fast factorization acceleration of mom compressive domain decomposition domain decomposition dd for integral equation can be achieved by aggregating standard basis functions into specialized basis functions on each sub domain this results in a strong compression of the mom matrix which allows an iteration free e g lu decomposition solution also for electrically large problems fast matrix vector product algorithms can be used in the matrix filling and compression process of the employed aggregate functions approach this hybrid approach has received considerable attention in recent literature in order to quantitatively assess the performance advantages and limitations of this class of methods we start by proposing and demonstrating the use of the adaptive integral method aim fast factorization to accelerate the synthetic function expansion sfx dd approach the method remains iteration free with a significant boost in memory and time performances with analytical predictions of complexity scalings confirmed by numerical results then we address the complexity scaling of both stand alone dd and its combined use with fast mom this is done analytically and discussed with respect to known literature accounts of various implementations of the dd paradigm with nonobvious results that highlight needs and limitations and yielding practical indications

training free generic object detection using locally adaptive regression kernels we present a generic detection localization algorithm capable of searching for a visual object of interest without training the proposed method operates using a single example of an object of interest to find similar matches does not require prior knowledge learning about objects being sought and does not require any preprocessing step or segmentation of a target image our method is based on the computation of local regression kernels as descriptors from a query which measure the likeness of a pixel to its surroundings salient features are extracted from said descriptors and compared against analogous features from the target image this comparison is done using a matrix generalization of the cosine similarity measure we illustrate optimality properties of the algorithm using a naive bayes framework the algorithm yields a scalar resemblance map indicating the likelihood of similarity between the query and all patches in the target image by employing nonparametric significance tests and nonmaxima suppression we detect the presence and location of objects similar to the given query the approach is extended to account for large variations in scale and rotation high performance is demonstrated on several challenging data sets indicating successful detection of objects in diverse contexts and under different imaging conditions

probabilistic visual learning for object representation we present an unsupervised technique for visual learning which is based on density estimation in high dimensional spaces using an eigenspace decomposition two types of density estimates are derived for modeling the training data a multivariate gaussian for unimodal distributions and a mixture of gaussians model for multimodal distributions those probability densities are then used to formulate a maximum likelihood estimation framework for visual search and target detection for automatic object recognition and coding our learning technique is applied to the probabilistic visual modeling detection recognition and coding of human faces and nonrigid objects such as hands

numerical homogenization of the acoustic wave equations with a continuum of scales in this paper we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients namely when the bulk modulus and the density of the medium are only bounded we show that under a cordes type condition the second order derivatives of the solution with respect to harmonic coordinates are l 2 instead h 1 with respect to euclidean coordinates and the solution itself is in l 0 t h 2 instead of l 0 t h 1 with respect to euclidean coordinates then we propose an implicit time stepping method to solve the resulted linear system on coarse spatial scales and present error estimates of the method it follows that by pre computing the associated harmonic coordinates it is possible to numerically homogenize the wave equation without assumptions of scale separation or ergodicity

efficient analysis of large aperiodic antenna arrays using the domain green s function method an efficient method of moments mom based domain decomposition technique viz the domain green s function method dgfm is presented for analyzing large antenna arrays the dgfm is a perturbation technique where mutual coupling between array elements is accounted for during the formulation of an active impedance matrix for each domain array element the active current distribution on the entire array geometry is obtained by solving the smaller matrix equations related to the elements and not that of the problem as a whole this leads to a significant saving in both runtime and memory usage the method also takes into account the edge effects attributed to the finite size of the array complex excitations with nonlinear phase shift and is not limited to periodic array configurations the dgfm is an approximation and assumes a slowly varying current distribution between domains a novel way to mitigate the aforementioned by including secondary coupling effects is also discussed furthermore an efficient active impedance matrix fill strategy is presented where the active impedance matrix summation is truncated to include only a certain number of terms parallelization using both distributed and shared memory programming models have also been applied to the dgfm to further optimize runtime and memory usage

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

wavelet based numerical homogenization a numerical homogenization procedure for elliptic differential equations is presented it is based on wavelet decompositions of discrete operators in fine and coarse scale components followed by the elimination of the fine scale contributions if the operator is in divergence form this is preserved by the homogenization procedure for periodic problems results similar to classical effective coefficient theory are proved the procedure can be applied to problems that are not cell periodic

what is the goal of sensory coding a number of recent attempts have been made to describe early sensory coding in terms of a general information processing strategy in this paper two strategies are contrasted both strategies take advantage of the redundancy in the environment to produce more effective representations the first is described as a compact coding scheme a compact code performs a transform that allows the input to be represented with a reduced number of vectors cells with minimal rms error this approach has recently become popular in the neural network literature and is related to a process called principal components analysis pca a number of recent papers have suggested that the optimal compact code for representing natural scenes will have units with receptive field profiles much like those found in the retina and primary visual cortex however in this paper it is proposed that compact coding schemes are insufficient to account for the receptive field properties of cells in the mammalian visual pathway in contrast it is proposed that the visual system is near to optimal in representing natural scenes only if optimality is defined in terms of sparse distributed coding in a sparse distributed code all cells in the code have an equal response probability across the class of images but have a low response probability for any single image in such a code the dimensionality is not reduced rather the redundancy of the input is transformed into the redundancy of the firing pattern of cells it is proposed that the signature for a sparse code is found in the fourth moment of the response distribution i e the kurtosis in measurements with 55 calibrated natural scenes the kurtosis was found to peak when the bandwidths of the visual code matched those of cells in the mammalian visual cortex codes resembling wavelet transforms are proposed to be effective because the response histograms of such codes are sparse i e show high kurtosis when presented with natural scenes it is proposed that the structure of the image that allows sparse coding is found in the phase spectrum of the image it is suggested that natural scenes to a first approximation can be considered as a sum of self similar local functions the inverse of a wavelet possible reasons for why sensory systems would evolve toward sparse coding are presented

solution of electrically large problems with multilevel characteristic basis functions we present a multilevel version to the characteristic basis function method cbfm this technique extends the range of applicability of the conventional cbfm and allows a direct solution of problems even when they exceed 250 000 degrees of freedom in this paper it is shown how we can use the multilevel cbfm which is a natural extension of the conventional approach and which saves both time and memory and yet retains excellent accuracy in the computed far fields also the adaptive cross algorithm is used for fast calculation of the interaction between the blocks in the process of generating the reduced matrix

filter based mean field inference for random fields with higher order terms and product label spaces recently a number of cross bilateral filtering methods have been proposed for solving multi label problems in computer vision such as stereo optical flow and object class segmentation that show an order of magnitude improvement in speed over previous methods these methods have achieved good results despite using models with only unary and or pairwise terms however previous work has shown the value of using models with higher order terms e g to represent label consistency over large regions or global co occurrence relations we show how these higher order terms can be formulated such that filter based inference remains possible we demonstrate our techniques on joint stereo and object labelling problems as well as object class segmentation showing in addition for joint object stereo labelling how our method provides an efficient approach to inference in product label spaces we show that we are able to speed up inference in these models around 10 30 times with respect to competing graph cut move making methods as well as maintaining or improving accuracy in all cases we show results on pascalvoc 10 for object class segmentation and leuven for joint object stereo labelling

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

one shot detection with laplacian object and fast matrix cosine similarity one shot generic object detection involves searching for a single query object in a larger target image relevant approaches have benefited from features that typically model the local similarity patterns in this paper we combine local similarity encoded by local descriptors with a global context i e a graph structure of pairwise affinities among the local descriptors embedding the query descriptors into a low dimensional but discriminatory subspace unlike principal components that preserve global structure of feature space we actually seek a linear approximation to the laplacian eigenmap that permits us a locality preserving embedding of high dimensional region descriptors our second contribution is an accelerated but exact computation of matrix cosine similarity as the decision rule for detection obviating the computationally expensive sliding window search we leverage the power of fourier transform combined with integral image to achieve superior runtime efficiency that allows us to test multiple hypotheses for pose estimation within a reasonably short time our approach to one shot detection is training free and experiments on the standard data sets confirm the efficacy of our model besides low computation cost of the proposed codebook free object detector facilitates rather straightforward query detection in large data sets including movie videos

spatio spectral concentration of convolutions differential equations may possess coefficients that vary on a spectrum of scales because coefficients are typically multiplicative in real space they turn into convolution operators in spectral space mixing all wavenumbers however in many applications only the largest scales of the solution are of interest and so the question turns to whether it is possible to build effective coarse scale models of the coefficients in such a manner that the large scales of the solution are left intact here we apply the method of numerical homogenisation to deterministic linear equations to generate sub grid scale models of coefficients at desired frequency cutoffs we use the fourier basis to project filter and compute correctors for the coefficients the method is tested in 1d and 2d scenarios and found to reproduce the coarse scales of the solution to varying degrees of accuracy depending on the cutoff we relate this method to mode elimination renormalisation group rg and discuss the connection between accuracy and the cutoff wavenumber the tradeoff is governed by a form of the uncertainty principle for convolutions which states that as the convolution operator is squeezed in the spectral domain it broadens in real space as a consequence basis sparsity is a high virtue and the choice of the basis can be critical

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

on the relationship between multiple scattering macro basis functions and krylov subspace iterative methods a mathematical link is provided between the krylov subspace iterative approach based on the full orthogonalization method fom and the macro basis functions mbf approach based on a multiple scattering methodology the link refers to the subspaces created by those methods as well as to the orthogonality conditions which they satisfy both approaches are applied to the same method of moments mom system of equations that is preconditioned based on a closest interaction rule and where blocks of the mom impedance matrix are compressed using a rank revealing method mbf and fom approaches are compared numerically with a special attention given to accuracy for perfectly conducting objects comprising an array of tapered slot antennas spheres and an aircraft the respective advantages of both methods are briefly discussed and further prospects are given

supervised discrete hashing with relaxation data dependent hashing has recently attracted attention due to being able to support efficient retrieval and storage of high dimensional data such as documents images and videos in this paper we propose a novel learning based hashing method called supervised discrete hashing with relaxation sdhr based on supervised discrete hashing sdh sdh uses ordinary least squares regression and traditional zero one matrix encoding of class label information as the regression target code words thus fixing the regression target in sdhr the regression target is instead optimized the optimized regression target matrix satisfies a large margin constraint for correct classification of each example compared with sdh which uses the traditional zero one matrix sdhr utilizes the learned regression target matrix and therefore more accurately measures the classification error of the regression model and is more flexible as expected sdhr generally outperforms sdh experimental results on two large scale image data sets cifar 10 and mnist and a large scale and challenging face data set frgc demonstrate the effectiveness and efficiency of sdhr

fast analysis of large antenna arrays using the characteristic basis function method and the adaptive cross approximation algorithm the characteristic basis function method cbfm has been hybridized with the adaptive cross approximation aca algorithm to construct a reduced matrix equation in a time efficient manner and to solve electrically large antenna array problems in core with a solve time orders of magnitude less than those in the conventional methods various numerical examples are presented that demonstrate that the proposed method has a very good accuracy computational efficiency and reduced memory storage requirement specifically we analyze large 1 d and 2 d arrays of electrically interconnected tapered slot antennas tsas the entire computational domain is subdivided into many smaller subdomains each of which supports a set of characteristic basis functions cbfs we also present a novel scheme for generating the cbfs that do not conform to the edge condition at the truncated edge of each subdomain and provide a minor overlap between the cbfs in adjacent subdomains as a result the cbfs preserve the continuity of the surface current across the subdomain interfaces thereby circumventing the need to use separate ldquoconnectionrdquo basis functions

a single level low rank ie qr algorithm for pec scattering problems using efie formulation this paper presents a single level matrix compression algorithm termed ie qr based on a low rank approximation to speed up the electric field integral equation efie formulation it is shown with the number of groups chosen to be proportional to n sup 1 2 where n is the number of unknowns the memory and cpu time for the resulting algorithm are both o n sup 1 5 the unique features of the algorithm are a the ie qr algorithm is based on the near rank deficiency property for well separated groups this near rank deficiency assumption holds true for many integral equation methods such as laplacian radiation and scattering problems in electromagnetics em the same algorithm can be adapted to other applications outside em with few or no modifications and b the rank estimation is achieved by a dual rank process which ranks the transmitting and receiving groups respectively thus the ie qr algorithm can achieve matrix compression without assembling the entire system matrix also a geometric neighboring preconditioner is presented in this paper this geometric neighboring preconditioner when used in conjunction with gmres is proven to be both efficient and effective for solving the compressed matrix equations

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

a nonconformal domain decomposition scheme for the analysis of multiscale structures we present a domain decomposition dd framework for the analysis of impenetrable structures it allows for the electric field integral equation efie and combined field integral equation cfie and for open closed and open closed structures the dd results in an effective preconditioner for large and complex problems exploiting iterative solution and fast factorizations the dd employs specialized transmission conditions among the domains and the use of discontinuous galerkin dg allows conformal as well as nonconformal discretizations of domain boundaries the nonconformal nature of the decomposition gives considerable flexibility in the meshing the strategy is highly parallelizable as all the operations involving the subdomains can be performed in parallel the proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes

an iteration free mom approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems we describe a numerically efficient strategy for solving a linear system of equations arising in the method of moments for solving electromagnetic scattering problems this novel approach termed as the characteristic basis function method cbfm is based on utilizing characteristic basis functions cbfs special functions defined on macro domains blocks that include a relatively large number of conventional sub domains discretized by using triangular or rectangular patches use of these basis functions leads to a significant reduction in the number of unknowns and results in a substantial size reduction of the mom matrix this in turn enables us to handle the reduced matrix by using a direct solver without the need to iterate in addition the paper shows that the cbfs can be generated by using a sparse representation of the impedance matrix resulting in lower computational cost and that in contrast to the iterative techniques multiple excitations can be handled with only a small overhead another important attribute of the cbfm is that it is readily parallelized numerical results that demonstrate the accuracy and time efficiency of the cbfm for several representative scattering problems are included in the paper

contour fft based spectral domain mbf analysis of large printed antenna arrays a fast spectral domain method is proposed to evaluate the reaction terms between the macro basis functions in regular and non regular arrays made of identical printed antennas the presented technique first exploits the filtering capabilities of the macro basis functions in the spectral domain the method is then strongly accelerated with the help of a newly formulated fast fourier transform fft based technique which is applicable to a contour integration in the complex plane we name the method as contour fft c fft besides an effective homogeneous medium term treated with multipoles a computational complexity of order n log2 n is achieved for the tabulation of substrate related reaction terms for any possible relative positions the complexity of the proposed method is independent from the complexity of the elements numerical results obtained with the proposed method are compared with those from a pre validated reference solution based on the traditional macro basis functions technique an excellent agreement is observed

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

efficient subwindow search a branch and bound framework for object localization most successful object recognition systems rely on binary classification deciding only if an object is present or not but not providing information on the actual object location to estimate the object s location one can take a sliding window approach but this strongly increases the computational cost because the classifier or similarity function has to be evaluated over a large set of candidate subwindows in this paper we propose a simple yet powerful branch and bound scheme that allows efficient maximization of a large class of quality functions over all possible subimages it converges to a globally optimal solution typically in linear or even sublinear time in contrast to the quadratic scaling of exhaustive or sliding window search we show how our method is applicable to different object detection and image retrieval scenarios the achieved speedup allows the use of classifiers for localization that formerly were considered too slow for this task such as svms with a spatial pyramid kernel or nearest neighbor classifiers based on the lambda2 distance we demonstrate state of the art localization performance of the resulting systems on the uiuc cars data set the pascal voc 2006 data set and in the pascal voc 2007 competition

correlated logistic model with elastic net regularization for multilabel image classification in this paper we present correlated logistic corrlog model for multilabel image classification corrlog extends conventional logistic regression model into multilabel cases via explicitly modeling the pairwise correlation between labels in addition we propose to learn the model parameters of corrlog with elastic net regularization which helps exploit the sparsity in feature selection and label correlations and thus further boost the performance of multilabel classification corrlog can be efficiently learned though approximately by regularized maximum pseudo likelihood estimation and it enjoys a satisfying generalization bound that is independent of the number of labels corrlog performs competitively for multilabel image classification on benchmark data sets mulan scene mit outdoor scene pascal voc 2007 and pascal voc 2012 compared with the state of the art multilabel classification algorithms

what does the retina know about natural scenes by examining the experimental data on the statistical properties of natural scenes together with retinal contrast sensitivity data we arrive at a first principle theoretical hypothesis for the purpose of retinal processing and its relationship to an animal s environment we argue that the retinal goal is to transform the visual input as much as possible into a statistically independent basis as the first step in creating a redundancy reduced representation in the cortex as suggested by barlow the extent of this whitening of the input is limited however by the need to suppress input noise our explicit theoretical solutions for the retinal filters also show a simple dependence on mean stimulus luminance they predict an approximate weber law at low spatial frequencies and a de vries rose law at high frequencies assuming that the dominant source of noise is quantum we generate a family of contrast sensitivity curves as a function of mean luminance this family is compared to psychophysical data

mathematical models with exact renormalization for turbulent transport the advection diffusion of a passive scalar by incompressible velocity fields which admit a statistical description and involve a continuous range of excited spatial and or temporal scales is very important in applications ranging from fully developed turbulence to the diffusion of tracers in heterogeneous porous media a variety of renormalization theories which typically utilize partial resummation of divergent perturbation series according to various recipes have been applied to this problem in various contexts in this paper a simple model problem for the advection diffusion of a passive scalar is introduced and the complete renormalization theory is developed with full mathematical rigor explicit formulas for the anomalous time scaling in various regimes as well as the green s function for the large scale long time ensemble average are developed here formulas for the renormalized higher order statistics are also developed the simple form of the model problem is deceptive the renormalization theory for this problem exhibits a remarkable range of different renormalization phenomena as parameters in the velocity statistics are varied these phenomena include the existence of several distinct anomalous scaling regimes as the spectral parameter tilde varepsilon is varied as well as explicit regimes in tilde varepsilon where the effective equation for the ensemble average is not a simple diffusion equation but instead involves an explicit random nonlocal eddy diffusivity we use fourier analysis and the feynman kac formula as main tools in the explicit exact renormalization theory developed here

a fast impedance and pattern computation scheme for finite antenna arrays a fast numerical method well suited to the analysis of moderate size arrays made of complex elements is presented it combines macro basis functions and multipole approaches without an iterative procedure this method is exploited to estimate the impedance matrix and active element patterns for the latter an efficient formulation is provided as a series of pattern multiplication problems examples are shown for arrays of broadband dipoles the computational gain obtained for the reduction of the original method of moments system of equations is briefly described

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

analysis of large complex structures with the synthetic functions approach an innovative procedure is presented that allows the method of moments mom analysis of large and complex antenna and scattering problems at a reduced memory and cpu cost bounded within the resources provided by a standard 32 bit personal computer the method is based on the separation of the overall geometry into smaller portions called blocks and on the degrees of freedom of the field the blocks need not be electrically unconnected on each block basis functions are generated with support on the entire block that are subsequently used as basis functions for the analysis of the complete structure only a small number of these functions is required to obtain an accurate solution therefore the overall number of unknowns is drastically reduced with consequent impact on storage and solution time these entire domain basis functions are called synthetic functions they are generated from the solution of the electromagnetic problem for the block in isolation under excitation by suitably defined sources the synthetic functions are obtained from the responses to all sources via a procedure based on the singular value decomposition because of the strong reduction of the global number of unknowns one can store the mom matrix and afford a direct solution the method is kernel free and can be implemented on existing mom codes

a local spectral method for graphs with applications to improving graph partitions and exploring data graphs locally the second eigenvalue of the laplacian matrix and its associated eigenvector are fundamental features of an undirected graph and as such they have found widespread use in scientific computing machine learning and data analysis in many applications however graphs that arise have several local regions of interest and the second eigenvector will typically fail to provide information fine tuned to each local region in this paper we introduce a locally biased analogue of the second eigenvector and we demonstrate its usefulness at highlighting local properties of data graphs in a semi supervised manner to do so we first view the second eigenvector as the solution to a constrained optimization problem and we incorporate the local information as an additional constraint we then characterize the optimal solution to this new problem and show that it can be interpreted as a generalization of a personalized pagerank vector and finally as a consequence we show that the solution can be computed in nearly linear time in addition we show that this locally biased vector can be used to compute an approximation to the best partition near an input seed set in a manner analogous to the way in which the second eigenvector of the laplacian can be used to obtain an approximation to the best partition in the entire input graph such a primitive is useful for identifying and refining clusters locally as it allows us to focus on a local region of interest in a semi supervised manner finally we provide a detailed empirical evaluation of our method by showing how it can applied to finding locally biased sparse cuts around an input vertex seed set in social and information networks

action recognition from one example we present a novel action recognition method based on space time locally adaptive regression kernels and the matrix cosine similarity measure the proposed method uses a single example of an action as a query to find similar matches it does not require prior knowledge about actions foreground background segmentation or any motion estimation or tracking our method is based on the computation of novel space time descriptors from the query video which measure the likeness of a voxel to its surroundings salient features are extracted from said descriptors and compared against analogous features from the target video this comparison is done using a matrix generalization of the cosine similarity measure the algorithm yields a scalar resemblance volume with each voxel indicating the likelihood of similarity between the query video and all cubes in the target video using nonparametric significance tests by controlling the false discovery rate we detect the presence and location of actions similar to the query video high performance is demonstrated on challenging sets of action data containing fast motions varied contexts and complicated background further experiments on the weizmann and kth data sets demonstrate state of the art performance in action categorization