outlier detection with the kernelized spatial depth function statistical depth functions provide from the deepest point a center outward ordering of multidimensional data in this sense depth functions can measure the extremeness or outlyingness of a data point with respect to a given data set hence they can detect outliers observations that appear extreme relative to the rest of the observations of the various statistical depths the spatial depth is especially appealing because of its computational efficiency and mathematical tractability in this article we propose a novel statistical depth the kernelized spatial depth ksd which generalizes the spatial depth via positive definite kernels by choosing a proper kernel the ksd can capture the local structure of a data set while the spatial depth fails we demonstrate this by the half moon data and the ring shaped data based on the ksd we propose a novel outlier detection algorithm by which an observation with a depth value less than a threshold is declared as an outlier the proposed algorithm is simple in structure the threshold is the only one parameter for a given kernel it applies to a one class learning setting in which normal observations are given as the training data as well as to a missing label scenario where the training set consists of a mixture of normal observations and outliers with unknown labels we give upper bounds on the false alarm probability of a depth based detector these upper bounds can be used to determine the threshold we perform extensive experiments on synthetic data and data sets from real applications the proposed outlier detector is compared with existing methods the ksd outlier detector demonstrates a competitive performance

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

high breakdown linear discriminant analysis abstract the classification rules of linear discriminant analysis are defined by the true mean vectors and the common covariance matrix of the populations from which the data come because these true parameters are generally unknown they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population however these sample statistics are notoriously susceptible to contamination by outliers a problem compounded by the fact that the outliers may be invisible to conventional diagnostics high breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers regardless of their severity in this article we motivate and develop a high breakdown criterion for linear discriminant analysis and give an algorithm for its implementation the procedure is intended to supplement rather than replace the usual sample moment methodology of discri

configurations in abelian categories ii ringel hall algebras abstract this is the second in a series on configurations in an abelian category a given a finite poset i an i configuration is a finite collection of objects j and morphisms j k or j k j k in a satisfying some axioms where j k i configurations describe how an object x in a decomposes into subobjects the first paper defined configurations and studied moduli spaces of i configurations in a using the theory of artin stacks it showed well behaved moduli stacks obj a m i a of objects and configurations in a exist when a is the abelian category coh p of coherent sheaves on a projective scheme p or mod k q of representations of a quiver q write cf obj a for the vector space of q valued constructible functions on the stack obj a motivated by the idea of ringel hall algebras we define an associative multiplication on cf obj a using pushforwards and pullbacks along 1 morphisms between configuration moduli stacks so that cf obj a is a q algebra we also study representations of cf obj a the lie subalgebra cf ind obj a of functions supported on indecomposables and other algebraic structures on cf obj a then we generalize all these ideas to stack functions sf obj a a universal generalization of constructible functions containing more information when ext i x y 0 for all x y a and i 1 or when a coh p for p a calabi yau 3 fold we construct lie algebra morphisms from stack algebras to explicit algebras which will be important in the sequels on invariants counting semistable objects in a

gromov witten invariants in algebraic geometry gromov witten invariants for arbitrary non singular projective vari eties and arbitrary genus are constructed using the techniques from k behrend b fantechi the intrinsic normal cone

linear reconstruction measure steered nearest neighbor classification framework the linear reconstruction measure lrm which determines the nearest neighbors of the query sample in all known training samples by sorting the minimum l 2 norm error linear reconstruction coefficients is introduced in this paper the intuitive interpretation and mathematical proofs are presented to reveal the efficient working mechanism of lrm through analyzing the physical meaning of coefficients and regularization items we find that lrm provides more useful information and advantages than the conventional similarity measure model which calculates the distance between two entities i e conventional point to point c ptp inspired by the advantages of lrm the linear reconstruction measure steered nearest neighbor classification framework lrm nncf is designed with eight classifiers according to different decision rules and models of lrm evaluation on several face databases and the experimental results demonstrate that these proposed classifiers can achieve greater performance than the c ptp based 1 nns and competitive recognition accuracy and robustness compared with the state of the art classifiers

robust regression discriminative methods e g kernel regression svm have been extensively used to solve problems such as object recognition image alignment and pose estimation from images these methods typically map image features mathbf x to continuous e g pose or discrete e g object category values a major drawback of existing discriminative methods is that samples are directly projected onto a subspace and hence fail to account for outliers common in realistic training sets due to occlusion specular reflections or noise it is important to notice that existing discriminative approaches assume the input variables mathbf x to be noise free thus discriminative methods experience significant performance degradation when gross outliers are present despite its obvious importance the problem of robust discriminative learning has been relatively unexplored in computer vision this paper develops the theory of robust regression rr and presents an effective convex approach that uses recent advances on rank minimization the framework applies to a variety of problems in computer vision including robust linear discriminant analysis regression with missing data and multi label classification several synthetic and real examples with applications to head pose estimation from images image and video classification and facial attribute classification with missing data are used to illustrate the benefits of rr

maximum correntropy criterion for robust face recognition in this paper we present a sparse correntropy framework for computing robust sparse representations of face images for recognition compared with the state of the art l1norm based sparse representation classifier src which assumes that noise also has a sparse representation our sparse algorithm is developed based on the maximum correntropy criterion which is much more insensitive to outliers in order to develop a more tractable and practical approach we in particular impose nonnegativity constraint on the variables in the maximum correntropy criterion and develop a half quadratic optimization technique to approximately maximize the objective function in an alternating way so that the complex optimization problem is reduced to learning a sparse representation through a weighted linear least squares problem with nonnegativity constraint at each iteration our extensive experiments demonstrate that the proposed method is more robust and efficient in dealing with the occlusion and corruption problems in face recognition as compared to the related state of the art methods in particular it shows that the proposed method can improve both recognition accuracy and receiver operator characteristic roc curves while the computational cost is much lower than the src algorithms

robust regression for face recognition in this paper we address the problem of robust face recognition by formulating the pattern recognition task as a problem of robust estimation using a fundamental concept that in general patterns from a single object class lie on a linear subspace barsi and jacobs 2003 1 we develop a linear model representing a probe image as a linear combination of class specific galleries in the presence of noise the well conditioned inverse problem is solved using the robust huber estimation and the decision is ruled in favor of the class with the minimum reconstruction error the proposed robust linear regression classification rlrc algorithm is extensively evaluated for two important cases of robustness i e illumination variations and random pixel corruption illumination invariant face recognition is demonstrated on three standard databases under exemplary evaluation protocols reported in the literature comprehensive comparative analysis with the state of art illumination tolerant approaches indicates a comparable performance index for the proposed rlrc algorithm the efficiency of the proposed approach in the presence of severe random noise is validated under several exemplary noise models such as dead pixel problem salt and pepper noise speckle noise and additive white gaussian noise awgn the rlrc algorithm is found to be favorable compared with the benchmark generative approaches

classification in an informative sample subspace we have developed an informative sample subspace iss method that is suitable for projecting high dimensional data onto a low dimensional subspace for classification purposes in this paper we present an iss algorithm that uses a maximal mutual information criterion to search a labelled training data set directly for the subspace s projection base vectors we evaluate the usefulness of the iss method using synthetic data as well as real world problems experimental results demonstrate that the iss algorithm is effective and can be used as a general method for representing high dimensional data in a low dimensional subspace for classification

linear regression for face recognition in this paper we present a novel approach of face identification by formulating the pattern recognition problem in terms of linear regression using a fundamental concept that patterns from a single object class lie on a linear subspace we develop a linear model representing a probe image as a linear combination of class specific galleries the inverse problem is solved using the least squares method and the decision is ruled in favor of the class with the minimum reconstruction error the proposed linear regression classification lrc algorithm falls in the category of nearest subspace classification the algorithm is extensively evaluated on several standard databases under a number of exemplary evaluation protocols reported in the face recognition literature a comparative study with state of the art algorithms clearly reflects the efficacy of the proposed approach for the problem of contiguous occlusion we propose a modular lrc approach introducing a novel distance based evidence fusion def algorithm the proposed methodology achieves the best results ever reported for the challenging problem of scarf occlusion

why can lda be performed in pca transformed space abstract pca plus lda is a popular framework for linear discriminant analysis lda in high dimensional and singular case in this paper we focus on building a theoretical foundation for this framework moreover we point out the weakness of the previous lda based methods and suggest a complete pca plus lda algorithm experimental results on orl face image database indicate that the proposed method is more effective than the previous ones

limit stable objects on calabi yau 3 folds the notion of limit stability is introduced in 31 to give a limiting degeneration of bridgeland stability in this article we give the survey of the results in 31 30 we introduce the limit stability counting invariants of limit stable objects and see that the wall crossing phenomena yields the rationality conjecture of pandharipandethomas generating functions

chern classes of reflexive sheaves on normal surfaces we define chern classes of reflexive sheaves using wahl s relative local chern classes of vector bundles the main result of the paper bounds contributions of singularities of a sheaf to the riemann roch formula using it we are able to prove inequality in wahl s conjecture on relative asymptotic rr formula for rank 2 vector bundles moreover we prove that if wahl s conjecture is true for a singularity then it is true for any its quotient this implies wahl s conjecture for quotient singularities and for quotients of cones over elliptic curves

curve counting via stable pairs in the derived category for a nonsingular projective 3 fold x we define integer invariants virtually enumerating pairs c d where c x is an embedded curve and d c is a divisor a virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of x the resulting invariants are conjecturally equivalent after universal transformations to both the gromov witten and dt theories of x for calabi yau 3 folds the latter equivalence should be viewed as a wall crossing formula in the derived category

extracting non negative basis images using pixel dispersion penalty non negativity matrix factorization nmf and its variants have been explored in the last decade and are still attractive due to its ability of extracting non negative basis images however most existing nmf based methods are not ready for encoding higher order data information one reason is that they do not directly explicitly model structured data information during learning and therefore the extracted basis images may not completely describe the parts in an image 1 very well in order to solve this problem the structured sparse nmf has been recently proposed in order to learn structured basis images it however depends on some special prior knowledge i e one needs to exhaustively define a set of structured patterns in advance in this paper we wish to perform structured sparsity learning as automatically as possible to that end we propose a pixel dispersion penalty pdp which effectively describes the spatial dispersion of pixels in an image without using any manually predefined structured patterns as constraints in pdp we consider each part based feature pattern of an image as a cluster of non zero pixels that is the non zero pixels of a local pattern should be spatially close to each other furthermore by incorporating the proposed pdp we develop a spatial non negative matrix factorization spatial nmf and a spatial non negative component analysis spatial nca in spatial nca the non negativity constraint is only imposed on basis images and such constraint on coefficients is released so both subtractive and additive combinations of non negative basis images are allowed for reconstructing any images extensive experiments are conducted to validate the effectiveness of the proposed pixel dispersion penalty we also experimentally show that spatial nca is more flexible for extracting non negative basis images and obtains better and more stable performance

fourier mukai transforms for elliptic surfaces we compute a large number of moduli spaces of stable bun dles on a general algebraic elliptic surface using a new class of relative fourier mukai transforms

face recognition via collaborative representation its discriminant nature and superposed representation collaborative representation methods such as sparse subspace clustering ssc and sparse representation based classification src have achieved great success in face clustering and classification by directly utilizing the training images as the dictionary bases in this paper we reveal that the superior performance of collaborative representation relies heavily on the sufficiently large class separability of the controlled face datasets such as extended yale b on the uncontrolled or undersampled dataset however collaborative representation suffers from the misleading coefficients of the incorrect classes to address this limitation inspired by the success of linear discriminant analysis lda we develop a superposed linear representation classifier slrc to cast the recognition problem by representing the test image in term of a superposition of the class centroids and the shared intra class differences in spite of its simplicity and approximation the slrc largely improves the generalization ability of collaborative representation and competes well with more sophisticated dictionary learning techniques on the experiments of ar and frgc databases enforced with the sparsity constraint slrc achieves the state of the art performance on feret database using single sample per person

combining reconstructive and discriminative subspace methods for robust classification and regression by subsampling linear subspace methods that provide sufficient reconstruction of the data such as pca offer an efficient way of dealing with missing pixels outliers and occlusions that often appear in the visual data discriminative methods such as lda which on the other hand are better suited for classification tasks are highly sensitive to corrupted data we present a theoretical framework for achieving the best of both types of methods an approach that combines the discrimination power of discriminative methods with the reconstruction property of reconstructive methods which enables one to work on subsets of pixels in images to efficiently detect and reject the outliers the proposed approach is therefore capable of robust classification with a high breakdown point we also show that subspace methods such as cca which are used for solving regression tasks can be treated in a similar manner the theoretical results are demonstrated on several computer vision tasks showing that the proposed approach significantly outperforms the standard discriminative methods in the case of missing pixels and images containing occlusions and outliers

an introduction to motivic hall algebras abstract we give an introduction to joyce s construction of the motivic hall algebra of coherent sheaves on a variety m when m is a calabi yau threefold we define a semi classical integration map from a poisson subalgebra of this hall algebra to the ring of functions on a symplectic torus this material will be used in bridgeland 2011 3 to prove some basic properties of donaldson thomas curve counting invariants on calabi yau threefolds

the mckay correspondence as an equivalence of derived categories the classical mckay correspondence relates representations of a finite subgroup g sl 2 c to the cohomology of the well known minimal resolution of the kleinian singularity c2 g gonzalez sprinberg and verdier 10 interpreted the mckay correspondence as an isomorphism on k theory observing that the representation ring of g is equal to the g equivariant k theory of c2 more precisely they identify a basis of the k theory of the resolution consisting of the classes of certain tautological sheaves associated to the irreducible representations of g

two stage nonnegative sparse representation for large scale face recognition this paper proposes a novel nonnegative sparse representation approach called two stage sparse representation tsr for robust face recognition on a large scale database based on the divide and conquer strategy tsr decomposes the procedure of robust face recognition into outlier detection stage and recognition stage in the first stage we propose a general multisubspace framework to learn a robust metric in which noise and outliers in image pixels are detected potential loss functions including l1 l2 1 and correntropy are studied in the second stage based on the learned metric and collaborative representation we propose an efficient nonnegative sparse representation algorithm to find an approximation solution of sparse representation according to the l1 ball theory in sparse representation the approximated solution is unique and can be optimized efficiently then a filtering strategy is developed to avoid the computation of the sparse representation on the whole large scale dataset moreover theoretical analysis also gives the necessary condition for nonnegative least squares technique to find a sparse solution extensive experiments on several public databases have demonstrated that the proposed tsr approach in general achieves better classification accuracy than the state of the art sparse representation methods more importantly a significant reduction of computational costs is reached in comparison with sparse representation classifier this enables the tsr to be more suitable for robust face recognition on a large scale dataset

configurations in abelian categories iv invariants and changing stability conditions this is the last in a series on configurations in an abelian category a given a finite poset i an i configuration is a finite collection of objects j and morphisms j k or j k j k in a satisfying some axioms where j k are subsets of i configurations describe how an object x in a decomposes into subobjects the first paper defined configurations and studied moduli spaces of configurations in a using artin stacks it showed well behaved moduli stacks obja m i a of objects and configurations in a exist when a is the abelian category coh p of coherent sheaves on a projective scheme p or mod kq of representations of a quiver q the second studied algebras of constructible functions and stack functions on obja the third introduced stability conditions t on a and showed the moduli space objss of semistable objects in class is a constructible subset in obja so its characteristic function ss is a constructible function it formed algebras h pa h to h pa h to of constructible and stack functions on obja and proved many identities in them in this paper if t and t are stability conditions on a we write ss in terms of the ss and deduce the algebras h pa h to are independent of t we study invariantsiss or iss i counting semistable objects or configurations in a which satisfy additive and multiplicative identities we compute them completely when a mod kq or a coh p for p a smooth curve we also find invariants with special properties when a coh p for p a smooth surface with kp 1 nef or a calabi yau 3 fold

three dimensional flops and noncommutative rings limburgs univ ctr dept math b 3590 diepenbeek belgium van den bergh m limburgs univ ctr dept math univ campus b 3590 diepenbeek belgium vdbergh luc ac be

robust linear and support vector regression the robust huber m estimator a differentiable cost function that is quadratic for small errors and linear otherwise is modeled exactly in the original primal space of the problem by an easily solvable simple convex quadratic program for both linear and nonlinear support vector estimators previous models were significantly more complex or formulated in the dual space and most involved specialized numerical algorithms for solving the robust huber linear estimator numerical test comparisons with these algorithms indicate the computational effectiveness of the new quadratic programming model for both linear and nonlinear support vector problems results are shown on problems with as many as 20000 data points with considerably faster running times on larger problems

composite binary losses we study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function we characterise when margin losses can be proper composite losses explicitly show how to determine a symmetric loss in full from half of one of its partial losses introduce an intrinsic parametrisation of composite binary losses and give a complete characterisation of the relationship between proper losses and classification calibrated losses we also consider the question of the best surrogate binary loss we introduce a precise notion of best and show there exist situations where two convex surrogate losses are incommensurable we provide a complete explicit characterisation of the convexity of composite binary losses in terms of the link function and the weight function associated with the proper loss which make up the composite loss this characterisation suggests new ways of surrogate tuning as well as providing an explicit characterisation of when bregman divergences on the unit interval are convex in their second argument finally in an appendix we present some new algorithm independent results on the relationship between properness convexity and robustness to misclassification noise for binary losses and show that all convex proper losses are non robust to misclassification noise

adaptive weighted learning for linear regression problems via kullback leibler divergence in this paper we propose adaptive weighted learning for linear regression problems via the kullback leibler kl divergence the alternative optimization method is used to solve the proposed model meanwhile we theoretically demonstrate that the solution of the optimization algorithm converges to a stationary point of the model in addition we also fuse global linear regression and class oriented linear regression and discuss the problem of parameter selection experimental results on face and handwritten numerical character databases show that the proposed method is effective for image classification particularly for the case that the samples in the training and testing set have different characteristics

face recognition using flda with single training image per person fisher linear discriminant analysis flda has been widely used for feature extraction in face recognition however it cannot be used when each object has only one training sample because the intra class variations cannot be statistically measured in this case in this paper a novel method is proposed to solve this problem by evaluating the within class scatter matrix from the available single training image by using singular value decomposition svd we decompose the face image into two complementary parts a smooth general appearance image and a difference image the later is used to approximately evaluate the within class scatter matrix and thus the flda can be applied to extract the discriminant face features experimental results show that the proposed method is efficient and it can achieve higher recognition accuracy than many existing schemes

monge ampere equations and moduli spaces of manifolds of circular type abstract a bounded manifold of circular type is a complex manifold m of dimension n admitting a bounded exhaustive real function u defined on m minus a point x o so that a it is a smooth solution on m x o to the monge ampere equation d d c u n 0 b x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of m at x o c d d c e u 0 at any point of m x o this class of manifolds naturally includes all smoothly bounded strictly linearly convex domains and all smoothly bounded strongly pseudoconvex circular domains of c n a set of modular parameters for bounded manifolds of circular type is considered in particular for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form it is also shown that the class of normalizing maps for an n dimensional manifold m is a new holomorphic invariant with the following property it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when m is a non convex circular domain while it is of dimension n 2 2 n when m is a strictly linearly convex domain new characterizations of the circular domains and of the unit ball are also obtained

algebraic cobordism revisited we define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities the main result is the equivalence of double point cobordism to the theory of algebraic cobordism previously defined by levine and morel double point cobordism provides a simple geometric presentation of algebraic cobordism theory as a corollary the lazard ring given by products of projective spaces rationally generates all nonsingular projective varieties modulo double point degenerations

configurations in abelian categories iii stability conditions and identities this is the third in a series on configurations in an abelian category given a finite poset i an i configuration s p is a finite collection of objects s j and morphisms j k or in satisfying some axioms where j k are subsets of i configurations describe how an object x in decomposes into subobjects the first paper defined configurations and studied moduli spaces of configurations in using the theory of artin stacks it showed well behaved moduli stacks of objects and configurations in exist when is the abelian category coh p of coherent sheaves on a projective scheme p or of representations of a quiver q the second studied algebras of constructible functions and stack functions on this paper introduces weak stability conditions t t on we show the moduli spaces of t semistable indecomposable t semistable and t stable objects in class a are constructible sets in and some associated configuration moduli spaces constructible in so their characteristic functions and are constructible we prove many identities relating these constructible functions and their stack function analogues under pushforwards we introduce interesting algebras of constructible and stack functions and study their structure in the fourth paper we show are independent of t t and construct invariants of

regression analysis of locality preserving projections via sparse penalty recent studies have shown that linear subspace algorithms such as principal component analysis linear discriminant analysis and locality preserving projections have attracted tremendous attention in many fields of information processing however the projection results obtained by these algorithms are linear combination of the original features which is difficult to be interpreted psychologically and physiologically motivated by compressive sensing theory we formulate the generalized eigenvalue problem under cs framework which then allows us to apply a sparsity penalty and minimization procedure to locality preserving projections the proposed algorithm is called sparse locality preserving projections which performs locality preserving projections in the lasso regression framework that dimensionality reduction feature selection and classification are merged into one analysis the method is also extended to its regularized form to improve its generalization the proposed algorithm is a combination of locality preserving with sparse penalty additionally the algorithm can be performed in either supervised or unsupervised tasks experimental results on toy and real data sets show that our methods are effective and demonstrate much higher performance

the orbifold topological vertex abstract we develop a topological vertex formalism for computing the donaldson thomas invariants of calabi yau orbifolds the basic combinatorial object is the orbifold vertex v g a generating function for the number of 3d partitions asymptotic to 2d partitions and colored by representations of a finite abelian group g acting on c 3 in the case where g z n acting on c 3 with transverse a n 1 quotient singularities we give an explicit formula for v g in terms of schur functions we discuss applications of our formalism to the donaldson thomas crepant resolution conjecture and to the orbifold donaldson thomas gromov witten correspondence we also explicitly compute the donaldson thomas partition function for some simple orbifold geometries the local football p a b 1 and the local b z 2 gerbe

the quantum mckay correspondence for polyhedral singularities let g be a polyhedral group namely a finite subgroup of so 3 nakamura s g hilbert scheme provides a preferred calabi yau resolution y of the polyhedral singularity 3 g the classical mckay correspondence describes the classical geometry of y in terms of the representation theory of g in this paper we describe the quantum geometry of y in terms of r an ade root system associated to g namely we give an explicit formula for the gromov witten partition function of y as a product over the positive roots of r in terms of counts of bps states gopakumar vafa invariants our result can be stated as a correspondence each positive root of r corresponds to one half of a genus zero bps state as an application we use the crepant resolution conjecture to provide a full prediction for the orbifold gromov witten invariants of 3 g

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

parabolic refined invariants and macdonald polynomials a string theoretic derivation is given for the conjecture of hausel letellier and rodriguez villegas on the cohomology of character varieties with marked points their formula is identified with a refined bps expansion in the stable pair theory of a local root stack generalizing previous work of the first two authors in collaboration with pan haiman s geometric construction for macdonald polynomials is shown to emerge naturally in this context via geometric engineering in particular this yields a new conjectural relation between macdonald polynomials and refined local orbifold curve counting invariants the string theoretic approach also leads to a new spectral cover construction for parabolic higgs bundles in terms of holomorphic symplectic orbifolds

donaldson thomas type invariants via microlocal geometry we prove that donaldson thomas type invariants are equal to weighted euler characteristics of their moduli spaces in particular such invariants depend only on the scheme structure of the moduli space not the symmetric obstruction theory used to define them we also introduce new invariants generalizing donaldson thomas type invariants to moduli problems with open moduli space these are useful for computing donaldson thomas type invariants over stratifications

appearance models based on kernel canonical correlation analysis this paper introduces a new approach to constructing appearance models based on kernel canonical correlation analysis kernel cca kernel cca is a non linear extension of cca where a non linear transformation of the input data is performed implicitly using kernel methods although in this respect it is similar to other generalized linear methods kernel cca is especially well suited for relating two sets of measurements the benefits of our method compared to standard feature extraction methods based on pca will be illustrated experimentally for the task of estimating an object s pose from raw brightness images

blockwise projection matrix versus blockwise data on undersampled problems analysis comparison and applications linear subspace methods are extensively used in many areas such as pattern recognition and machine learning among them block subspace methods are efficient in terms of the computational complexity in this paper we perform a thorough analysis on block subspace methods and give a theoretical framework for understanding block subspace methods it reveals the relationship between block subspace methods and classical subspace methods we theoretically show that blockwise pca has larger reconstruction errors than classical pca and classical lda has stronger discriminant power than blockwise lda in the case of the same number of reduced features in addition based on the fisher criterion we also give a strategy for selecting an approximate block size for classification problems the comprehensive experiments on face images and gene expression data are used to evaluate our results and a comparative analysis for various methods is made experimental results demonstrate that overly combining subspaces of block subspace methods without considering the subspace distance may yield undesirable performance on undersampled problems

configurations in abelian categories i basic properties and moduli stacks abstract this is the first in a series of papers on configurations in an abelian category a given a finite partially ordered set i an i configuration is a finite collection of objects j and morphisms j k or j k j k in a satisfying some axioms where j k are subsets of i configurations describe how an object x in a decomposes into subobjects and are useful for studying stability conditions on a we define and motivate the idea of configurations and explain some natural operations upon them subconfigurations quotient configurations substitution refinements and improvements then we study moduli spaces of i configurations in a and natural morphisms between them using the theory of artin stacks we prove well behaved moduli stacks exist when a is the abelian category of coherent sheaves on a projective scheme p or of representations of a quiver q in the sequels given a stability condition t on a we will show the moduli spaces of semi stable objects or configurations are constructible subsets in the moduli stacks of all objects or configurations we associate infinite dimensional algebras of constructible functions to a quiver q using the method of ringel hall algebras and define systems of invariants of p that count semi stable coherent sheaves on p and satisfy interesting identities

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

topological orbifold models and quantum cohomology rings we discuss the topological sigma model on an orbifold target space we describe the moduli space of classical minima for computing correlation functions involving twisted operators and show through a detailed computation of an orbifold ofcp1 by the dihedral groupd4 how to compute the complete ring of observables through this procedure we compute all the rings of dihedralcp1 orbifolds we then considercp2 d4 and show how the techniques of topologicalanti topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds