multiple kernel learning for dimensionality reduction in solving complex visual learning tasks adopting multiple descriptors to more precisely characterize the data has been a feasible way for improving performance the resulting data representations are typically high dimensional and assume diverse forms hence finding a way of transforming them into a unified space of lower dimension generally facilitates the underlying tasks such as object recognition or clustering to this end the proposed approach termed mkl dr generalizes the framework of multiple kernel learning for dimensionality reduction and distinguishes itself with the following three main contributions first our method provides the convenience of using diverse image descriptors to describe useful characteristics of various aspects about the underlying data second it extends a broad set of existing dimensionality reduction techniques to consider multiple kernel learning and consequently improves their effectiveness third by focusing on the techniques pertaining to dimensionality reduction the formulation introduces a new class of applications with the multiple kernel learning framework to address not only the supervised learning problems but also the unsupervised and semi supervised ones

hubert l arabie p meulman j 2006 the structural representation of proximity matrices with matlab philadelphia siam xvi 214 pp us 79 00 isbn 0898716071

the approximation of two mode proximity matrices by sums of order constrained matrices a least squares strategy is proposed for representing a two mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries the primary class of constraints considered define q forms or anti q forms for a two mode matrix where after suitable and separate row and column reorderings the entries within each row and within each column are nondecreasing or nonincreasing to a maximum or minimum and thereafter nonincreasing or nondecreasing several other types of order constraints are also mentioned to show how alternative structures can be considered using the same computational strategy

information based objective functions for active data selection learning can be made more efficient if we can actively select particularly salient data points within a bayesian learning framework objective functions are discussed that measure the expected informativeness of candidate measurements three alternative specifications of what we want to gain information about lead to three different criteria for data selection all these criteria depend on the assumption that the hypothesis space is correct which may prove to be their main weakness

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

one class classification with gaussian processes detecting instances of unknown categories is an important task for a multitude of problems such as object recognition event detection and defect localization this article investigates the use of gaussian process gp priors for this area of research focusing on the task of one class classification we analyze different measures derived from gp regression and approximate gp classification we also study important theoretical connections to other approaches and discuss their underlying assumptions experiments are performed using a large number of datasets and different image kernel functions our findings show that our approaches can outperform the well known support vector data description approach indicating the high potential of gaussian processes for one class classification furthermore we show the suitability of our methods in the area of attribute prediction defect localization bacteria recognition and background subtraction these applications and experiments highlight the easy applicability of our method as well as its state of the art performance compared to established methods

a three dimensional ball quotient in this paper we determine a very particular example of a picard modular variety of general type on its non singular models there exist many holomorphic differential forms in a forthcoming paper we will show that one can construct calabi yau manifolds by considering quotients of this variety and resolving singularities

partial eigenvalue decomposition for large image sets using run length encoding abstract pattern recognition using eigenvectors is a recent active research area finding eigenvectors of a large image set however has been considered to require too much computation to be practical we therefore propose a new method for reducing computation of the partial eigenvalue decomposition based on run length encoding in this method called the constant regions method spatial encoding is used to reduce storage and computation then coeigenvectors are computed and later converted to eigenvectors for simple images and when the number of pixels in an image is much larger than the number of images the resulting algorithm is shown to grow as the first power of the basic image dimension rather than the fourth power as for conventional methods for comparison the power method the conjugate gradient method and a so called direct method for computing the partial eigenvalue decomposition are also presented and recommendations are given for when each method should be used the advantage of the proposed method are verified by tests in which the first several eigenvectors are computed for sets of images having varying complexity this algorithm is useful for a research area of pattern recognition using eigenvectors

fast matching of large point sets under occlusions the problem of isometric point pattern matching can be modeled as inference in small tree width graphical models whose embeddings in the plane are said to be globally rigid although such graphical models lead to efficient and exact solutions they cannot generally handle occlusions as even a single missing point may break the rigidity of the graph in question in addition such models can efficiently handle point sets of only moderate size in this paper we propose a new graphical model that is not only adapted to handle occlusions but is much faster than previous approaches for solving the isometric point pattern matching problem we can match point patterns with thousands of points in a few seconds

an eigendecomposition approach to weighted graph matching problems an approximate solution to the weighted graph matching problem is discussed for both undirected and directed graphs the weighted graph matching problem is that of finding the optimum matching between two weighted graphs which are graphs with weights at each arc the proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem using the eigendecompositions of the adjacency matrices in the case of the undirected graph matching problem or hermitian matrices derived from the adjacency matrices in the case of the directed graph matching problem a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other simulation results are given to evaluate the performance of the proposed method

the kodaira dimension of the moduli of k3 surfaces the global torelli theorem for projective k3 surfaces was first proved by piatetskii shapiro and shafarevich 35 years ago opening the way to treating moduli problems for k3 surfaces the moduli space of polarised k3 surfaces of degree 2d is a quasi projective variety of dimension 19 for general d very little has been known hitherto about the kodaira dimension of these varieties in this paper we present an almost complete solution to this problem our main result says that this moduli space is of general type for d 61 and for d 46 50 54 57 58 60

quadratic nonnegative matrix factorization in nonnegative matrix factorization nmf a nonnegative matrix is approximated by a product of lower rank factorizing matrices most nmf methods assume that each factorizing matrix appears only once in the approximation thus the approximation is linear in the factorizing matrices we present a new class of approximative nmf methods called quadratic nonnegative matrix factorization qnmf where some factorizing matrices occur twice in the approximation we demonstrate qnmf solutions to four potential pattern recognition problems in graph partitioning two way clustering estimating hidden markov chains and graph matching we derive multiplicative algorithms that monotonically decrease the approximation error under a variety of measures we also present extensions in which one of the factorizing matrices is constrained to be orthogonal or stochastic empirical studies show that for certain application scenarios qnmf is more advantageous than other existing nonnegative matrix factorization methods

local distance functions a taxonomy new algorithms and an evaluation we present a taxonomy for local distance functions where most existing algorithms can be regarded as approximations of the geodesic distance defined by a metric tensor we categorize existing algorithms by how where and when they estimate the metric tensor we also extend the taxonomy along each axis how we introduce hybrid algorithms that use a combination of techniques to ameliorate overfitting where we present an exact polynomial time algorithm to integrate the metric tensor along the lines between the test and training points under the assumption that the metric tensor is piecewise constant when we propose an interpolation algorithm where the metric tensor is sampled at a number of references points during the offline phase the reference points are then interpolated during the online classification phase we also present a comprehensive evaluation on tasks in face recognition object recognition and digit recognition

an interactive approach to solving correspondence problems finding correspondences among objects in different images is a critical problem in computer vision even good correspondence procedures can fail however when faced with deformations occlusions and differences in lighting and zoom levels across images we present a methodology for augmenting correspondence matching algorithms with a means for triaging the focus of attention and effort in assisting the automated matching for guiding the mix of human and automated initiatives we introduce a measure of the expected value of resolving correspondence uncertainties we explore the value of the approach with experiments on benchmark data

graph theoretic representations for proximity matrices through strongly anti robinson or circular strongly anti robinson matrices there are various optimization strategies for approximating through the minimization of a least squares loss function a given symmetric proximity matrix by a sum of matrices each subject to some collection of order constraints on its entries we extend these approaches to include components in the approximating sum that satisfy what are called the strongly anti robinson sar or circular strongly anti robinson csar restrictions a matrix that is sar or csar is representable by a particular graph theoretic structure where each matrix entry is reproducible from certain minimum path lengths in the graph one published proximity matrix is used extensively to illustrate the types of approximation that ensue when the sar or csar constraints are imposed

graph rigidity cyclic belief propagation and point pattern matching a recent paper caetano et al 2006 proposed a provably optimal polynomial time method for performing near isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model its fundamental result is that the chordal graph in question is shown to be globally rigid implying that exact inference provides the same matching solution as exact inference in a complete graphical model this implies that the algorithm is optimal when there is no noise in the point patterns in this paper we present a new graph which is also globally rigid but has an advantage over the graph its maximal clique size is smaller rendering inference significantly more efficient however this graph is not chordal and thus standard junction tree algorithms cannot be directly applied nevertheless we show that loopy belief propagation in such a graph converges to the optimal solution this allows us to retain the optimality guarantee in the noiseless case while substantially reducing both memory requirements and processing time our experimental results show that the accuracy of the proposed solution is indistinguishable when there is noise in the point patterns

approximate geometric pattern matching under rigid motions we present techniques for matching point sets in two and three dimensions under rigid body transformations we prove bounds on the worst case performance of these algorithms to be within a small constant factor of optimal and conduct experiments to show that the average performance of these matching algorithms is often better than that predicted by the worst case bounds

gaussian processes for object categorization discriminative methods for visual object category recognition are typically non probabilistic predicting class labels but not directly providing an estimate of uncertainty gaussian processes gps provide a framework for deriving regression techniques with explicit uncertainty models we show here how gaussian processes with covariance functions defined based on a pyramid match kernel pmk can be used for probabilistic object category recognition our probabilistic formulation provides a principled way to learn hyperparameters which we utilize to learn an optimal combination of multiple covariance functions it also offers confidence estimates at test points and naturally allows for an active learning paradigm in which points are optimally selected for interactive labeling we show that with an appropriate combination of kernels a significant boost in classification performance is possible further our experiments indicate the utility of active learning with probabilistic predictive models especially when the amount of training data labels that may be sought for a category is ultimately very small

near optimal sensor placements in gaussian processes theory efficient algorithms and empirical studies when monitoring spatial phenomena which can often be modeled as gaussian processes gps choosing sensor locations is a fundamental task there are several common strategies to address this task for example geometry or disk models placing sensors at the points of highest entropy variance in the gp model and a d or e optimal design in this paper we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected we prove that the problem of finding the configuration that maximizes mutual information is np complete to address this issue we describe a polynomial time approximation that is within 1 1 e of the optimum by exploiting the submodularity of mutual information we also show how submodularity can be used to obtain online bounds and design branch and bound search procedures we then extend our algorithm to exploit lazy evaluations and local structure in the gp yielding significant speedups we also extend our approach to find placements which are robust against node failures and uncertainties in the model these extensions are again associated with rigorous theoretical approximation guarantees exploiting the submodularity of the objective function we demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real world data sets

vector valued modular forms on a three dimensional ball recently there came up growing interest in structure theorems for vector valued modular forms one reason may be harder s conjecture bg conjecture 3 in van der geer s talk different methods have been developed to get structure theorems for modules of vector valued modular forms ao cg do ib sa sat wi at the beginning the case of siegel modular forms has been studied but meanwhile also other groups have found interest for example in the paper cg clery and van der geer determined generators for some modules of vector valued picard modular forms on the two dimensional ball in this paper we consider the case of a three dimensional ball with the action of the picard modular group 3 3 see sect 3 the corresponding modular variety of dimension 3 is a copy of the segre cubic we obtain similar results as in cg but with completely different methods

an algorithm for restricted least squares regression abstract a commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints here a simple iterative algorithm is presented and shown to converge to the desired solution several examples are presented including finding the closest concave convex function to a set of points and other general quadratic programming problems the dual problem to the basic problem is also discussed and a solution for it is given in terms of the algorithm finally extensions to expressions other than least squares are given

image categorization graph edit distance edge direction histogram this paper presents a novel algorithm for computing graph edit distance ged in image categorization this algorithm is purely structural i e it needs only connectivity structure of the graph and does not draw on node or edge attributes there are two major contributions 1 introducing edge direction histogram edh to characterize shape features of images it is shown that ged can be employed as distance of edhs this algorithm is completely independent on cost function which is difficult to be defined exactly 2 computing distance of edhs with earth mover distance emd which takes neighborhood bins into account so as to compute distance of edhs correctly a set of experiments demonstrate that the newly presented algorithm is available for classifying and clustering images and is immune to the planar rotation of images compared with ged from spectral seriation our algorithm can capture the structure change of graphs better and consume 12 79 time used by the former one the average classification rate is 5 and average clustering rate is 25 higher than the spectral seriation method

large scale gaussian process inference with generalized histogram intersection kernels for visual recognition tasks we present new methods for fast gaussian process gp inference in large scale scenarios including exact multi class classification with label regression hyperparameter optimization and uncertainty prediction in contrast to previous approaches we use a full gaussian process model without sparse approximation techniques our methods are based on exploiting generalized histogram intersection kernels and their fast kernel multiplications we empirically validate the suitability of our techniques in a wide range of scenarios with tens of thousands of examples whereas plain gp models are intractable due to both memory consumption and computation time in these settings our results show that exact inference can indeed be done efficiently in consequence we enable every important piece of the gaussian process framework learning inference hyperparameter optimization variance estimation and online learning to be used in realistic scenarios with more than a handful of data

bayesian classification with gaussian processes we consider the problem of assigning an input vector to one of m classes by predicting p c x for c 1 m for a two class problem the probability of class one given x is estimated by spl sigma y x where spl sigma y 1 1 e sup y a gaussian process prior is placed on y x and is combined with the training data to obtain predictions for new x points we provide a bayesian treatment integrating over uncertainty in y and in the parameters that control the gaussian process prior the necessary integration over y is carried out using laplace s approximation the method is generalized to multiclass problems m 2 using the softmax function we demonstrate the effectiveness of the method on a number of datasets

efficient hyperkernel learning using second order cone programming the kernel function plays a central role in kernel methods most existing methods can only adapt the kernel parameters or the kernel matrix based on empirical data recently ong et al introduced the method of hyperkernels which can be used to learn the kernel function directly in an inductive setting however the associated optimization problem is a semidefinite program sdp which is very computationally expensive even with the recent advances in interior point methods in this paper we show that this learning problem can be equivalently reformulated as a second order cone program socp which can then be solved more efficiently than sdps comparison is also made with the kernel matrix learning method proposed by lanckriet et al experimental results on both classification and regression problems with toy and real world data sets show that our proposed socp formulation has significant speedup over the original sdp formulation moreover it yields better generalization than lanckriet et al s method with a speed that is comparable or sometimes even faster than their quadratically constrained quadratic program qcqp formulation