more natural to use another basis for L 2 (R n ), making necessary the consideration of new fast algorithms in order to make these techniques feasible. One such case is the use of the basis of Hermite functions and their tensor products.. The Hermite transform expresses a function f (x) ∈ L 2 (R) in the complete orthonormal L 2 (R)-basis of Hermite functions. where. 2 H n (x) (1) and h n = 2 n n! √ π provided H n (x) is the nth Hermite polynomial. The Hermite polynomials are determined by the three-term recurrence relation $ This work is supported by NIH, grant number NIH R01GM075310-02.. with initial conditions H −1 (x) = 0, H 0 (x) = 1. Thus, any f ∈ L 2 (R) can be represented as. wheref (n) is the nth Hermite coefficient and is defined bŷ. The Hermite functions have the useful property that they are eigenfunctions for the Fourier transform (see [36] for various details of the Hermite functions). Moreover, in higher dimensions (in which case we mean the product of Hermite functions in the independent variables) the Hermite transform behaves well under rotation: given f ∈ L 2 (R 3 ) and a given R ∈ SO(3), then if f is ''Hermite-limited" (i.e., has a finite expansion in terms of Hermite functions), then Rf (defined by Rf (x) = f (R −1 x)) is also Hermite-limited. This is effectively a consequence of the fact that the Hermite functions are also eigenfunctions for the Laplacian (in any number of dimensions), and that the Laplacian commutes with rotation. Thus, there is a relatively simple transformation between coefficients that depends only on R [30] .. Our interest in the Hermite transform arises from this nice rotational invariance, as it applies to a particular problem in protein structure determination (cf. Section 6). In real applications such as this, there are many considerations. In particular, questions of discretization and then questions of efficient and reliable computation are paramount. Thus, we have two algorithmic goals:. (1) Analysis: computation of a discrete Hermite transform, realized from a sampling of the real line that takes a finite collection of function values (sample values) and returns Hermite coefficients. (2) Synthesis: computation of the function values at a discrete set of points from a finite collection of Hermite coefficients.. Analysis and synthesis are sometimes also referred to as the ''forward" and ''inverse" transforms, respectively.. In this paper, we explore aspects of the related notions of forward and inverse discrete Hermite transforms. In Section 2, we derive efficient algorithms for the forward and inverse transforms: O(M log 2 M) algorithms for computing both the forward and inverse discrete Hermite transform from a set of O(M) sample points. Note that in its extension to n dimensions (the cases of n = 2, 3 provide the motivating applications for this work), this amounts to algebraic algorithms that take advantage of a three-term recurrence that require O(M n log 2 M) operations versus O(M 2n ) operations, if accomplished directly (i.e., ''naively"). These complexity results are augmented by an investigation of numerical aspects of the problem. In Section 3, we take into account that the situation of interest is one in which the function f has compact support, whose range of definition is essentially arbitrary. We investigate some of the trade-offs that arise in the accompanying flexibility in the choice of range of integration. This is critical for the applications of interest in which the data is clearly limited in space, but does not come with a fixed range of support (i.e., there is no a priori fixed set of units that make it necessary to use one grid over another). Section 4 provides an error analysis of these numerical methods. We have implemented our algorithm (see [1] to obtain the software) and a discussion of some standard numerical experiments is given in Section 5. Finally, in Section 6 we sketch the applications which these efficient transforms were designed to facilitate. In particular, we close with some 2D experiments using simulated EM image data for a particular protein complex. The success of this last experiment is evidence for the utility of this approach.

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Near-optimal scheduling of device activation in water distribution systems to reduce the impact of a contamination event This paper proposes an innovative procedure for identifying, in the event of accidental or intentional contamination of a water distribution system, the optimal scheduling of activation of a pre-selected set of flow control devices which will serve to minimise the volume of contaminated water consumed by users after the detection of the contaminant in the system. The constraints are represented by the number of available response teams and the maximum speed at which these teams can travel along the roadway. The optimal scheduling of device activation is sought by means of an optimisation process based on a genetic algorithm (GA) which interacts with a mixed integer linear programming (MILP) solver in order to ensure the feasibility of the scheduling identified. The optimisation procedure is coupled to a hydraulic and quality simulator, which enables a calculation of the volumes of contaminated water consumed by users, and a dynamic cache memory, which, by storing information on the system's behaviour as the optimisation process progresses, serves to limit the computational times. The application of the procedure to a highly complex real water distribution system shows that the optimisation process is robust and efficacious and produces a smaller volume of contaminated water consumed by the users than when the activation of all the devices was completed in the shortest amount of time. This study addresses the problem of determining the optimal scheduling of activation of flow control devices in a water distribution system in the case of a contamination event (accidental or deliberate), given an assigned number of available response teams.. The proposed procedure for solving the problem is based on a GA coupled to a MILP solver, whose function is to bring the schedules generated by the GA into line with 'feasibility' constraints. The proposed procedure represents an innovative element in the technical literature within this sector, as it is typically assumed that the activations of devices in response to a contamination event take place simultaneously. However, such simultaneity is not possible given that the devices must generally be operated on site, utility companies have a limited number of response teams to carry out such operations and the teams must travel along a roadway at a speed which has an upper limit.. The results obtained when the procedure was applied to a complex real case showed it to be robust and efficacious.. The procedure is capable of providing feasible solutions for scheduling the activation of devices in the system in such a way as to significantly contain the impact of the contamination event on the population served, which means limiting the contaminated volumes consumed.. It was observed, in particular, that the largest benefits are gained where the specific contamination scenario underway is known, but even where the specific contamination scenario underway is not known the procedure represents a useful tool for defining a feasible reference solution for scheduling activations so as to minimise the contaminated volume consumed on average over a broad range of possible contamination scenarios.. In both cases (known or unknown contamination scenario), the scheduling solutions provided by the procedure result in a smaller volume of contaminated water consumed than would be the case if activation of all devices were to be completed in the least amount of time possible. This result highlights that, given the complexity of the phenomenon of contaminant propagation in a tightly meshed distribution network and its nonlinearity, 'the sooner the better' is not necessarily true.. It is important to observe, moreover, that hydraulic simulations and quality simulations in particular entail lengthy computation. However, the procedure makes use of a cache memory which avoids the need to repeat numerous simulations corresponding to the same set of device activation times, as well as a multi-start approach which enables a simple parallel implementation of the procedure without impairing its efficacy; these represent valid means of reducing the computational burden. However, the execution times remain quite high and thus the proposed procedure cannot be applied in real time but, instead, is useful for creating offline a 'reference manual' of the optimal scheduling for each possible contamination scenario, together with the devices' assignment to each team and the order in which the devices must be activated, to be used by the water agency manager in situations of crisis.. To conclude two further considerations can be made.. Firstly, it is worth noting that the solution identified is optimal with respect to the minimisation of the volume of contaminated water consumed; the solution, being feasible, is also accompanied by a division and ordering of tasks among the various teams, so that the devices can really be activated in the times indicated by the solution itself.. Indeed, one could observe that the division of the tasks among the various teams is not optimised in order to minimise the travel of each team. This aspect is, however, secondary with respect to the minimisation of the volume of contaminated water consumed, which reasonably represents the major concern for a water agency manager/ technician. However, if of interest, the division of the tasks among the various teams furnished by the procedure could be further improved a posteriori in order to minimise the transfers of the teams along the roadway.. Secondly, deterministic model inputs and parameters are assumed in the procedure here presented. Indeed, model inputs and parameters, such as water demands, pipe roughnesses, etc. can be affected by uncertainty and this uncertainty can be represented through many different techniques such as probabilistic, fuzzy or grey approaches (Alvisi & Franchini ) . This aspect has not been considered in the presented study but represents a challenge for future research where uncertainty will be considered.

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State estimation for a class of nonlinear systems We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of nonlinearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin's damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example. State observers have been intensely exploited since the work of Luenberger (1966) to model, control, or identify linear and nonlinear systems, as in the studies by Krener and Isidori (1983) , Zeitz (1987) , Bastin and Gevers (1988) , Boutat et al. (2009), and Zheng et al. (2009) , relating to nonlinear systems transformable into a canonical form. The key idea in such approaches is to produce approximate measures of nonlinearity of the order 1, as in Extended Luenberger Observers (ELOs) (Ciccarella et al., 1993) . The approximation of nonlinearities in the canonical form (which results in an ELO) has already been suggested (Bestle and Zeitz, 1983) , and this approach can be extended to higher order approximations (Röbenack and Lynch, 2004 ). An observer using a Partial nonlinear Observer Canonical Form (POCF) (Röbenack and Lynch, 2006) has weaker observability and integrability existence conditions than the well-established nonlinear Observer Canonical Form (OCF).. Nonlinear sliding mode observers use a quasi-Newtonian approach, applied after pseudo-differentiation of the output signal (Hui andŻak, 2005; Veluvolu et al., 2007; Efimov and Fridman, 2011) . State observers using Extended Kalman Filters (EKFs) provide another method of transforming nonlinear systems (Boutayeb and Aubry, 1999; Khémiri et al., 2011) . In particular, Besançon et al. (2010) exploit an adaptive observer based on Kalman filters for physical systems to which Liénard transformations can be applied. Finding an appropriate method for parameter synthesis remains one of the major difficulties with state observers for nonlinear systems (cf. the works of Tornambè (1992) , Besançon et al. (2004) , Boizot et al. (2010) and Farza et al. (2011) , where high-gain state observers to deal with this problem were proposed). High-gain state observers reduce observation errors for a range of predetermined amplitudes or fluctuations by making the observations independent from parameters. A weak point of this method is its sensitivity to noise and uncertainty.. In network identification and encryption, observers with delays are used to synchronize chaotic oscillators, as shown in several studies (Feki, 2009; Ibrir, 2009; Ghosh et al., 2010) . Noise and uncertainty are not critical factors in such a context. This can be very different in the case of industrial processes, as shown in a recent study by Bodizs et al. (2011) , where the performances of observers using ELOs, EKFs or Integrated Kalman Filters (IKFs) are compared. The influence of noise and uncertainty on these observer types was emphasized, with more reliable results produced by ELOs, which permits the exact state reconstruction of highly perturbed systems. For PI and ELO observer classes, Söffker et al. (1995) as well as Morales and Ramirez (2002) demonstrated a compensation effect on measurement errors. Abdessameud and Khelfi (2006) as well as Chen et al. (2011) addressed the problem of uncertainty of nonlinear models.. In the present study here, we deal with a specific class of nonlinear SISO (Single Input Single Output) systems, described by Fliess (1990) , called the generalized controller canonical form. In principle, every uniformly observable (Hermann and Krener, 1977; Gauthier and Bornard, 1981) sufficiently smooth SISO system with input u and output y can be transformed into this normal form,ẋ. with the following definitions.

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Charge Group Partitioning in Biomolecular Simulation Molecular simulation techniques are increasingly being used to study biomolecular systems at an atomic level. Such simulations rely on empirical force fields to represent the intermolecular interactions. There are many different force fields available-each based on a different set of assumptions and thus requiring different parametrization procedures. Recently, efforts have been made to fully automate the assignment of force-field parameters, including atomic partial charges, for novel molecules. In this work, we focus on a problem arising in the automated parametrization of molecules for use in combination with the gromos family of force fields: namely, the assignment of atoms to charge groups such that for every charge group the sum of the partial charges is ideally equal to its formal charge. In addition, charge groups are required to have size at most k. We show N P-hardness and give an exact algorithm capable of solving practical problem instances to provable optimality in a fraction of a second. In the context of drug development, biomolecular systems such as proteinpeptide [29] , protein-ligand [24] and protein-lipid interactions [8] can be studied with the use of molecular simulations [2, 26] using a force field model that describes the interatomic interactions. Many biomolecular force fields are available, including amber [10], charmm [9], opls [16] and gromos [19, 21, 23] . These force fields have in common that the non-bonded intermolecular interactions are represented in terms of interatomic pair potentials.. Typically, the number of atoms in biomolecular systems are in the range of 10 4 to 10 6 . To observe relevant biological phenomena, time scales in the order of nano-to milliseconds need to be simulated. For such large-scale systems, evaluating all atom-atom interactions is practically infeasible. One way of dealing with this is to only consider interactions of atoms whose distance is within a pre-specified cut-off radius. Since not all interactions are considered, an error is introduced. The magnitude of the error due to omitting atom-atom interactions is inversely proportional to the distance between the atoms. More problematically, there are discontinuities as atoms move in and out of the cut-off radius.. Errors and discontinuities are reduced by combining atoms into charge groups, for which individual centers of geometry are determined. If the distance between two centers of geometry lies within the cut-off distance then all interactions between the atoms of the involved charge groups are considered. Ideally, charge groups should be neutral as interactions are then reduced to dipole-dipole interactions that scale inversely proportional to the cubed interatomic distance. Charge groups should not be too large. This is because the effective cut-off distance of an individual atom in a given charge group is given by the cut-off distance minus the distance to the center of geometry of the charge group. If the distance of an atom to the center of geometry becomes large, the effective cutoff becomes small, leading to errors and discontinuities as described above. For the same reason, charge groups should be connected as interatomic bonds indicate spatial proximity.. To simulate a molecule, a force field requires a specific topology, which includes the atom types, bonds and angles, the atomic charges and the charge group assignment. Most biomolecular force fields come with a set of topologies for frequently simulated molecules such as amino acids, lipids, nucleotides and cofactors. Novel molecules and compounds, however, require the construction of novel topologies. Such a situation occurs, for instance, when assessing the binding affinity of a novel drug-like compound to a certain protein.. Manually building topologies for novel compounds is a tedious and timeconsuming task especially when a large chemical library needs to be screened, for example when determining binding affinities for large sets of potential drug compounds to a newly discovered protein target. Therefore, automated approaches are needed.. Here, we focus on the gromos family of force fields, which has been specifically tailored to simulate biochemical processes, including protein-drug binding and peptide folding. A widely used topology generator for the gromos force field is prodrg [22] . However, the charge group assignment by prodrg for amino acid topologies contained several large charge groups comprising disconnected atoms, which is inconsistent with gromos [17]. The Automated Topology Builder (atb) is a recent method for automated generation of gromos topologies [18] . The assignment of atomic charges and charge groups by the atb proceeds in three consecutive stages. Firstly, partial charges are computed using quantum calculations. Subsequently, the symmetry of the molecule is exploited to ensure

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Incremental Unsupervised-Learning of Appearance Manifold with View-Dependent Covariance Matrix for Face Recognition from Video Sequences We propose an appearance manifold with view-dependent covariance matrix for face recognition from video sequences in two learning frameworks: the supervised-learning and the incremental unsupervisedlearning. The advantages of this method are, first, the appearance manifold with view-dependent covariance matrix model is robust to pose changes and is also noise invariant, since the embedded covariance matrices are calculated based on their poses in order to learn the samples' distributions along the manifold. Moreover, the proposed incremental unsupervisedlearning framework is more realistic for real-world face recognition applications. It is obvious that it is difficult to collect large amounts of face sequences under complete poses (from left sideview to right sideview) for training. Here, an incremental unsupervised-learning framework allows us to train the system with the available initial sequences, and later update the system's knowledge incrementally every time an unlabelled sequence is input. In addition, we also integrate the appearance manifold with view-dependent covariance matrix model with a pose estimation system for improving the classification accuracy and easily detecting sequences with overlapped poses for merging process in the incremental unsupervisedlearning framework. The experimental results showed that, in both frameworks, the proposed appearance manifold with view-dependent covariance matrix method could recognize faces from video sequences accurately. key words: appearance manifold, view-dependent covariance matrix, incremental learning, video-based face recognition, eigenspace Face recognition has long been an active area of research. Over the years, numerous works have been proposed that focus on recognizing 3D objects and human faces from stillimages, such as [1] - [11] . Recently, video-based face recognition has attracted much attention since face recognition using video presents various advantages and also challenges over still-image based recognition.. For an efficient video-based face recognition process, first, every image (frame) in a video sequence is input in a feature extraction module, so that it becomes a lowdimensional vector in a feature space. One most widely used feature extractor in the pattern recognition field is the Principal Component Analysis (PCA) with its eigenspace representation [1] , [2] . In a video, face images may vary Manuscript received July 10, 2008 . Manuscript revised December 3, 2008 . † The authors are with the Department of Media Science, Graduate School of Information Science, Nagoya University, Nagoyashi, 464-8601 Japan.. † † The author is with the Faculty of Economics and Information, Gifu Shotoku Gakuen University, Gifu-shi, 500-8288 Japan.. a) E-mail: lina@murase.m.is.nagoya-u.ac.jp DOI: 10.1587/transinf.E92.D.642. significantly due to environmental changes, such as lighting condition, pose, facial expression, etc. In addition, various degradation effects might also influence the images in a video sequence, such as low-quality video and cropping errors due to inaccuracies of a tracking system. Therefore, a robust recognition system should be able to handle various image variations. It is well known that an appearance manifold could capture image variations, especially pose changes, in eigenspace. Addressing various problems, many appearance manifold models have been proposed, such as the simple manifold [3] , [4] , the probabilistic appearance manifold [5] , [6] , the layer-transparent manifold [9] , etc. Moreover, in our previous work, we have introduced various models of appearance manifold with view-dependent covariance matrix which could robustly recognize 3D objects from still-images under various degradation effects [11] .. In the past years, several works have reported the use of appearance manifold for face recognition from video sequences. Among them, Raytchev and Murase [12] proposed a pairwise clustering method which calculates the interaction levels (attraction and repulsion) of every input sequence. A merging or splitting process is then applied according to the interaction's decision. Zhou et al. proposed a probabilistic approach which uses joint posterior distribution of motion vectors and estimates the temporal information of video sequences by propagating the identity variables over time [13] . Similar to [13] , the work of Lee et al. in [14] , [15] , utilized local linear models and a transition matrix which propagates the probabilistic likelihood of the linear models to capture the temporal information. Meanwhile, Liu et al. processed the temporal information of video sequences using the adaptive Hidden Markov Models (HMM) method [16] .. Proposing a different appearance manifold model from the previous works, the novelty of our approach lies in the scheme of embedding view-dependent covariance matrices in appearance manifolds for recognizing faces from video sequences in an incremental unsupervised-learning framework. The advantages of this model are, first, the appearance manifold with view-dependent covariance matrix model is robust to pose changes and also noise invariant since the embedded covariance matrices are calculated based on their poses in order to learn the samples' distributions along the manifold. Moreover, the proposed incremen- tal unsupervised-learning framework is more realistic for a real-world face recognition application. It is obvious that it is difficult to collect large amounts of face sequences under complete poses (from left sideview to right sideview) for training purpose. Here, an incremental unsupervisedlearning framework allows us to train the system with the available initial sequences, and later update the system's knowledge incrementally every time an unlabelled sequence is input.. In addition, the integration of a pose estimation system in the appearance manifold with view-dependent covariance matrix model also plays an important role in improving the classification accuracy, since, put in the terminology in [12] , the images of the same object under a different viewing condition is different. Thus, it is clear that one is likely to obtain the classification results based on the availability (similarity) of a pose instead of its identity. Therefore, to increase the classification accuracy of the system, the most similar pose of a face in each manifold is searched (i.e. using a pose estimation system), before identifying the person. The pose estimation system also helps the merging process in the incremental unsupervised-learning framework to easily detect video sequences with overlapped poses.. In this paper, we address a video-based face recognition problem using the appearance manifold with viewdependent covariance matrix in two learning frameworks: the supervised-learning and the incremental unsupervisedlearning. Figure 1 shows the outline of the proposed videobased face recognition system. In the supervised-learning framework, the training samples are labelled and used to represent the identity categories in the form of appearance manifolds with view-dependent covariance matrices. Meanwhile, in the incremental unsupervised-learning framework, the system first learns the initial categories through the initial manifolds and later updates its knowledge on identity categories by learning the unlabelled input sequences incrementally. Since the structure and the number of the category (class) changes every time a new pattern comes into the system, it is necessary to update the system's knowledge, either by constructing a new category or by modifying the structure of the existing categories through merging processes between sequences which have some overlapped poses with strong similarities.. We organized the rest of this paper as follows. Our appearance manifold model and the classification process for video-based face recognition in a supervised-learning framework is described in Sect. 2. In Sect. 3, the detailed classification process of video-based face recognition in an incremental unsupervised-learning framework is presented. Experimental results and discussions are described in Sects. 4 and 5, respectively. Finally, we concluded this paper and described the future works in Sect. 6. We have proposed the appearance manifold with viewdependent covariance matrix for face recognition from video sequences in two learning frameworks: the supervised-learning and the incremental unsupervisedlearning. In the supervised-learning framework, the training samples are labelled and an appearance manifold with viewdependent covariance matrix is used to represent an identity category. Meanwhile, in the incremental unsupervisedlearning framework, the system first learns the initial categories through the initial manifolds, then the unlabelled input sequences are incrementally learned in order to update the existing identity categories of the system. The advantages of this method are, first, the appearance manifold with view-dependent covariance matrix model is robust to pose changes and also noise invariant, since the embedded covariance matrices are calculated based on their poses in order to learn the samples' distributions along the manifold. Moreover, the proposed incremental unsupervised-learning framework is more realistic for a real-world face recognition application, since it allows us to train the system with the available initial sequences, and later update the system's knowledge incrementally every time an unlabelled sequence is input. We also integrated the appearance manifold with view-dependent covariance matrix model with a pose estimation system in order to improve the classification accuracy of the system and to easily detect the overlapped poses in video sequences which is useful for the merging process in the incremental unsupervised-learning framework. The merging process is performed in order to merge the manifolds which have some overlapped poses with strong similarities. The experimental results showed that in both frameworks, the proposed appearance manifold with viewdependent covariance matrix method outperforms the simple manifold model in recognizing faces from video sequences.. Our future work will concentrate on recognizing faces from continuous video sequences, with both vertical and horizontal pose directions, sudden pose changes, and other varying conditions. In Sect. 4, we have shown the performances of the proposed VC method and its comparisons with the SM method, where all results showed that the VC method outperformed the SM method in various conditions in both supervised and incremental unsupervised-learning frameworks. In this section, we focus and discuss in more detail the performance of the proposed VC method in incremental unsupervised-learning framework. As we have mentioned earlier, the advantage of an incremental unsupervised-learning framework is that the system could learn and update its knowledge automatically as the unlabelled sequences are input incrementally into the system. However, one critical point in the incremental unsupervised-learning is that the classification ability of the system is highly dependent on the initial settings (i.e. the threshold value, the updating weight, the number of the initial manifold, etc.) and the condition of the input sequences (i.e. the sequence's length, the number of overlapped poses, the input order, etc.). Thus, using different initial settings and/or processing different conditions of input sequences could give different classification results. Table 3 presents the classification rates of two experiments which have the same initial settings but different conditions of input sequences. For the initial setting, we constructed 10 initial manifolds of 10 persons, defined α = 0.5 and β = 2.0, and used the Nearest Neighbor algorithm as the pose estimation system. In the testing process, the sequence's length and the input order of the unlabelled sequences were set differently. In the first experiment, the system relatively processed longer input sequences within the range of 5-8 sequence's length than in the second experiment whose sequence's length was within the range of 1-8. The number of unlabelled input sequences were 100 sequences (randomly input from 5 sequences for 20 persons) which also shows how many times the system was updated. From Table 3 , it can be seen that for both experiments, the VC method outperformed the SM method with 85% highest accuracy rate, 12% false acceptance rate and 18% false rejection rate. Meanwhile, the SM method only gave 18% accuracy rate, with 100% false acceptance and 64% false rejection rates for both experiments.. Next, Fig. 9 shows the visualization of face manifolds using the VC method with poses from −90. • (left sideview) to +90. • (right sideview) from the frontal pose. Figure 9 (a) shows the visualization of a face manifold of a person which was constructed from the sequences of Dataset 1 and Dataset 2 in a supervised-learning framework. Mean- while, Fig. 9 (b) and Fig. 9 (c) show the visualization of face manifolds of a same identity (person) in the incremental unsupervised-learning frameworks (the initial manifolds were constructed from sequences of Dataset 1, and later the unlabelled sequences of Dataset 2 were input incrementally to update the initial manifold). The input sequences for Fig. 9 (b) had a 7 sequence's length, while, in Fig. 9 (c), shorter sequences with 3 sequence's length were input. From Fig. 9 , it can be seen that the constructed manifolds in the incremental unsupervised-learning frameworks are similar to each other and also to the construction result of the manifold in the supervised-learning framework. Finally, in order to emphasize the superiority of the proposed method, the accuracy rates of the PCA and nonlinear RBF Kernel PCA in combination with the simple Nearest Neighbor (NN) classifier and the appearance manifold with View-dependent Covariance (VC) are presented in Table 4 . For the combinations with NN, the training classes included only the samples of the training poses. Meanwhile, for the combinations with VC, the manifolds with view-dependent covariance matrix were constructed. Here, constructing a manifold means attaining estimation of continuous poses by interpolating the classes (the mean vectors and the covariance matrices) of two consecutive training poses to obtain those of the untrained poses. Thus, the proposed VC method synthesized more pose variabilities than the NN method, since it has training classes with more complete poses (training poses + interpolation poses).. Due to the fact that the appearance of a person's face is highly dependent on its pose, it is obvious that an appearance-based method which can capture more pose variabilities can give more accurate recognition. Moreover, in the proposed VC method, the covariance matrices were embedded in the appearance manifold. Therefore, the advantage of the proposed VC method includes the abilities to capture pose variability and also learn the sample's distribution of each pose. As the consequence, the proposed VC method can give higher recognition accuracies than the NN method. Table 4 shows that for both the linear PCA and the RBF Kernel PCA feature extraction techniques, the proposed VC method gave higher recognition accuracies than that of the NN method. The results also show that the VC method worked better for both the linear PCA and the nonlinear RBF Kernel PCA feature extraction techniques.. Furthermore, the structure of a manifold in the proposed VC method is feature-space independent because a manifold is constructed only by the interpolation of classes of two consecutive training poses. As an interpolation technique can be applied to any feature-space, the structure of the constructed manifold is also not affected by the linearity or non-linearity of the feature-space.

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


Assessing Information Technologies for Health. Editorial Objectives: To provide an editorial introduction to the 2006 IMIA Yearbook of Medical Informatics with an overview of its contents and contributors. Methods: A brief overview of the main theme of “Assessing Information Technology for Health Care”, and an outline of the purposes, readership, contents, new format, and acknowledgment of contributions for the 2006 IMIA Yearbook. Results: Assessing information technology (IT) in biomedicine and health care is emphasized in a number of survey and review articles. Synopses of a selection of best papers for the past 12 months are included, as are original papers on the history of medical informatics by pioneers in the field, and selected research and education programs. Information about IMIA and its constituent societies is given, as well as the authors, reviewers, and advisors to the Yearbook. Conclusions: The 2006 IMIA Yearbook of Medical Informatics highlights as its theme one of the most significant yet difficult aspects of information technology in health: the assessment of IT as part of the complex enterprise of biomedical research and practice. It is being published in a new format with a wide range of original survey and review articles. Haux R, Kulikowski C, editors. IMIA Yearbook of Medical Informatics 2006. Methods Inf Med 2006; 45 Suppl 1: S2-4.

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


User-friendly

software

for

the

analysis

of

brain

lesions

(ABLe)

We

previously

developed

a

software

package

called

ABLe

(Analysis

of

Brain

Lesions)

which

characterizes

brain

lesions

in

terms

of

lesion

volume

and

intersection

with

cytoarchitecture

(e.g.

Brodmann

areas).

Since

our

previous

publication,

there

have

been

significant

improvements

to

this

software

package

which

utilize

methods

standard

to

the

neuroimaging

community.

These

features

include

spatial

normalization

to

the

MNI

template

brain

(standard

of

the

International

Consortium

for

Brain

Mapping),

and

use

of

the

Volume

Occupancy

Talairach

Labels

(VOTL)

and

Automated

Anatomical

Labeling

(AAL)

atlases

for

full

brain

quantification

of

structures

impacted

by

the

lesion.

Methods

for

multi-subject

studies

including

lesion-symptom

mapping

proposed

by

Bates

et

al

have

been

extended

in

ABLe

to

produce

an

exploratory

analysis

summarizing

correlations

between

subjects

with

overlapping

lesions

and

behavioral

deficit.

A

subset

of

data

from

an

ongoing

traumatic

head

injury

study

correlating

deficit

with

brain

anatomy

is

used

to

demonstrate

the

power

of

this

software

package.

The

characterization

of

lesion

location

in

the

brain

is

an

important

step

in

studying

brain

function.

Putative

brain

centers

or

networks

that

control

motor,

sensation

and

cognition

can

be

assessed

by

correlating

deficits

with

lesion

location

across

a

group

of

subjects.

Originally,

autopsies

were

used

to

confirm

brain

lesion

location

otherwise

estimated

by

entry

site

using

skull

films.

Now

magnetic

resonance

imaging

(MRI)

and

computed

tomography

(CT)

scans

are

used

for

this

analysis

because

these

methods

allow

for

in-vivo

analysis

of

brain

lesions.

Because

cytoarchitecture

regions

(i.e.

Brodmann

areas)

are

thought

to

represent

functionally

distinct

brain

regions,

lesion

location

is

often

characterized

by

which

regions

are

involved.

As

yet,

there

is

no

way

to

directly

parcellate

Brodmann

areas

on

imaging

and

therefore,

estimates

must

be

made..

Previous

techniques

for

characterizing

lesion

location

on

tomographic

images

(e.g.

MRI

or

CT)

involved

placing

an

overlay

of

a

template

(e.g.

see

the

template

system

designed

by

Damasio

and

Damasio,

on

top

of

the

tomographic

film.

This

template

interpolates

the

Brodmann

areas

(BAs),

originally

determined

by

Brodmann

on

the

surface

of

the

brain,

to

axial

image

slices.

While

this

is

a

relatively

straight

forward

method

of

detecting

where

the

lesions

intersect

functional

areas,

it

is

limited

by

the

correspondence

of

the

template

to

the

individual

brain.

There

are

many

limitations

to

this

technique.

First,

considerable

interindividual

brain

variation

exists,

so

that

the

templates

may

poorly

overlap.

In

addition,

the

imaging

plane

orientation

may

not

correspond

to

that

of

the

template..

For

these

reasons,

our

group

previously

developed

software

which

addresses

these

limitations

and

is

easy

to

use.

This

software,

known

as

ABLe

(Analysis

of

Brain

Lesions)

first

published

in

has

already

been

used

in

several

studies

ABLe

was

designed

to

be

userfriendly,

requiring

little

sophistication

with

computing

by

the

user.

The

design

focus

was

to

standardize

a

method

of

brain

lesion

processing

for

potentially

large

numbers

of

MRI

or

CT

scans

by

a

trained

technologist

familiar

with

normal

and

pathologic

neuroanatomy.

In

ABLe

a

digitized

brain

atlas

was

derived

from

the

Damasio

templates

described

above

and

used

to

determine

regions

affected

by

the

lesion.

This

atlas

is

only

defined

on

the

cortex;

therefore

internal

brain

structures,

such

as

the

basal

ganglia

are

not

included.

The

BAs

are

defined

on

axial

slices,

approximately

apart.

If

a

small

lesion

lies

in

between

these

slices

it

may

not

be

detected..

Since

the

publication

describing

ABLe

the

VOTL

and

AAL

atlases

have

been

added

to

ABLe

in

order

to

gain

full

brain

coverage.

In

addition,

several

image

processing

and

lesion

visualization

techniques

common

to

the

neuroimaging

community

have

been

integrated

into

this

single

software

package.

The

purpose

of

this

article

is

to

provide

a

detailed

description

of

these

methods

to

the

scientific

community..

A

small

number

of

other

software

packages

have

also

been

developed

to

characterize

brain

lesions

using

tomographic

images

and

digital

atlases.

These

include

MRIcro

Brainvox

and

BRAID

While

each

program

has

its

strengths

and

weaknesses,

they

each

address

the

problem

of

analyzing

brain

lesions

across

multiple

subjects.

A

brief

analysis

of

the

merits

of

these

programs

compared

with

ABLe

is

included

in

the

Discussion

section.

The

Analysis

of

Brain

Lesions

(ABLe)

program

is

a

semi-automated

method

of

characterizing

brain

lesions.

In

certain

situations

it

is

not

advisable

for

a

patient

to

have

an

MRI

as

is

the

case

when

a

patient

has

an

intracranial

metal

plate

or

retained

metal

in

the

brain

from

shell

fragments.

In

this

situation,

x-ray

computed

tomography

(CT)

images

of

the

brain

can

be

safely

acquired.

ABLe

supports

both

MRI

and

CT

scans..

Since

the

time

of

the

original

publication

ABLe

has

been

enhanced

by

adding

methods

requested

by

the

clinical

neuroscience

user

community.

These

include

spatial

normalization

to

the

MNI

template

brain,

and

use

of

the

VOTL

and

AAL

brain

atlases.

The

level

of

group

analysis

has

been

supplemented

by

allowing

for

two-group

(double

dissociation)

and

behavioral

analysis,

an

extension

of

the

work

performed

by

Bates

et

al

An

advantage

of

the

two

group

analysis

is

that

a

control

group

(patients

with

brain

lesions

but

with

a

different

deficit

from

the

primary

group

of

interest)

can

be

included

in

the

lesion

analysis

as

suggested

by

Rorden

et

al

An

advantage

of

the

Behavioral

Analysis

module

is

that

it

can

be

used

in

an

exploratory

analysis.

One

does

not

need

a

priori

knowledge

of

a

deficit

from

a

group

of

patients

as

was

required

for

the

Single

Subject

Analysis..

The

modularity

of

the

ABLe

program

has

allowed

for

additional

improvements

such

as

the

importation

of

lesion

masks

created

from

rd

party

software

(e.g.

MRIcro).

This

modularity

will

support

future

additions

to

ABLe

which

may

include

probabilistic

brain

atlases

as

described

by

Eickhoff

et

al

and

a

method

of

hierarchical

clustering

to

group

patients

with

similar

Brodmann

area

involvement..

The

techniques

described

herein

improve

previous

methods

of

brain

lesion

analysis.

In

the

not

so

recent

past,

a

template

of

brain

structures

printed

on

a

transparency

was

overlaid

on

a

MRI

film

to

assess

which

structures

intersect

with

the

brain

lesion.

Inaccuracies

were

caused

by

the

fact

that

the

size

of

the

brain

and

its

orientation

in

the

MRI

scan

was

often

different

from

the

template

on

the

transparency.

In

recent

years,

other

software

packages

have

also

been

developed

to

characterize

brain

lesions

using

digital

atlases.

MRIcro

is

widely

available

and

allows

the

user

to

trace

lesions

either

on

the

subject's

brain

image

or

directly

on

the

template

brain

image.

Tracing

on

the

subject's

brain

requires

this

image

to

be

spatially

normalized.

This

spatial

normalization

process

is

not

part

of

MRIcro

and

the

user

is

suggested

to

perform

this

operation

using

the

SPM

software

package

This

process

is

available

for

MRI

and

not

CT

data.

On

the

other

hand,

tracing

the

lesion

directly

on

the

MNI

template

brain

removes

the

step

of

spatial

normalization

but

requires

more

expertise

of

the

user

and

may

incorporate

more

bias

than

direct

tracing

on

the

native

MRI.

ABLe

incorporates

the

spatial

normalization

process

with

the

click

of

a

single

button

and

allows

for

both

MRI

and

CT

image

data.

MRIcro

allows

for

group

analysis

by

subtracting

overlapping

lesions

from

a

control

group

with

overlapping

lesions

from

a

group

that

has

a

deficit

of

interest.

ABLe

performs

a

similar

operation

in

the

"Two

Group

Analysis"

mode.

In

addition,

ABLe

provides

data

driven

group

analysis

via

an

extension

of

the

voxel

based

lesion

symptom-mapping

method

(Behavior

Analysis

module

in

ABLe).

ABLe

has

the

choice

of

digital

atlases

and

contains

reporting

features,

including

percentage

of

structures

intersected

by

the

lesion

which

are

available

in

html

or

ascii

text

format

for

spreadsheet

use.

ABLe

has

improved

visualization

allowing

for

the

user

to

see

the

spatially

normalized

MRI

containing

the

lesion

with

a

Brodmann

area

overlay.

The

user

may

choose

to

overlay

all

Brodmann

areas

at

once

or

select

from

a

list..

The

Brainvox

package,

published

in

was

designed

to

be

interactive

brain

imaging

software

to

investigate

subjects

with

acquired

lesions.

Like

ABLe,

this

software

has

a

point

and

click

graphical

user

interface

and

includes

a

slice/contour

based

tracing

module

for

delineation

of

the

lesion.

Based

on

manually

defined

anatomic

landmarks,

the

software

transfers

the

tracings

from

the

subject

brain

to

a

template

brain.

Brainvox

supports

superposition

of

lesions

from

a

group

of

subjects

in

a

common

space.

This

is

similar

to

ABLe's

single

group

Analysis

module.

With

their

module,

Brainvox

shows

the

probability

that

a

lesion

is

associated

with

a

deficit.

ABLe

supports

the

voxel

based

lesion-symptom

mapping

(VLSM)

method

for

this

form

of

statistical

analysis.

Brainvox

was

developed

on

the

SGI

UNIX

system

and

is

not

widely

available.

ABLe

software

is

supported

on

SGI

as

well

as

Linux,

Mac

OSX

and

Sun

Solaris

platforms

and

is

widely

available

to

researchers.

The

importance

of

the

development

of

Brainvox

should

be

stated

as

it

paved

the

way

for

analyzing

brain

lesions

with

digital

images

using

group

lesion

overlay

as

well

as

lesion-deficit

probabilistic

associations..

A

software

and

database

system

known

as

BRAID

(Brain

Image

Database)

was

developed

for

the

clinical

purpose

of

understanding

brain

structure-function

relationships

(e.g.

anatomic

correlates

of

deficit).

Like

ABLe,

the

input

to

BRAID

is

manually

delineated

lesions

on

MRI

scans

which

are

then

registered

to

the

Talairach

coordinate

system.

These

lesion

volumes

are

computed

with

proprietary

software

and

the

registration

is

performed

outside

of

BRAID.

ABLe

contains

both

of

these

functions

as

part

of

an

integrated

package.

Both

BRAID

and

ABLe

have

several

digital

atlases

to

choose

from

and

compute

lesion

fraction

per

anatomic

structure.

ABLe

also

computes

percentage

of

the

structure

intersected

by

the

lesion.

BRAID

visualizes

the

lesion

on

top

of

the

atlas.

ABLe

includes

the

high

resolution

MRI

as

well

as

the

atlas

in

this

visualization.

The

BRAID

supports

statistical

lesion-deficit

reporting

via

contingency

testing

with

a

chi-squared

test,

whereas

ABLe

utilizes

the

voxel

based

lesion-symptom

mapping

method.

The

BRAID

system

is

not

widely

available

for

researchers..

While

there

is

some

overlap

in

the

functionality

of

these

programs,

we

believe

that

ABLe

has

a

richer

feature

set

allowing

the

researcher

flexibility

in

defining

the

lesion,

choosing

a

brain

atlas,

and

performing

a

series

of

group

analyses..

There

are

certain

limitations

associated

with

semi-automated

lesion

analyses.

Tracing

lesion

margins

is

difficult

because

these

borders

may

be

poorly

defined.

Manual

tracing

also

introduces

intra/inter-user

variability.

Automation

in

lesion

delineation

is

difficult

because

in

CT,

lesions

often

have

overlapping

intensity

values

(i.e.

Hounsefiled

units)

with

cerebral

spinal

fluid

and

may

be

connected

with

ventricles

making

their

automatic

segmentation

complex.

A

suggestion

is

to

have

the

same

or

individuals

perform

the

ABLe

analyses.

These

individuals

could

be

technologists

with

experience

in

neuroanatomy..

Imperfect

image

registration

(spatial

normalization)

to

a

brain

template

may

cause

inaccuracies

in

the

fraction

of

structures

reported

as

intersecting

with

the

lesion.

Individual

variation

can

also

cause

a

misclassification

of

intersecting

structures.

These

include

the

fact

that

the

location

and

extent

of

cytoarchitectural

structures

may

differ

among

individuals.

There

is

some

evidence

that

this

may

be

more

prominent

in

some

structures

such

as

frontal

association

areas

Our

results

from

placing

diameter

spherical

synthetic

lesions

in

Broca's

area

and

the

primary

motor

cortex

(Table

demonstrate

the

accuracy

of

the

ABLe

method.

However,

while

one

of

these

lesions

was

placed

on

the

precentral

gyrus,

the

postcentral

gyrus

and

BA

are

reported.

This

is

because

the

border

of

the

pre-and

post-central

gyrus

is

variable

across

subjects

and

the

AIR

registration

process

used

in

ABLe

is

a

parameter

linear

fit

which

does

not

warp

each

gryal

pattern

to

match

the

template.

The

reporting

of

BA

represents

one

of

the

limitations

of

the

method.

However,

while

there

are

regions

in

the

AAL

atlas

and

Brodmann

areas,

only

the

structures

listed

below

were

reported

by

ABLe.

This

demonstrates

the

accuracy

of

our

neuroradiologist

in

finding

Broca's

area

and

the

primary

motor

strip

on

CT

images

as

well

as

the

total

ABLe

process

of

spatial

normalization

to

the

MNI

target

brain

and

integration

of

the

VOTL

and

AAL

atlases..

In

cases

of

brain

tumors

or

ex

vacuo

phenomena

with

stroke,

the

lesion

may

deform

the

normal

brain

anatomy

via

a

mass

effect.

Under

these

circumstances,

displaced

brain

structures

will

not

be

aligned

with

their

corresponding

location

on

the

brain

atlas,

thus

introducing

error

in

the

reporting

of

structures

or

percentage

of

structures

intersecting

the

lesion.

In

these

situations,

incorporating

methods

of

atlas

deformation

such

as

those

developed

by

Cuadra

et

al

may

improve

the

accuracy

of

our

method.

Nevertheless,

ABLe

provides

an

improved

technique

to

semi-automatically

characterize

human

brain

lesions

in

MRI

and

CT

scans..

A

primary

design

goal

of

the

ABLe

software

was

user

friendliness.

This

was

accomplished

by

developing

a

graphical

user

interface

(GUI)

that

simplifies

the

lesion

characterization

workflow

from

lesion

definition

to

final

summary

report.

The

ABLe

GUI

was

developed

using

ImageScript,

which

is

an

extension

of

the

TCL/TK

scripting

language

and

serves

as

the

MEDx

API.

In

addition,

several

functions

in

ABLe

were

coded

in

the

C

and

C++

programming

languages

and

have

been

compiled

on

Linux

and

Solaris

platforms.

The

ABLe

software

is

available

for

researchers

to

use

as

it

is

a

module

in

the

MEDx

image

analysis

and

visualization

software

package,

which

has

worldwide

distribution.

The

development

of

ABLe

is

ongoing

as

a

collaborative

project

with

several

institutes

at

the

National

Institutes

of

Health.

Improvements

to

this

program

based

on

recommendations

from

the

community

are

welcome

via

the

following

list

serv

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


A study of dynamic finite size scaling behavior of the scaling functions - calculation of dynamic critical index of Wolff algorithm In this work we have studied the dynamic scaling behavior of two scaling functions and we have shown that scaling functions obey the dynamic finite size scaling rules. Dynamic finite size scaling of scaling functions opens possibilities for a wide range of applications.As an application we have calculated the dynamic critical exponent (z) of Wolff's cluster algorithm for 2-, 3-and 4-dimensional Ising models. Configurations with vanishing initial magnetization are chosen in order to avoid complications due to initial magnetization.The observed dynamic finite size scaling behavior during early stages of the Monte Carlo simulation yields z for Wolff's cluster algorithm for 2-, 3-and 4-dimensional Ising models with vanishing values which are consistent with the values obtained from the autocorrelations. Especially, the vanishing dynamic critical exponent we obtained for d = 3 implies that the Wolff algorithm is more efficient in eliminating critical slowing down in Monte Carlo simulations than previously reported. Finite size scaling and universality arguments have been used to study the critical parameters of spin systems over two decades [1] . Jansen, Schaub and Schmittmann [2] showed that for a dynamic relaxation process, in which a system is evolving according to a dynamics of Model A [3] and is quenched from a very high temperature to the critical temperature, a universal dynamic scaling behavior within the short-time regime exists [4, 5, 6] . The existence of finite size scaling even in the early stages of the Monte Carlo simulation has been tested for various spin systems [5, 6, 7, 8, 9, 10, 11, 12] , the dynamic critical behavior is well-studied and it has been shown that the dynamic finite size scaling relation holds for the magnetization and for the moments of the magnetization. For the k th moment of the magnetization of a spin system, dynamic finite size scaling relation can be written as [2] . where L is the spatial size of the system, β and ν are the well-known critical exponents, t is the simulation time, ǫ = (T − T c )/T c is the reduced temperature and x 0 is an independent exponent which is the anomalous dimension of the initial magnetization (m 0 ). In Eq. (1) τ is the autocorrelation time, τ ∼ L z and z is the dynamic critical exponent.. The relation given in Eq.(1) can be used to study the known critical exponents as well as exponents z and x 0 . Moments of the magnetization have their own anomalous dimensions (kβ/ν) And using these quantities (in order to obtain dynamic exponents z and x 0 ) one may expect some ambiguities due to correction to scaling and errors on determining the anomalous dimension of the given thermodynamic quantity. The ambiguities due to the anomalous dimension of the thermodynamic quantity can be avoided if one considers quantities which are themselves scaling functions. Moreover, scaling functions are extremely powerful to identify the order of the phase transition, as well as locating the transition point of statistical mechanical systems on finite lattices.. In this work we propose that the dynamic finite size scaling relation also holds for the scaling functions and the scaling relation can be written similarly to the moments of the magnetization,. Our aim is to study dynamic finite size scaling behavior of the scaling functions by using Eq.(2).. In our calculations two different scaling functions are used. The first such quantity is. Binder's cumulant [13, 14, 15 ]. Binder's cumulant is widely used in order to obtain the critical parameters as well as to determine the type of the phase transition. This quantity involves the ratio of the moments of the magnetization or energy. In this work we have used the definition of Binder's cumulant which involves the ratio of the moments of the magnetization. Simplest such quantity can be given as. In the usual definition of Binder's cumulant, < S n > is the thermal average of the n th moment of the configuration average of the spin. In dynamic case, starting from a totally random configuration (m 0 = 0), runs are repeated until predetermined number of iterations are reached for each lattice size. The thermodynamic quantities are calculated as the configuration averages at each iteration. In order to calculate Binder's cumulant iteration by iteration, the configuration averages of the magnetization and its higher moments are calculated. Various moments of the magnetization are divided iteration by iteration in order to obtain the required form of Binder's cumulant,. Here the averages are calculated over the configurations obtained at each iteration. In this work we use Binder's cumulant for n = 2 by using the the relation. The second quantity is the scaling function (F ) based on the surface renormalization. This function is studied in detail for the Ising model [16, 17, 18] and q-state Potts model [19, 20, 21] . In order to calculate this function, one considers the direction of the majority of spins of two parallel surfaces which are L/2 distance away from each other. For Ising spins, F can be written in the form [18] ,. where S i is the sum of the spins in the i th surface. Similar to the calculations of Binder's cumulant, iteration-dependent calculation of F requires the configuration averages which are obtained for each iteration yielding a Monte Carlo time dependent expression,. F (t) can be used in calculating the dynamic finite size scaling relation given in Eq.(2).. In Wolff's algorithm [22] , only spins belonging to a certain cluster around the seed spin are considered and updated at each Monte Carlo step. In equilibrium, the dynamic critical exponent of the Wolff's algorithm can not be obtained directly from the observed autocorrelation times (τ W ′ ), instead the autocorrelation time (τ W ) is governed by the average size (< C > of the clusters. τ W can be obtained by the relation,. The dynamic critical exponents of cluster algorithms are calculated using the autocorrelation times of spin systems in thermal equilibrium [22, 23, 24, 25, 26, 27, 28] . In these studies the dynamic critical exponent is observed to be much less than the value obtained by use of local algorithms. For 2-dimensional Ising model Wolff obtained z ∼ 0.25 [25] .. More recently, Heerman and Burkitt [26] suggested that data are consistent with a logarithmic divergence, but it is very difficult to distinguish between the logarithm and a small power [27] . For the 3-dimensional case, Tamayo et al [28] calculated the dynamic critical exponent as z ∼ 0.44(10). Wolff calculated a smaller value of z = 0.28 (2) [25] using energy autocorrelations. In 4-dimensions, Tamayo et al [28] obtained z with a vanishing value. This result is also consistent with the mean-field solution for the Ising model in four and higher dimensions. In a recent publication it has been shown that various alternative cluster algorithms posses similar dynamic behavior [29] The efficiency of the Wolff's algorithm is directly related to the size of the updated clusters, hence the efficiency increases during the quenching process, as the number of iterations increases. Both the average cluster size and susceptibility have the same anomalous dimension, hence in obtaining τ from the observed behavior of the dynamic variable, one can replace < S 2 > by < C >. In our calculations both quantities have been used in order to scale time variable for quantities B 2 (t) and F (t) considered. Wolff's algorithm is one of the most difficult algorithms to calculate the dynamic critical exponent. Simply the difficulty arises from the comparison between the number of updated spins and the total number of spins. At each iteration only a single cluster is updated. In the literature, for 2-, 3-and 4-dimensions, small dynamic critical exponents are obtained [22, 23, 24, 25, 26, 27, 28] , but further studies of the data suggest that for all three dimensions the dynamic critical exponent of the Ising model can be considered as zero. The measurement of the dynamic critical exponent in thermal equilibrium is extremely difficult, since the correlation length around the phase transition point is as large as the size of the lattice. In dynamic finite size scaling, since the correlation length remains smaller than the lattice size, it is expected that statistically independent configurations lead to better statistics since there are no finite size effects.. In this work we have considered the dynamic scaling behavior of Binder's cumulant (B 2 (t)) and the renormalization function (F (t)) for 2-, 3-and 4-dimensional Ising models. We have observed that these scaling functions can be used to identify the critical point and the critical exponents during the initial stages of the thermalization. In our calculations, we have observed that our results are consistent with vanishing dynamic critical exponent.. Despite the fact that obtaining good statistics is extremely time consuming for large lattices, finite size effects do not play any role in obtaining the results. One can see from the results of dynamic scaling that scaling is very good and the errors are very small, hence this method is a good candidate to calculate the dynamic critical exponent for any spin model and for any algorithm. The most striking result of our calculations is that the dynamic critical exponent for 3-dimensional Ising model is obtained as z = 0.02 ± 0.09, instead of previously reported range of values z = 0.28 − 0.44 [28, 25] . This is a clear indication that the efficiency of the Wolff's algorithm is better than previously thought, especially in eliminating critical slowing down of Monte Carlo simulations. This means that using this algorithm, very large lattices at criticality can be considered, without unusually large statistical errors building up. Table Captions Table 1 .. The values of calculated dynamic critical exponents (z) (using Eq. (9) Table 1 .

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


An evidence-based approach to damage location on an aircraft structure This paper discusses the use of evidence-based classifiers for the identification of damage. In particular, a neural network approach to Dempster-Shafer theory is demonstrated on the damage location problem for an aircraft wing. The results are compared with a probabilistic classifier based on a multi-layer perceptron neural network and shown to give similar results. The question of fusing classifiers is considered and it is shown that a combination of the Dempster-Shafer and MLP classifiers gives a significant improvement over the use of individual classifiers for the aircraft wing data. The recent past has seen considerable use of machine learning techniques for Structural Health Monitoring (SHM). The basic idea of the approach is to use data measured from undamaged and damaged structures in order to train a learning machine to assign a condition label to previously unseen data. The simplest problem of SHM is arguably damage detection. This is most easily carried out in the machine learning context by using a novelty detector [1] . Novelty detection involves the construction of a model of the normal condition of a system or structure, which can then be used in a hypothesis test on unseen data to establish whether the new data corresponds to normal condition or not. The advantage of the novelty detection approach is that it can be carried out using unsupervised learning, i.e. with only samples of undamaged data. If a more detailed diagnosis of a system is required, e.g. it is necessary to specify the type or location of damage in a structure, this can still be done using machine learning methods. For higher levels of diagnostics, algorithms based on classification or regression are applicable; however, these must be applied in a supervised learning context and examples of data from both the undamaged and damaged conditions can be used [2] .. The most popular classifiers for damage location and quantification so far have been those based on Multi-Layer Perceptron (MLP) neural networks [3] (although there is growing popularity for classifiers based on the concepts of statistical learning theory -like support vector machines [2] ). Training of MLP networks as classifiers is usually accomplished by using the 1 of M strategy [3] which implicitly assumes a Bayesian probabilistic basis for the classification. While probability theory is only one (but arguably the most important) of a group of theories which can quantify and propagate uncertainty, other theories of uncertainty, perhaps with the exception of fuzzy set theory, have been largely unexplored in the context of damage identification.. The object of this paper is to design a classifier for damage location based on the Dempster-Shafer theory of evidence [4] . To the knowledge of the authors, DS theory was first used in the context of SHM by researchers at El Paso as in [5] . The theory has also been used in the context of machine condition monitoring [6] . The reason for exploring the possibilities of DS theory is that it extends probability in a number of ways which are potentially exploitable in an SHM context. For the moment though, the current paper is looking only to demonstrate that the method is competitive with the probability-based MLP approach on an experimental case study of an aircraft wing.. The DS classifier here is also implemented using a neural network structure [7] .. The layout of the paper is as follows. Section Two provides a pedagogical introduction to DS theory and places its use in the context of SHM. Section Three briefly describes the neural network implementation of the DS Classifier. Section Four describes the case study discussed in this paper and the results of the analysis are given in Section Five and compared with existing results from a multi-layer perceptron neural network. Section Six discusses the fusion of the two classifiers in both the Bayesian and DS frameworks. The paper ends with some discussion and conclusions. The main conclusion here is that the Dempster-Shafer approach to classification im- Table 8 : Confusion matrix for DS-fused classifiers using 9 log features -testing set.. classification probability of 89.7% compared to 89.2% for the MLP. On 9-feature data the DS network gives a classification rate of 98.3%, compared with 98.2% for the MLP.. One possible advantage of the DS approach is the fact that it can assign patterns to the frame of discernment and thus indicate to the analyst that there is insufficient evidence to make a classification. The effect is small here, with only 0.7% of the probability mass assigned to Θ in the case of the 4-feature data. Taking this effect into account, one can say that the probability of misclassification of the DS network is 9.6% compared to 10.8% for the MLP network. It is conceivable that situations in SHM could arise where this scale of difference could be important.. Another advantage of using the DS approach is to provide the possibility of methodological diversity in order to use data fusion with the results from a MLP classifier.. When the two classifiers are fused on the 4-feature set here, the classification rate is increased by 2.9% to 92.6%. This is small but significant change in the context of SHM problems and is much larger here than the improvement in rate seen by exploiting the ignorance from the DS-classifier. When the classifiers are fused on the 9-feature data, the improvement is smaller, giving an overall classification rate of 98.5. The overall goal in SHM must be a zero misclassification rate, in the sense that the classifier will reject the data rather than produce an error. Further work on the classifiers shown here will consider strategies for data rejection other than the value of the ignorance in the DS-classifier. 29

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 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 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 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 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