estimation and classification of fmri hemodynamic response patterns in this paper we propose an approach to modeling functional magnetic resonance imaging fmri data that combines hierarchical polynomial models bayes estimation and clustering a cubic polynomial is used to fit the voxel time courses of event related design experiments the coefficients of the polynomials are estimated by bayes estimation in a two level hierarchical model which allows us to borrow strength from all voxels the voxel specific bayes polynomial coefficients are then transformed to the times and magnitudes of the minimum and maximum points on the hemodynamic response curve which are in turn used to classify the voxels as being activated or not the procedure is demonstrated on real data from an event related design experiment of visually guided saccades and shown to be an effective alternative to existing methods

fuzzy clustering for data time arrays with inlier and outlier time trajectories in many knowledge discovery and data mining tasks fuzzy clustering is one of the most common tools for data partitioning in this paper dynamic fuzzy clustering models for classifying a set of multivariate time trajectories time series sequences are developed in particular by adopting an exploratory approach based on a geometric algebraic formulation of the data time array different kinds of dynamic fuzzy clustering models based on cross sectional and longitudinal aspects are suggested furthermore a modified version of the previous clustering models that can be seen as a generalization of these models is proposed by utilizing these models we can obtain beneficial effects in the clustering process when anomalous trajectories trajectories with anomalous positions and slopes are present in the dataset in fact the models are suitable for detecting structures of time trajectories with anomalous patterns that are not uniformly distributed over the structure s domains and are characterized by strange slopes in these models the disruptive effect of the anomalous trajectories is neutralized and smoothed and the information on the influence of individual time trajectories on the detected groups is given furthermore some remarks on dynamic three way extensions of a few robust fuzzy clustering models for two way data are suggested demonstrative examples are shown and a comparison assessment based on artificial multivariate time varying data is carried out

ranking fmri time courses by minimum spanning trees assessing coactivation in fmri abstract in fmri time courses with similar temporal activation patterns may belong to different brain regions i e these regions are functionally connected coactivated a group of time courses tcs corresponding to a particular type of temporal activation pattern should be maximally self consistent homogeneous we demonstrate that ordering a group of multidimensional fmri time courses by a minimum spanning tree mst may be used to investigate the temporal homogeneity of a group of tcs we show the utility of mst ranking for data driven analysis methods in investigating coactivation in fmri mst ranking is equally useful for hypothesis led methods furthermore mst ranking enables pairwise comparisons of groups clusters i e any collection of tcs no matter how derived of fmri time courses

searchlight based multi voxel pattern analysis of fmri by cross validated manova abstract multi voxel pattern analysis mvpa is a fruitful and increasingly popular complement to traditional univariate methods of analyzing neuroimaging data we propose to replace the standard decoding approach to searchlight based mvpa measuring the performance of a classifier by its accuracy with a method based on the multivariate form of the general linear model following the well established methodology of multivariate analysis of variance manova we define a measure that directly characterizes the structure of multi voxel data the pattern distinctness d our measure is related to standard multivariate statistics but we apply cross validation to obtain an unbiased estimate of its population value independent of the amount of data or its partitioning into training and test sets the estimate d can therefore serve not only as a test statistic but also as an interpretable measure of multivariate effect size the pattern distinctness generalizes the mahalanobis distance to an arbitrary number of classes but also the case where there are no classes of trials because the design is described by parametric regressors it is defined for arbitrary estimable contrasts including main effects pattern differences and interactions pattern changes in this way our approach makes the full analytical power of complex factorial designs known from univariate fmri analyses available to mvpa studies moreover we show how the results of a factorial analysis can be used to obtain a measure of pattern stability the equivalent of cross decoding

on clustering fmri time series analysis of fmri time series is often performed by extracting one or more parameters for the individual voxels methods based e g on various statistical tests are then used to yield parameters corresponding to probability of activation or activation strength however these methods do not indicate whether sets of voxels are activated in a similar way or in different ways typically delays between two activated signals are not identified in this article we use clustering methods to detect similarities in activation between voxels we employ a novel metric that measures the similarity between the activation stimulus and the fmri signal we present two different clustering algorithms and use them to identify regions of similar activations in an fmri experiment involving a visual stimulus

comparing methods of analyzing fmri statistical parametric maps approaches for the analysis of statistical parametric maps spms can be crudely grouped into three main categories in which different philosophies are applied to delineate activated regions these being type i error control thresholding false discovery rate fdr control thresholding and posterior probability thresholding to better understand the properties of these main approaches we carried out a simulation study to compare the approaches as they would be used on real data sets using default settings we find that posterior probability thresholding is the most powerful approach and type i error control thresholding provides the lowest levels of type i error false discovery rate control thresholding performs in between the other approaches for both these criteria although for some parameter settings this approach can approximate the performance of posterior probability thresholding based on these results we discuss the relative merits of the three approaches in an attempt to decide upon an optimal approach we conclude that viewing the problem of delineating areas of activation as a classification problem provides a highly interpretable framework for comparing the methods within this framework we highlight the role of the loss function which explicitly penalizes the types of errors that may occur in a given analysis

plurality and resemblance in fmri data analysis abstract we apply nine analytic methods employed currently in imaging neuroscience to simulated and actual bold fmri signals and compare their performances under each signal type starting with baseline time series generated by a resting subject during a null hypothesis study we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple convolved with spatially varying hemodynamic responses and highly spatially interactive we then apply these same nine methods to bold fmri time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study paired comparisons of results across methods include a voxel specific concordance correlation coefficient for reproducibility and a resemblance measure that accommodates spatial autocorrelation of differences in activity surfaces receiver operating characteristic curves show considerable model differences in ranges less than 10 significance level false positives and greater than 80 power true positives concordance and resemblance measures reveal significant differences between activity surfaces in both data sets these measures can assist researchers by identifying groups of models producing similar and dissimilar results and thereby help to validate consolidate and simplify reports of statistical findings a pluralistic strategy for fmri data analysis can uncover invariant and highly interactive relationships between local activity foci and serve as a basis for further discovery of organizational principles of the brain results also suggest that a pluralistic empirical strategy coupled formally with substantive prior knowledge can help to uncover new brain behavior relationships that may remain hidden if only a single method is employed

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

an efficient k nearest neighbor search for multivariate time series multivariate time series mts datasets are common in various multimedia medical and financial applications in order to efficiently perform k nearest neighbor searches for mts datasets we present a similarity measure eros extended frobenius norm an index structure muse multilevel distance based index structure for eros and a feature subset selection technique ropes recursive feature elimination on common principal components for eros eros is based on principal component analysis and computes the similarity between two mts items by measuring how close the corresponding principal components are using the eigenvalues as weights muse constructs each level as a distance based index structure without using the weights up to z levels which are combined at the query time with the weights ropes utilizes both the common principal components and the weights recursively in order to select a subset of features for eros the experimental results show the superiority of our techniques as compared to earlier approaches

cluster significance testing using the bootstrap many of the statistical methods currently employed to analyze fmri data depend on a response template however the true form of the hemodynamic response and thereby the response template is often unknown consequently cluster analysis provides a complementary template free method for exploratory analysis of multidimensional fmri data sets clustering algorithms currently being applied to fmri data separate the data into a predefined number of clusters k a poor choice of k will result in erroneously partitioning well defined clusters although several clustering algorithms have been successfully applied to fmri data techniques for statistically testing cluster separation are still lacking to address this problem we suggest a method based on fisher s linear discriminant and the bootstrap also introduced in this paper is a measure based on the projection of multidimensional data from two clusters onto the vector maximizing the ratio of the between to the within cluster sums of squares the resulting one dimensional distribution may be readily visualized and used as a heuristic for estimating cluster homogeneity these methods are demonstrated for the self organizing maps clustering algorithm when applied to event related fmri data

curvature based method for determining the number of clusters abstract determining the number of clusters is one of the research questions attracting considerable interests in recent years majority of the existing methods require parametric assumptions and substantiated computations in this paper we propose a simple yet powerful method for determining the number of clusters based on curvature our technique is computationally efficient and straightforward to implement we compare our method with 6 other approaches on a wide range of simulated and real world datasets theoretical motivation underlying the proposed method is also presented

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

analysis of fmri data using improved self organizing mapping and spatio temporal metric hierarchical clustering the self organizing mapping som and hierarchical clustering hc methods are integrated to detect brain functional activation functional magnetic resonance imaging fmri data are first processed by som to obtain a primary merged neural nodes image and then by hc to obtain further brain activation patterns the conventional euclidean distance metric was replaced by the correlation distance metric in som to improve clustering and merging of neural nodes to improve the use of spatial and temporal information in fmri data a new spatial distance node coordinates in the 2 d lattice and temporal correlation correlation degree of each time course in the exemplar matrix are introduced in hc to merge the primary som results two simulation studies and two in vivo fmri data that both contained block design and event related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods our results demonstrate that the improved som and hc methods are clearly superior to the statistical parametric mapping spm independent component analysis ica and conventional som methods in the block design especially in the event related experiment as revealed by their performance measured by receiver operating characteristic roc analysis our results also suggest that the proposed new integrated approach could be useful in detecting block design and event related fmri data

how to avoid spurious cluster validation a methodological investigation on simulated and fmri data abstract this paper presents an evaluation of a common approach that has been considered as a promising option for exploratory fmri data analyses the approach includes two stages creating from the data a sequence of partitions with increasing number of subsets clustering and selecting the one partition in this sequence that exhibits the clearest indications of an existing structure cluster validation in order to achieve that the selected partition is actually the best characterization of the data structure previous studies were directed to find the most appropriate validity function s in our analysis protocol we first optimize the sequence of partitions according to the given objective function our study showed that an insufficient optimization of the partition for one or more numbers of clusters can easily yield a spurious validation result which in turn may lead the analyst to a misleading interpretation of the fmri experiment however a sufficient optimization for each included number of clusters provided the basis for a reliable adequate characterization of the data furthermore it enabled an adequate evaluation of the validity functions these findings were obtained independently for three clustering algorithms representing the hard and fuzzy clustering variant and three up to date cluster validity functions the findings were derived from analyses of gaussian clusters simulated data sets that mimic typical fmri response signals and real fmri data based on our results we propose a number of options of how to configure improved clustering tools

bayesian spatiotemporal model of fmri data this research describes a new bayesian spatiotemporal model to analyse block design bold fmri studies in the temporal dimension we parameterise the hemodynamic response function s hrf shape with a potential increase of signal and a subsequent exponential decay in the spatial dimension we use gaussian markov random fields gmrf priors on activation characteristics parameters location and magnitude that embody our prior knowledge that evoked responses are spatially contiguous and locally homogeneous the result is a spatiotemporal model with a small number of parameters all of them interpretable simulations from the model are performed in order to ascertain the performance of the sampling scheme and the ability of the posterior to estimate model parameters as well as to check the model sensitivity to signal to noise ratio results are shown on synthetic data and on real data from a block design fmri experiment

cluster analysis in kinetic modelling of the brain a noninvasive alternative to arterial sampling in emission tomography quantification of brain tracer uptake metabolism or binding requires knowledge of the cerebral input function traditionally this is achieved with arterial blood sampling we propose a noninvasive alternative via the use of a blood vessel time activity curve tac extracted directly from dynamic positron emission tomography pet scans by cluster analysis five healthy subjects were injected with the 5ht 2a receptor ligand 18 f altanserin and blood samples were subsequently taken from the radial artery and cubital vein eight regions of interest roi tacs were extracted from the pet data set hierarchical k means cluster analysis was performed on the pet time series to extract a cerebral vasculature roi the number of clusters was varied from k 1 to 10 for the second of the two stage method determination of the correct number of clusters was performed by the within variance measure and by 3d visual inspection of the homogeneity of the determined clusters the cluster determined input curve was then used in logan plot analysis and compared with the arterial and venous blood samples and additionally with one of the currently used alternatives to arterial blood sampling the simplified reference tissue model srtm and logan analysis with cerebellar tac as an input there was a good agreement p 0 05 between the values of distribution volume dv obtained from the k means clustered input function and those from the arterial blood samples this work acts as a proof of principle that the use of cluster analysis on a pet data set could obviate the requirement for arterial cannulation when determining the input function for kinetic modelling of ligand binding and that this may be a superior approach as compared to the other noninvasive alternatives

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

a connectivity based method for defining regions of interest in fmri data in this paper we describe a new methodology for defining brain regions of interset rois in functional magnetic resonance imaging fmri data the rois are defined based on their functional connectivity to other rois i e rois are defined as sets of voxels with similar connectivity patterns to other rois the method relies on 1 a spatially regularized canonical correlation analysis for identifying maximally correlated signals which are not due to correlated noise 2 a test for merging rois which have similar connectivity patterns to the other rois and 3 a graph cuts optimization for assigning voxels to rois since our method is fully connectivity based the extracted rois and their corresponding time signals are ideally suited for a subsequent brain connectivity analysis

contextual clustering for analysis of functional mri data presents a contextual clustering procedure for statistical parametric maps spm calculated from time varying three dimensional images the algorithm can be used for the detection of neural activations from functional magnetic resonance images fmri an important characteristic of spm is that the intensity distribution of background nonactive area is known whereas the distributions of activation areas are not the developed contextual clustering algorithm divides an spm into background and activation areas so that the probability of detecting false activations by chance is controlled i e hypothesis testing is performed unlike the much used voxel by voxel testing neighborhood information is utilized an important difference this is achieved by using a markov random field prior and iterated conditional modes icm algorithm however unlike in the conventional use of icm algorithm the classification is based only on the distribution of background the results from the authors simulations and human fmri experiments using visual stimulation demonstrate that a better sensitivity is achieved with a given specificity in comparison to the voxel by voxel thresholding technique the algorithm is computationally efficient and can be used to detect and delineate objects from a noisy background in other applications

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

ellipsoidal support vector clustering for functional mri analysis as an exploratory approach the clustering of fmri time series has proved its effectiveness in analyzing the functional mri especially in the detection of activated regions due to the arbitrary distribution of fmri time series in the temporal domain imposing simple assumption on the data structure usually could be misleading and limit the detector s performance therefore a true data driven clustering algorithm that adapts to the data structure is preferred and only high level control over the clustering procedure is desired support vector clustering svc is a suitable one in some extent because of its advantages such as no cluster shape restriction no need to explicitly specify the number of clusters and the mechanism in outlier elimination in this work we propose an extension of the svc to step further toward a data sensitive detector this approach is named as ellipsoidal support vector clustering esvc to be robust to noise the clustering is performed on features extracted from the fmri time series via fourier transform experimental results on simulated and real data sets demonstrate the effectiveness of incorporating data structure in clustering fmri time series

universal ratio of magnetization moments in two dimensional ising models the authors calculate the universal critical point ratios of the square of the second and the fourth moment of the magnetization for ferromagnetic ising models on the square and on the triangular lattices periodic boundary conditions are used in accordance with the four fold and six fold rotational symmetries of the respective lattices these results which are obtained by means of an analysis of finite size data computed with a transfer matrix technique have an accuracy of the order of one millionth this analysis is also applied to rectangular systems with arbitrary aspect ratios

spontaneous edge order and geometric aspects of two dimensional potts models using suitable monte carlo methods and finite size scaling we investigate critical and tricritical surface phenomena of two dimensional potts models for the critical two and three state models we determine a surface scaling dimension describing percolation properties of the so called potts clusters near the edges on this basis we propose an exact expression describing this exponent for the whole critical branch for tricritical potts models we find that varying the surface coupling constant or the surface magnetic field can induce a continuous phase transition at bulk tricriticality and sufficiently strong surface couplings spontaneous one dimensional order occurs on the edges we determine several critical exponents describing these edge transitions on the basis of these results and conformal field theory we conjecture exact expressions for these exponents

a coherence based approach for the pattern recognition of time series abstract a pattern recognition approach based on the frequency domain measure of squared coherence is a useful approach to identify linearly related groupings of time series over different periods of time it is considered in an application to identify similar patterns of the yearly rates of change in the gross domestic product gdp of twenty two highly developed countries in an econophysics context the approach is also tested in simulation studies using linearly related time series and it is shown to have a very good success rate of correct pattern matching

non parametric bayesian graph models reveal community structure in resting state fmri modeling of resting state functional magnetic resonance imaging rs fmri data using network models is of increasing interest it is often desirable to group nodes into clusters to interpret the communication patterns between nodes in this study we consider three dierent nonparametric bayesian

the simple cubic lattice gas with nearest neighbour exclusion ising universality abstract the lattice gas with nearest neighbour exclusion on the simple cubic lattice is studied by means of statistically accurate monte carlo simulations with an efficient cluster algorithm our results for critical exponents are y h 2 47 1 and y t 1 60 2 these results agree well with the three dimensional ising universality class we explain the discrepancy with an earlier study the critical activity is z c 1 0559 1 the size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the monte carlo algorithm coincides with the critical point

efficient certifiably optimal clustering with applications to latent variable graphical models motivated by the task of clustering either d variables or d points into k groups we investigate efficient algorithms to solve the peng wei p w k means semi definite programming sdp relaxation the p w sdp has been shown in the literature to have good statistical properties in a variety of settings but remains intractable to solve in practice to this end we propose force a new algorithm to solve this sdp relaxation compared to off the shelf interior point solvers our method reduces the computational complexity of solving the sdp from widetilde mathcal o d 7 log epsilon 1 to widetilde mathcal o d 6 k 2 epsilon 1 arithmetic operations for an epsilon optimal solution our method combines a primal first order method with a dual optimality certificate search which when successful allows for early termination of the primal method we show for certain variable clustering problems that with high probability force is guaranteed to find the optimal solution to the sdp relaxation and provide a certificate of exact optimality as verified by our numerical experiments this allows force to solve the p w sdp with dimensions in the hundreds in only tens of seconds for a variation of the p w sdp where k is not known a priori a slight modification of force reduces the computational complexity of solving this problem as well from widetilde mathcal o d 7 log epsilon 1 using a standard sdp solver to widetilde mathcal o d 4 epsilon 1

ising universality in three dimensions a monte carlo study we investigate three ising models on the simple cubic lattice by means of monte carlo methods and finite size scaling these models are the spin 1 2 ising model with nearest neighbour interactions a spin 1 2 model with nearest neighbour and third neighbour interactions and a spin 1 model with nearest neighbour interactions the results are in accurate agreement with the hypothesis of universality analysis of the finite size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field we find that the correction to scaling amplitudes are strongly dependent on the introduction of further neighbour interactions or a third spin state in a spin 1 ising model these corrections appear to be very small this is very helpful for the determination of the universal constants of the ising model the renormalization exponents of the ising model are determined as yt 1 587 2 yh 2 4815 15 and yi 0 82 6 the universal ratio q m2 2 m4 is equal to 0 6233 4 for periodic systems with cubic symmetry the critical point of the nearest neighbour spin 1 2 model is kc 0 2216546 10

correlator beware correlation has limited selectivity for fmri data analysis abstract groups of time courses created from fmri data by the frequently used correlation analysis are often highly heterogeneous this heterogeneity is due to the limited selectivity of correlation when trying to match brain time courses to an externally imposed activation paradigm thus this process unnecessarily generates many type i errors false positives furthermore as a consequence of the heterogeneity time courses identified and grouped by correlation may in fact describe different activations after demonstrating this inadequacy we give one particular approach to partition such a heterogeneous group into internally more homogeneous subgroups using kendall s coefficient of concordance w and show its applicability and application to both simulated and in vivo data such group partition and purification will help subsequent inferential methods to deal more efficiently with false positives

chow groups are finite dimensional in some sense when s is a surface with pg s 0 mumford proved that its chow group a s is not finite dimensional in some sense in this paper we propose another definition of finite dimensionality for the chow groups using this new definition at least the chow group of some surface s with pg s 0 for example the product of two curves becomes finite dimensional the finite dimensionality of the chow groups follows from the finite dimensionality of the chow motives it turns out that the finite dimensionality of the chow motives is a very strong property for example we can prove bloch s conjecture representability of the chow groups of surfaces with pg s 0 under the assumption that the chow motive of s is finite dimensional

graphical representations and cluster algorithms ii we continue the study initiated in part i of graphical representations and cluster algorithms for various models in or related to statistical mechanics for certain models e g the blume emery griffths model and various generalizations we develop fortuin kasteleyn type representations which lead immediately to swendsen wang type algorithms for other models e g the random cluster model that are defined by a graphical representation we develop cluster algorithms without reference to an underlying spin system in all cases phase transitions are related to percolation or incipient percolation in the graphical representation which via the ic algorithm allows for the rapid simulation of these systems at the transition point pertinent examples include the continuum widom rowlinson model the restricted 1 step solid on solid model and the xy model

percolation between vacancies in the two dimensional blume capel model using suitable monte carlo methods and finite size scaling we investigate the blume capel model on the square lattice we construct percolation clusters by placing nearest neighbor bonds between vacancies with a variable bond probability pb at the tricritical point we locate the percolation threshold of these vacancy clusters at pbc 0 706 336 at this point we determine the fractal dimension of the vacancy clusters as xf 0 13085 21 160 and the exponent governing the renormalization flow in the pb direction as yp 0 4262 17 40 for bond probability pbpbc the vacancy clusters maintain strong critical correlations the fractal dimension is xf 0 07502 3 40 and the leading correction exponent is yp 0 452 19 40 the above values fit well in the kac table for the tricritical ising model these vacancy clusters have much analogy with those consisting of ising spins of the same sign although the associated quantities and magnetization m are energylike and magnetic quantities respectively however along the critical line of the blume capel model the vacancies are more or less uniformly distributed over the whole lattice in this case no critical percolation correlations are observed in the vacancy clusters at least in the physical region pb 1

dirac operators in tensor categories and the motive of quaternionic modular forms we define a motive whose realizations afford modular forms of arbitrary weight on an indefinite division quaternion algebra this generalizes work of iovita spiess to odd weights in the spirit of jordan livne it also generalizes a construction of scholl to indefinite division quaternion algebras and provides the first motivic construction of new subspaces of modular forms