on the comparisons of decorrelation approaches for non gaussian neutral vector variables as a typical non gaussian vector variable a neutral vector variable contains nonnegative elements only and its l norm equals one in addition its neutral properties make it significantly different from the commonly studied vector variables e g the gaussian vector variables due to the aforementioned properties the conventionally applied linear transformation approaches e g principal component analysis pca and independent component analysis ica are not suitable for neutral vector variables as pca cannot transform a neutral vector variable which is highly negatively correlated into a set of mutually independent scalar variables and ica cannot preserve the bounded property after transformation in recent work we proposed an efficient nonlinear transformation approach i e the parallel nonlinear transformation pnt for decorrelating neutral vector variables in this article we extensively compare pnt with pca and ica through both theoretical analysis and experimental evaluations the results of our investigations demonstrate the superiority of pnt for decorrelating the neutral vector variables

uncertainty characterization of the orthogonal procrustes problem with arbitrary covariance matrices abstract this paper addresses the weighted orthogonal procrustes problem of matching stochastically perturbed point clouds formulated as an optimization problem with a closed form solution a novel uncertainty characterization of the solution of this problem is proposed resorting to perturbation theory concepts which admits arbitrary transformations between point clouds and individual covariance and cross covariance matrices for the points of each cloud the method is thoroughly validated through extensive monte carlo simulations and particularly interesting cases where nonlinearities may arise are further analyzed

moving reproducing and dying beyond flatland malthusian flocks in dimensions d 2 we show that malthusian flocks i e coherently moving collections of self propelled entities such as living creatures which are being born and dying during their motion belong to a new universality class in spatial dimensions dg2 we calculate the universal exponents and scaling laws of this new universality class to o ensuremath epsilon in an ensuremath epsilon 4 ensuremath d expansion and find these are different from the canonical exponents previously conjectured to hold for immortal flocks i e those without birth and death and shown to hold for incompressible flocks in dg2 our expansion should be quite accurate in d 3 allowing precise quantitative comparisons between our theory simulations and experiments

structured learning of binary codes with column generation for optimizing ranking measures hashing methods aim to learn a set of hash functions which map the original features to compact binary codes with similarity preserving in the hamming space hashing has proven a valuable tool for large scale information retrieval we propose a column generation based binary code learning framework for data dependent hash function learning given a set of triplets that encode the pairwise similarity comparison information our column generation based method learns hash functions that preserve the relative comparison relations within the large margin learning framework our method iteratively learns the best hash functions during the column generation procedure existing hashing methods optimize over simple objectives such as the reconstruction error or graph laplacian related loss functions instead of the performance evaluation criteria of interest multivariate performance measures such as the auc and ndcg our column generation based method can be further generalized from the triplet loss to a general structured learning based framework that allows one to directly optimize multivariate performance measures for optimizing general ranking measures the resulting optimization problem can involve exponentially or infinitely many variables and constraints which is more challenging than standard structured output learning we use a combination of column generation and cutting plane techniques to solve the optimization problem to speed up the training we further explore stage wise training and propose to optimize a simplified ndcg loss for efficient inference we demonstrate the generality of our method by applying it to ranking prediction and image retrieval and show that it outperforms several state of the art hashing methods

a survey on learning to hash nearest neighbor search is a problem of finding the data points from the database such that the distances from them to the query point are the smallest learning to hash is one of the major solutions to this problem and has been widely studied recently in this paper we present a comprehensive survey of the learning to hash algorithms categorize them according to the manners of preserving the similarities into pairwise similarity preserving multiwise similarity preserving implicit similarity preserving as well as quantization and discuss their relations we separate quantization from pairwise similarity preserving as the objective function is very different though quantization as we show can be derived from preserving the pairwise similarities in addition we present the evaluation protocols and the general performance analysis and point out that the quantization algorithms perform superiorly in terms of search accuracy search time cost and space cost finally we introduce a few emerging topics

a fast optimization method for general binary code learning hashing or binary code learning has been recognized to accomplish efficient near neighbor search and has thus attracted broad interests in recent retrieval vision and learning studies one main challenge of learning to hash arises from the involvement of discrete variables in binary code optimization while the widely used continuous relaxation may achieve high learning efficiency the pursued codes are typically less effective due to accumulated quantization error in this paper we propose a novel binary code optimization method dubbed discrete proximal linearized minimization dplm which directly handles the discrete constraints during the learning process specifically the discrete thus nonsmooth nonconvex problem is reformulated as minimizing the sum of a smooth loss term with a nonsmooth indicator function the obtained problem is then efficiently solved by an iterative procedure with each iteration admitting an analytical discrete solution which is thus shown to converge very fast in addition the proposed method supports a large family of empirical loss functions which is particularly instantiated in this paper by both a supervised and an unsupervised hashing losses together with the bits uncorrelation and balance constraints in particular the proposed dplm with a supervised ell 2 loss encodes the whole nus wide database into 64 b binary codes within 10 s on a standard desktop computer the proposed approach is extensively evaluated on several large scale data sets and the generated binary codes are shown to achieve very promising results on both retrieval and classification tasks

quantitative assessment of the toner and tu theory of polar flocks we present a quantitative assessment of the toner and tu theory describing the universal scaling of fluctuations in polar phases of dry active matter using large scale simulations of the vicsek model in two and three dimensions we find the overall phenomenology and generic algebraic scaling predicted by toner and tu but our data on density correlations reveal some qualitative discrepancies the values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995 in particular we identify a large crossover scale beyond which flocks are only weakly anisotropic we discuss the meaning and consequences of these results

composition factors of tensor products of truncated symmetric powers let g be the general linear group of degree n over an algebraically closed field k of characteristic p 0 we study the m fold tensor product s e m of the truncated symmetric algebra s e of the symmetric algebra s e of the natural module e for g we are particularly interested in the set of partitions occurring as the highest weight of a composition factor of s e m we explain how the determination of these composition factors is related to the determination of the set of composition factors of the m fold tensor product s e m of the symmetric algebra we give a complete description of the composition factors of s e m in terms of distinguished partitions our main interest is in the classical case but since the quantised version is essentially no more difficult we express our results in the general context throughout

parametric local multiview hamming distance metric learning abstract learning an appropriate distance metric is a crucial problem in pattern recognition to confront with the scalability issue of massive data hamming distance on binary codes is advocated since it permits exact sub linear knn search and meanwhile shares the advantage of efficient storage in this paper we study hamming metric learning in the context of multimodal data for cross view similarity search we present a new method called parametric local multiview hamming metric plmh which learns multiview metric based on a set of local hash functions to locally adapt to the data structure of each modality to balance locality and computational efficiency the hash projection matrix of each instance is parameterized with guaranteed approximation error bound as a linear combination of basis hash projections associated with a small set of anchor points the weak supervisory information side information provided by pairwise and triplet constraints are incorporated in a coherent way to achieve semantically effective hash codes a local optimal conjugate gradient algorithm with orthogonal rotations is designed to learn the hash functions for each bit and the overall hash codes are learned in a sequential manner to progressively minimize the bias experimental evaluations on cross media retrieval tasks demonstrate that plmh performs competitively against the state of the art methods

adaptive hash retrieval with kernel based similarity abstract indexing methods have been widely used for fast data retrieval on large scale datasets when the data are represented by high dimensional vectors hashing is often used as an efficient solution for approximate similarity search when a retrieval task does not involve supervised training data most hashing methods aim at preserving data similarity defined by a distance metric on the feature vectors hash codes generated by these approaches normally maintain the hamming distance of the data in accordance with the similarity function but ignore the local details of the distribution of data this objective is not suitable for k nearest neighbor search since the similarity to the nearest neighbors can vary significantly for different data samples in this paper we present a novel adaptive similarity measure which is consistent with k nearest neighbor search and prove that it leads to a valid kernel if the original similarity function is a kernel function next we propose a method which calculates hash codes using the kernel function with a low rank approximation our hashing framework is more effective than existing methods that preserve similarity over an arbitrary kernel the proposed similarity function hashing framework and their combination demonstrate significant improvement when compared with several alternative state of the art methods

metabelian lie powers of the natural module for a general linear group abstract consider a free metabelian lie algebra m of finite rank r over an infinite field k of prime characteristic p given a free generating set m acquires a grading its group of graded automorphisms is the general linear group g l r k so each homogeneous component m d is a finite dimensional g l r k module the homogeneous component m 1 of degree 1 is the natural module and the other m d are the metabelian lie powers of the title this paper investigates the submodule structure of the m d in the main result a composition series is constructed in each m d and the isomorphism types of the composition factors are identified both in terms of highest weights and in terms of steinberg s twisted tensor product theorem their dimensions are also given it turns out that the composition factors are pairwise non isomorphic from which it follows that the submodule lattice is finite and distributive by the birkhoff representation theorem any such lattice is explicitly recognizable from the poset of its join irreducible elements the poset relevant for m d is then determined by exploiting a 1975 paper of yu a bakhturin on identical relations in metabelian lie algebras

toward optimal manifold hashing via discrete locally linear embedding binary code learning also known as hashing has received increasing attention in large scale visual search by transforming high dimensional features to binary codes the original euclidean distance is approximated via hamming distance more recently it is advocated that it is the manifold distance rather than the euclidean distance that should be preserved in the hamming space however it retains as an open problem to directly preserve the manifold structure by hashing in particular it first needs to build the local linear embedding in the original feature space and then quantize such embedding to binary codes such a two step coding is problematic and less optimized besides the off line learning is extremely time and memory consuming which needs to calculate the similarity matrix of the original data in this paper we propose a novel hashing algorithm termed discrete locality linear embedding hashing dllh which well addresses the above challenges the dllh directly reconstructs the manifold structure in the hamming space which learns optimal hash codes to maintain the local linear relationship of data points to learn discrete locally linear embedding codes we further propose a discrete optimization algorithm with an iterative parameters updating scheme moreover an anchor based acceleration scheme termed anchor dllh is further introduced which approximates the large similarity matrix by the product of two low rank matrices experimental results on three widely used benchmark data sets i e cifar10 nus wide and youtube face have shown superior performance of the proposed dllh over the state of the art approaches

robust quantization for general similarity search the recent years have witnessed the emerging of vector quantization vq techniques for efficient similarity search vq partitions the feature space into a set of codewords and encodes data points as integer indices using the codewords then the distance between data points can be efficiently approximated by simple memory lookup operations by the compact quantization the storage cost and searching complexity are significantly reduced thereby facilitating efficient large scale similarity search however the performance of several celebrated vq approaches degrades significantly when dealing with noisy data in addition it can barely facilitate a wide range of applications as the distortion measurement only limits to ell 2 norm to address the shortcomings of the squared euclidean ell 2 2 norm loss function employed by the vq approaches in this paper we propose a novel robust and general vq framework named rgvq to enhance both robustness and generalization of vq approaches specifically a ell p q norm loss function is proposed to conduct the ell p norm similarity search rather than the ell 2 norm search and the q th order loss is used to enhance the robustness despite the fact that changing the loss function to ell p q norm makes vq approaches more robust and generic it brings us a challenge that a non smooth and non convex orthogonality constrained ell p q norm function has to be minimized to solve this problem we propose a novel and efficient optimization scheme and specify it to vq approaches and theoretically prove its convergence extensive experiments on benchmark data sets demonstrate that the proposed rgvq is better than the original vq for several approaches especially when searching similarity in noisy data

scalable similarity search with topology preserving hashing hashing based similarity search techniques is becoming increasingly popular in large data sets to capture meaningful neighbors the topology of a data set which represents the neighborhood relationships between its subregions and the relative proximities between the neighbors of each subregion e g the relative neighborhood ranking of each subregion should be exploited however most existing hashing methods are developed to preserve neighborhood relationships while ignoring the relative neighborhood proximities moreover most hashing methods lack in providing a good result ranking since there are often lots of results sharing the same hamming distance to a query in this paper we propose a novel hashing method to solve these two issues jointly the proposed method is referred to as topology preserving hashing tph tph is distinct from prior works by also preserving the neighborhood ranking based on this framework we present three different tph methods including linear unsupervised tph semisupervised tph and kernelized tph particularly our unsupervised tph is capable of mining semantic relationship between unlabeled data without supervised information extensive experiments on four large data sets demonstrate the superior performances of the proposed methods over several state of the art unsupervised and semisupervised hashing techniques

learning to hash with optimized anchor embedding for scalable retrieval sparse representation and image hashing are powerful tools for data representation and image retrieval respectively the combinations of these two tools for scalable image retrieval i e sparse hashing sh methods have been proposed in recent years and the preliminary results are promising the core of those methods is a scheme that can efficiently embed the high dimensional image features into a low dimensional hamming space while preserving the similarity between features existing sh methods mostly focus on finding better sparse representations of images in the hash space we argue that the anchor set utilized in sparse representation is also crucial which was unfortunately underestimated by the prior art to this end we propose a novel sh method that optimizes the integration of the anchors such that the features can be better embedded and binarized termed as sparse hashing with optimized anchor embedding the central idea is to push the anchors far from the axis while preserving their relative positions so as to generate similar hashcodes for neighboring features we formulate this idea as an orthogonality constrained maximization problem and an efficient and novel optimization framework is systematically exploited extensive experiments on five benchmark image data sets demonstrate that our method outperforms several state of the art related methods

learning discriminative binary codes for large scale cross modal retrieval hashing based methods have attracted considerable attention for efficient cross modal retrieval on large scale multimedia data the core problem of cross modal hashing is how to learn compact binary codes that construct the underlying correlations between heterogeneous features from different modalities a majority of recent approaches aim at learning hash functions to preserve the pairwise similarities defined by given class labels however these methods fail to explicitly explore the discriminative property of class labels during hash function learning in addition they usually discard the discrete constraints imposed on the to be learned binary codes and compromise to solve a relaxed problem with quantization to obtain the approximate binary solution therefore the binary codes generated by these methods are suboptimal and less discriminative to different classes to overcome these drawbacks we propose a novel cross modal hashing method termed discrete cross modal hashing dch which directly learns discriminative binary codes while retaining the discrete constraints specifically dch learns modality specific hash functions for generating unified binary codes and these binary codes are viewed as representative features for discriminative classification with class labels an effective discrete optimization algorithm is developed for dch to jointly learn the modality specific hash function and the unified binary codes extensive experiments on three benchmark data sets highlight the superiority of dch under various cross modal scenarios and show its state of the art performance

data dependent hashing based on p stable distribution the p stable distribution is traditionally used for data independent hashing in this paper we describe how to perform data dependent hashing based on p stable distribution we commence by formulating the euclidean distance preserving property in terms of variance estimation based on this property we develop a projection method which maps the original data to arbitrary dimensional vectors each projection vector is a linear combination of multiple random vectors subject to p stable distribution in which the weights for the linear combination are learned based on the training data an orthogonal matrix is then learned data dependently for minimizing the thresholding error in quantization combining the projection method and orthogonal matrix we develop an unsupervised hashing scheme which preserves the euclidean distance compared with data independent hashing methods our method takes the data distribution into consideration and gives more accurate hashing results with compact hash codes different from many data dependent hashing methods our method accommodates multiple hash tables and is not restricted by the number of hash functions to extend our method to a supervised scenario we incorporate a supervised label propagation scheme into the proposed projection method this results in a supervised hashing scheme which preserves semantic similarity of data experimental results show that our methods have outperformed several state of the art hashing approaches in both effectiveness and efficiency

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

iterative quantization a procrustean approach to learning binary codes for large scale image retrieval this paper addresses the problem of learning similarity preserving binary codes for efficient similarity search in large scale image collections we formulate this problem in terms of finding a rotation of zero centered data so as to minimize the quantization error of mapping this data to the vertices of a zero centered binary hypercube and propose a simple and efficient alternating minimization algorithm to accomplish this task this algorithm dubbed iterative quantization itq has connections to multiclass spectral clustering and to the orthogonal procrustes problem and it can be used both with unsupervised data embeddings such as pca and supervised embeddings such as canonical correlation analysis cca the resulting binary codes significantly outperform several other state of the art methods we also show that further performance improvements can result from transforming the data with a nonlinear kernel mapping prior to pca or cca finally we demonstrate an application of itq to learning binary attributes or classemes on the imagenet 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

flocks herds and schools a quantitative theory of flocking we present a quantitative continuum theory of flocking the collective coherent motion of large numbers of self propelled organisms in agreement with everyday experience our model predicts the existence of an ordered phase of flocks in which all members of even an arbitrarily large flock move together with the same mean velocity stackrel ensuremath rightarrow v ensuremath ne 0 this coherent motion of the flock is an example of spontaneously broken symmetry no preferred direction for the motion is picked out a priori in the model rather each flock is allowed to and does spontaneously pick out some completely arbitrary direction to move in by analyzing our model we can make detailed quantitative predictions for the long distance long time behavior of this broken symmetry state the goldstone modes associated with this spontaneously broken rotational symmetry are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole these goldstone modes mix with modes associated with conservation of bird number to produce propagating sound modes these sound modes lead to enormous fluctuations of the density of the flock far larger at long wavelengths than those in e g an equilibrium gas our model is similar in many ways to the navier stokes equations for a simple compressible fluid in other ways it resembles a relaxational time dependent ginsburg landau theory for an n d component isotropic ferromagnet in spatial dimensions dg4 the long distance behavior is correctly described by a linearized theory and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems for dl4 nonlinear fluctuation effects radically alter the long distance behavior making it different from that of any known equilibrium model in particular we find that in d 2 where we can calculate the scaling exponents exactly flocks exhibit a true long range ordered spontaneously broken symmetry state in contrast to equilibrium systems which cannot spontaneously break a continuous symmetry in d 2 the mermin wagner theorem we make detailed predictions for various correlation functions that could be measured either in simulations or by quantitative imaging of real flocks we also consider an anisotropic model in which the birds move preferentially in an easy e g horizontal plane and make analogous but quantitatively different predictions for that model as well for this anisotropic model we obtain exact scaling exponents for all spatial dimensions including the physically relevant case d 3

product quantization for nearest neighbor search this paper introduces a product quantization based approach for approximate nearest neighbor search the idea is to decompose the space into a cartesian product of low dimensional subspaces and to quantize each subspace separately a vector is represented by a short code composed of its subspace quantization indices the euclidean distance between two vectors can be efficiently estimated from their codes an asymmetric version increases precision as it computes the approximate distance between a vector and a code experimental results show that our approach searches for nearest neighbors efficiently in particular in combination with an inverted file system results for sift and gist image descriptors show excellent search accuracy outperforming three state of the art approaches the scalability of our approach is validated on a data set of two billion vectors

latent structure preserving hashing aiming at efficient similarity search hash functions are designed to embed high dimensional feature descriptors to low dimensional binary codes such that similar descriptors will lead to binary codes with a short distance in the hamming space it is critical to effectively maintain the intrinsic structure and preserve the original information of data in a hashing algorithm in this paper we propose a novel hashing algorithm called latent structure preserving hashing lsph with the target of finding a well structured low dimensional data representation from the original high dimensional data through a novel objective function based on nonnegative matrix factorization nmf with their corresponding kullback leibler divergence of data distribution as the regularization term via exploiting the joint probabilistic distribution of data lsph can automatically learn the latent information and successfully preserve the structure of high dimensional data to further achieve robust performance with complex and nonlinear data in this paper we also contribute a more generalized multi layer lsph ml lsph framework in which hierarchical representations can be effectively learned by a multiplicative up propagation algorithm once obtaining the latent representations the hash functions can be easily acquired through multi variable logistic regression experimental results on three large scale retrieval datasets i e sift 1m gist 1m and 500 k tinyimage show that ml lsph can achieve better performance than the single layer lsph and both of them outperform existing hashing techniques on large scale data

full space local topology extraction for cross modal retrieval with the ever increasing availability of various kinds of multimedia data cross modal retrieval which enables information retrieval from various types of data given various types of query has become a research hotspot hashing based techniques have been developed to solve this problem however most previous works cannot capture the shared underlying structure of real world multimodal data which degrades their retrieval performances in this paper we propose a novel hashing method based on the extraction of the common manifold structure shared among different feature spaces to faithfully represent the common structure two kinds of local topology information are exploited in our method local angles are incorporated within the extraction of local topology of each feature space which is then used to learn a common intermediate subspace after heterogeneous features being embedded into this subspace local similarities are exploited to extract the local topology between different feature spaces and learn compact hamming embeddings to facilitate cross modal retrieval the proposed method is referred to as full space local topology extraction for hashing extensive comparisons with other state of the art methods on three benchmark multimedia data sets demonstrate the superiority of our proposed method in terms of retrieval recall and search accuracy

a sparse embedding and least variance encoding approach to hashing hashing is becoming increasingly important in large scale image retrieval for fast approximate similarity search and efficient data storage many popular hashing methods aim to preserve the knn graph of high dimensional data points in the low dimensional manifold space which is however difficult to achieve when the number of samples is big in this paper we propose an effective and efficient hashing approach by sparsely embedding a sample in the training sample space and encoding the sparse embedding vector over a learned dictionary to this end we partition the sample space into clusters via a linear spectral clustering method and then represent each sample as a sparse vector of normalized probabilities that it falls into its several closest clusters this actually embeds each sample sparsely in the sample space the sparse embedding vector is employed as the feature of each sample for hashing we then propose a least variance encoding model which learns a dictionary to encode the sparse embedding feature and consequently binarize the coding coefficients as the hash codes the dictionary and the binarization threshold are jointly optimized in our model experimental results on benchmark data sets demonstrated the effectiveness of the proposed approach in comparison with state of the art methods

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

neighborhood discriminant hashing for large scale image retrieval with the proliferation of large scale community contributed images hashing based approximate nearest neighbor search in huge databases has aroused considerable interest from the fields of computer vision and multimedia in recent years because of its computational and memory efficiency in this paper we propose a novel hashing method named neighborhood discriminant hashing ndh for short to implement approximate similarity search different from the previous work we propose to learn a discriminant hashing function by exploiting local discriminative information i e the labels of a sample can be inherited from the neighbor samples it selects the hashing function is expected to be orthogonal to avoid redundancy in the learned hashing bits as much as possible while an information theoretic regularization is jointly exploited using maximum entropy principle as a consequence the learned hashing function is compact and nonredundant among bits while each bit is highly informative extensive experiments are carried out on four publicly available data sets and the comparison results demonstrate the outperforming performance of the proposed ndh method over state of the art hashing techniques

ldahash improved matching with smaller descriptors sift like local feature descriptors are ubiquitously employed in computer vision applications such as content based retrieval video analysis copy detection object recognition photo tourism and 3d reconstruction feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations in particular affine and intensity scale transformations however real transformations that an image can undergo can only be approximately modeled in this way and thus most descriptors are only approximately invariant in practice second descriptors are usually high dimensional e g sift is represented as a 128 dimensional vector in large scale retrieval and matching problems this can pose challenges in storing and retrieving descriptor data we map the descriptor vectors into the hamming space in which the hamming metric is used to compare the resulting representations this way we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples we show extensive experimental validation demonstrating the advantage of the proposed approach

a note on the adjoint action of a semisimple group on the coordinate algebra of an infinitesimal subgroup abstract let g be a connected semisimple simply connected algebraic group over an algebraically closed field k of positive characteristic the action of g on itself by conjugation induces on the coordinate algebra k g and hence on the coordinate algebra k g r of the infinitesimal subgroup g r the structure of a rational g module in the recent paper 3 by bendel nakano pillen and sobaje the authors ask whether the tensor product of k g r with the rth steinberg module st r has a good filtration here we show that this is the case provided that the characteristic of k is good for g we do so by relating k g r to a certain quotient of the coordinate algebra k g of the lie algebra g of g and using a koszul resolution we note that the argument may also be applied to certain polynomial modules occurring in the context of doty s conjecture 17 4 2 11

hashing on nonlinear manifolds learning based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate most of these methods are designed to generate binary codes preserving the euclidean similarity in the original space manifold learning techniques in contrast are better able to model the intrinsic structure embedded in the original high dimensional data the complexities of these models and the problems with out of sample data have previously rendered them unsuitable for application to large scale embedding however in this paper how to learn compact binary embeddings on their intrinsic manifolds is considered in order to address the above mentioned difficulties an efficient inductive solution to the out of sample data problem and a process by which nonparametric manifold learning may be used as the basis of a hashing method are proposed the proposed approach thus allows the development of a range of new hashing techniques exploiting the flexibility of the wide variety of manifold learning approaches available it is particularly shown that hashing on the basis of t distributed stochastic neighbor embedding outperforms state of the art hashing methods on large scale benchmark data sets and is very effective for image classification with very short code lengths it is shown that the proposed framework can be further improved for example by minimizing the quantization error with learned orthogonal rotations without much computation overhead in addition a supervised inductive manifold hashing framework is developed by incorporating the label information which is shown to greatly advance the semantic retrieval performance