pairwise sparsity preserving embedding for unsupervised subspace learning and classification two novel unsupervised dimensionality reduction techniques termed sparse distance preserving embedding sdpe and sparse proximity preserving embedding sppe are proposed for feature extraction and classification sdpe and sppe perform in the clean data space recovered by sparse representation and enhanced euclidean distances over noise removed data are employed to measure pairwise similarities of points in extracting informative features sdpe and sppe aim at preserving pairwise similarities between data points in addition to preserving the sparse characteristics this paper calculates the sparsest representation of all vectors jointly by a convex optimization the sparsest codes enable certain local information of data to be preserved and can endow sdpe and sppe a natural discriminating power adaptive neighborhood and robust characteristic against noise and errors in delivering low dimensional embeddings we also mathematically show sdpe and sppe can be effectively extended for discriminant learning in a supervised manner the validity of sdpe and sppe is examined by extensive simulations comparison with other related state of the art unsupervised algorithms show that promising results are delivered by our techniques

on a model of nonlocal continuum mechanics part i existence and regularity in this work we assume that the total stored energy functional for a body b depends not only on the local strain field but also on the spatial average of the strain field over the body weighted with an influence kernel we investigate the problem of minimizing the total stored energy subject to a given bulk displacement delta geq 0 after the general setup for this problem is reviewed we give sufficient conditions for an energy minimizing strain field e cdot to satisfy an integro differential euler lagrange equation the result is general and applies to material energies that display a wide variety of singular behavior through analysis of this euler lagrange equation for a special class of influence kernels we arrive at a regularity theorem which ensures that energy minimizing strain fields must be periodic piecewise smooth and possess a finite number of simple discontinuities we then combine this with a well known existence result for relaxed minimization problems to arrive at a genera

label propagation and higher order constraint based segmentation of fluid associated regions in retinal sd oct images the segmentation of the fluid associated region in the retina plays an important role in the treatment of retinal diseases such as diabetic retinopathy dr and age related macular degeneration amd the existing methods for the detection of the fluid region generally suffer from the limitation of the segmentation accuracy and the expensive time costs to overcome these problems in this paper we propose an interactive segmentation method for the fluid associated region in three dimensional 3 d spectral domain optical coherence tomography sd oct retinal imaging in which only a few seeds in one sd oct slice are needed after which the algorithm finishes the segmentation automatically to improve the segmentation accuracy the higher order constraint is introduced into the conventional markov random field mrf framework to impose the superpixel consistency to maintain temporal coherence of the 3 d sd oct slices the labeling information is propagated slice by slice via a proposed motion estimation based algorithm the proposed higher order based energy function can be efficiently solved by the max flow algorithm on a specified graph with several auxiliary nodes experiments on 28 sd oct cubes demonstrate the competitiveness of the proposed method compared with the state of the art methods

active reranking for web image search image search reranking methods usually fail to capture the user s intention when the query term is ambiguous therefore reranking with user interactions or active reranking is highly demanded to effectively improve the search performance the essential problem in active reranking is how to target the user s intention to complete this goal this paper presents a structural information based sample selection strategy to reduce the user s labeling efforts furthermore to localize the user s intention in the visual feature space a novel local global discriminative dimension reduction algorithm is proposed in this algorithm a submanifold is learned by transferring the local geometry and the discriminative information from the labelled images to the whole global image database experiments on both synthetic datasets and a real web image search dataset demonstrate the effectiveness of the proposed active reranking scheme including both the structural information based active sample selection strategy and the local global discriminative dimension reduction algorithm

semi supervised lpp algorithms for learning to rank based visual search reranking two feature dimensionality reduction methods for search reranking are proposed the sslpp algorithm improves lpp by incorporating the relevance degree information the proposed pcc sslpp algorithm models the correlation information into sslpp the proposed methods achieve better ndcg performance recent years have witnessed the success of learning to rank technique in visual search reranking generally dimensionality reduction is one of the important stages in this kind of method to deal with the high dimensional visual features however these methods are typically designed for classification and retrieval applications rather than ranking direct utilization of them cannot guarantee the best performance in ranking applications as ranking information e g relevance degree label is absent to solve this problem a semi supervised lpp algorithm called sslpp is proposed the method incorporates the relevance degree information into a manifold dimensionality reduction method i e locality preserving projections lpp to accurately preserve the correlation information between two images in the low intrinsic dimensional space a pearson correlation coefficient pcc based sslpp algorithm called pcc sslpp is further developed the pcc sslpp method models the correlation information between two images in the graph construction step of sslpp besides a novel visual search reranking scheme is also presented based on the proposed sslpp pcc sslpp and learning to rank experiments on two popular real world image reranking datasets demonstrate the effectiveness of the proposed scheme and algorithms in visual search reranking

spatiotemporal saliency detection for video sequences based on random walk with restart a novel saliency detection algorithm for video sequences based on the random walk with restart rwr is proposed in this paper we adopt rwr to detect spatially and temporally salient regions more specifically we first find a temporal saliency distribution using the features of motion distinctiveness temporal consistency and abrupt change among them the motion distinctiveness is derived by comparing the motion profiles of image patches then we employ the temporal saliency distribution as a restarting distribution of the random walker in addition we design the transition probability matrix for the walker using the spatial features of intensity color and compactness finally we estimate the spatiotemporal saliency distribution by finding the steady state distribution of the walker the proposed algorithm detects foreground salient objects faithfully while suppressing cluttered backgrounds effectively by incorporating the spatial transition matrix and the temporal restarting distribution systematically experimental results on various video sequences demonstrate that the proposed algorithm outperforms conventional saliency detection algorithms qualitatively and quantitatively

on the gibbsian thermostatics of mixtures in 1970 noll n developed a modern version of the elements of gibbsian thermostatics for describing the equilibrium of mixtures an important aspect of noll s work is that he considered the old fundamental basis of thermostatics within a modern variational setting and with mild hypotheses gave proofs to some central theorems in the subject noll considered the stable states of a mixture to be those that maximize an entropy functional over a certain convex set of measures and for the analysis of this variational problem he employed an elegant albeit not standard mathematical theory while his work could be considered a precursor to much of the present day studies on coexistent phases in continuum thermomechanics nevertheless it has remained relatively and undeservedly obscure perhaps because of its unusual mathematical setting

image clustering based on sparse patch alignment framework image clustering methods are efficient tools for applications such as content based image retrieval and image annotation recently graph based manifold learning methods have shown promising performance in extracting features for image clustering typical manifold learning methods adopt appropriate neighborhood size to construct the neighborhood graph which captures local geometry of data distribution because the density of data points distribution may be different in different regions of the manifold a fixed neighborhood size may be inappropriate in building the manifold in this paper we propose a novel algorithm named sparse patch alignment framework for the embedding of data lying in multiple manifolds specifically we assume that for each data point there exists a small neighborhood in which only the points that come from the same manifold lie approximately in a low dimensional affine subspace based on the patch alignment framework we propose an optimization strategy for constructing local patches which adopt sparse representation to select a few neighbors of each data point that span a low dimensional affine subspace passing near that point after that the whole alignment strategy is utilized to build the manifold experiments are conducted on four real world datasets and the results demonstrate the effectiveness of the proposed method

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

action recognition based on overcomplete independent components analysis existing works on action recognition rely on two separate stages 1 designing hand designed features or learning features from video data 2 classifying features using a classifier such as svm or adaboost motivated by two observations 1 independent component analysis ica is capable of encoding intrinsic features underlying video data and 2 videos of different actions can be easily distinguished by their intrinsic features we propose a simple but effective action recognition framework based on the recently proposed overcomplete ica model after a set of overcomplete ica basis functions are learned from the densely sampled 3d patches from training videos for each action a test video is classified as the class whose basis functions can reconstruct the sampled 3d patches from the test video with the smallest reconstruction error the experimental results on five benchmark datasets demonstrate that the proposed approach outperforms several state of the art works

on the upper critical dimension of lattice trees and lattice animals we give a rigorous proof of mean field critical behavior for the susceptibility 1 2 and the correlation length v 1 4 for models of lattice trees and lattice animals in two cases i for the usual model with trees or animals constructed from nearest neighbor bonds in sufficiently high dimensions and ii for a class of spread out or long range models in which trees and animals are constructed from bonds of various lengths above eight dimensions this provides further evidence that for these models the upper critical dimension is equal to eight the proof involves obtaining an infrared bound and showing that a certain square diagram is finite at the critical point and uses an expansion related to the lace expansion for the self avoiding walk

local residual similarity for image re ranking abstract similarity measurement is an essential component in image retrieval systems while previous work is focused on generic distance estimation this paper investigates the problem of similarity estimation within a local neighborhood defined in the original feature space specifically our method is characterized in two aspects i e local and residual first of all we focus on a subset of the top ranked relevant images to a query with which anchors are discovered by methods such as averaging or clustering the anchors are then subtracted from the neighborhood features resulting in residual representations the proposed local residual similarity lrs homogenizes the feature distances within the local neighborhood effective and efficient image re ranking is achieved by calculating lrs between the query and the top ranked images the method constrains that relevant images should appear similar in both original and local residual feature space we evaluate the proposed method on two image retrieval benchmarks with global cnn representations demonstrating a consistent improvement on performance with very limited extra computational cost

ensemble manifold regularization we propose an automatic approximation of the intrinsic manifold for general semi supervised learning ssl problems unfortunately it is not trivial to define an optimization function to obtain optimal hyperparameters usually cross validation is applied but it does not necessarily scale up other problems derive from the suboptimality incurred by discrete grid search and the overfitting therefore we develop an ensemble manifold regularization emr framework to approximate the intrinsic manifold by combining several initial guesses algorithmically we designed emr carefully so it 1 learns both the composite manifold and the semi supervised learner jointly 2 is fully automatic for learning the intrinsic manifold hyperparameters implicitly 3 is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption and 4 is scalable for a large number of candidate manifold hyperparameters from both time and space perspectives furthermore we prove the convergence property of emr to the deterministic matrix at rate root n extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework

biologically inspired feature manifold for scene classification biologically inspired feature bif and its variations have been demonstrated to be effective and efficient for scene classification it is unreasonable to measure the dissimilarity between two bifs based on their euclidean distance this is because bifs are extrinsically very high dimensional and intrinsically low dimensional i e bifs are sampled from a low dimensional manifold and embedded in a high dimensional space therefore it is essential to find the intrinsic structure of a set of bifs obtain a suitable mapping to implement the dimensionality reduction and measure the dissimilarity between two bifs in the low dimensional space based on their euclidean distance in this paper we study the manifold constructed by a set of bifs utilized for scene classification form a new dimensionality reduction algorithm by preserving both the geometry of intra bifs and the discriminative information inter bifs termed discriminative and geometry preserving projections dgpp and construct a new framework for scene classification in this framework we represent an image based on a new bif which combines the intensity channel the color channel and the c1 unit of a color image then we project the high dimensional bif to a low dimensional space based on dgpp and finally we conduct the classification based on the multiclass support vector machine svm thorough empirical studies based on the usc scene dataset demonstrate that the proposed framework improves the classification rates around 100 relatively and the training speed 60 times for different sites in comparing with previous gist proposed by siagian and itti in 2007

self avoiding walk in 5 or more dimensions using an expansion based on the renormalization group philosophy we prove that for a t step weakly self avoiding random walk in five or more dimensions the variance of the endpoint is of order t and the scaling limit is gaussian as t

automatic image annotation by semi supervised manifold kernel density estimation the insufficiency of labeled training data is a major obstacle in automatic image annotation to tackle this problem we propose a semi supervised manifold kernel density estimation ssmkde approach based on a recently proposed manifold kde method our contributions are twofold first ssmkde leverages both labeled and unlabeled samples and formulates all data in a manifold structure which enables a more accurate label prediction second the relationship between kde based methods and graph based semi supervised learning ssl methods is analyzed which helps to better understand graph based ssl methods extensive experiments demonstrate the superiority of ssmkde over existing kde based and graph based ssl methods

patch alignment manifold matting image matting is generally modeled as a space transform from the color space to the alpha space by estimating the alpha factor of the model the foreground of an image can be extracted however there is some dimensional information redundancy in the alpha space it usually leads to the misjudgments of some pixels near the boundary between the foreground and the background in this paper a manifold matting framework named patch alignment manifold matting is proposed for image matting in particular we first propose a part modeling of color space in the local image patch we then perform whole alignment optimization for approximating the alpha results using subspace reconstructing error furthermore we utilize nesterov s algorithm to solve the optimization problem finally we apply some manifold learning methods in the framework and obtain several image matting methods such as named isomap matting and its derived cascade isomap matting the experimental results reveal that the manifold matting framework and its two examples are effective when compared with several representative matting methods

texture recognition based on diffusion in networks a texture recognition method is proposed the image is modeled into networks the texture is characterized by the diffusion over the networks it is demonstrated that directed networks are better to texture recognition the proposed method outperform the state of the art much work has been done in the field of texture analysis and classification while promising classification methods have been proposed most of them rely on classical image analysis approaches this paper presents a texture classification method based on diffusion in directed networks first an image is modeled as a directed network by mapping each pixel as a node and connecting two nodes up to a maximum distance r to reveal texture properties links between two nodes are removed based on the pixel intensity difference once such a network is obtained the activity of each node is estimated by random walks and combined into a histogram to describe the image the main contribution of this paper is the use of directed networks which tends to provide better performance than in undirected cases also we have shown that the activity induced on these networks can be effectively used as texture descriptor experimental results show that the proposed method is favorably compared to traditional texture methods on widely used texture datasets the proposed method is also found to be promising for plant species classification using samples of leaf texture

toward improved ranking metrics in many computer vision algorithms a metric or similarity measure is used to determine the distance between two features the euclidean or ssd sum of the squared differences metric is prevalent and justified from a maximum likelihood perspective when the additive noise distribution is gaussian based on real noise distributions measured from international test sets we have found that the gaussian noise distribution assumption is often invalid this implies that other metrics which have distributions closer to the real noise distribution should be used in this paper we consider three different applications content based retrieval in image databases stereo matching and motion tracking in each of them we experiment with different modeling functions for the noise distribution and compute the accuracy of the methods using the corresponding distance measures in our experiments we compared the ssd metric the sad sum of the absolute differences metric the cauchy metric and the kullback relative information for several algorithms from the research literature which used the ssd or sad we showed that greater accuracy could be obtained by using the cauchy metric instead

semantic preserving distance metric learning and applications how do we accurately browse a large set of images or efficiently annotate the images from an image library image clustering methods are invaluable tools for applications such as content based image retrieval and image annotation to perform these tasks it is critical to have proper features to describe the visual and semantic content of images and to define an accurate distance metric to measure the dissimilarity between any two images however existing methods which adopt the features of color histograms edge direction histograms and shape context lack the ability to describe semantic content to solve this problem we propose a new approach that utilizes user provided pairwise constraints to describe the semantic relationship between two images a semantic preserving distance metric learning sp dml algorithm is developed to explore the complementary characteristics of the visual features and pairwise constraints in a unified feature space in this space the learned distance metric can be used to measure the dissimilarity between two images specifically the manifold structure adopted in sp dml is revealed by the image s visual features to integrate semantic contents in distance metric learning sp dml utilizes pairwise constraints to build semantic patches and align these patches to obtain the optimal distance metric for the new feature space experimental results in image clustering demonstrate that the performance of sp dml is appealing

adaptive hypergraph learning and its application in image classification recent years have witnessed a surge of interest in graph based transductive image classification existing simple graph based transductive learning methods only model the pairwise relationship of images however and they are sensitive to the radius parameter used in similarity calculation hypergraph learning has been investigated to solve both difficulties it models the high order relationship of samples by using a hyperedge to link multiple samples nevertheless the existing hypergraph learning methods face two problems i e how to generate hyperedges and how to handle a large set of hyperedges this paper proposes an adaptive hypergraph learning method for transductive image classification in our method we generate hyperedges by linking images and their nearest neighbors by varying the size of the neighborhood we are able to generate a set of hyperedges for each image and its visual neighbors our method simultaneously learns the labels of unlabeled images and the weights of hyperedges in this way we can automatically modulate the effects of different hyperedges thorough empirical studies show the effectiveness of our approach when compared with representative baselines

3d model retrieval and classification by semi supervised learning with content based similarity the rapid development of 3d digital technology has led to an increasing volume of 3d model data in addressing the management of such large scale data effective content based 3d model retrieval and recognition methods are highly desirable in 3d model retrieval and recognition tasks the distance measure between two 3d models plays an important role in this paper we propose a novel 3d model retrieval and recognition method that employs both a distance histogram and 3d moment invariants as features that are invariant to 3d object scaling translation and rotation disjoint information is used to measure the distance between the feature histograms and the euclidean distance is applied in calculating the distance between two moment features these measures are then combined as the 3d model distance using this distance measure the relationships between all 3d models in the dataset are formulated as a graph structure a semi supervised learning process is then conducted to estimate the relevance among the 3d models and this is employed for 3d model retrieval and classification to evaluate the effectiveness of the proposed method we conduct experiments on two datasets experimental results and a comparison with state of the art methods demonstrate that the proposed method achieves improved performance for 3d model retrieval and recognition tasks

a note on mean field behavior for self avoiding walk on branching planes we consider the critical behavior of the susceptibility of the self avoiding walk on the grapht z wheret is a bethe lattice with degreek andz is the one dimensional lattice by directly estimating the two point function using a method of grimmett and newman we show that the bubble condition is satisfied whenk 2 and therefore the critical exponent associated with the susceptibility equals 1

binary feature from intensity quantization and weakly spatial contextual coding for image search during the past few years a number of local binary feature descriptors for images have been proposed e g brief orb brisk and freak the binary descriptors have several advantages over the well established floating vector descriptors such as sift and surf for their fast computing speed and much low memory consumption nevertheless the binary descriptor still suffer from the poor performance in computer vision applications for its low discriminative power and hamming distance metric to improve the capability of binary descriptors some works focusing on the points selection pattern algorithm in the descriptor extraction are proposed these works mostly adopt more optimal selection pattern brisk and freak to enhance the performance of binary descriptors rather than random chosen pattern in our study however the points selection algorithm does not have much contributions for the promotion on performance therefore in this paper we try to solve the problem of low discriminative power and robustness through two novel methods intensity difference quantization and weakly spatial context coding the experimental results on the public datasets show that our method can significantly boost the performance of binary features and highly enhance the retrieval accuracy of the image search system even though our proposed method increases slightly memory usage and computing efficiency compared to the original binary descriptors

multiview alignment hashing for efficient image search hashing is a popular and efficient method for nearest neighbor search in large scale data spaces by embedding high dimensional feature descriptors into a similarity preserving hamming space with a low dimension for most hashing methods the performance of retrieval heavily depends on the choice of the high dimensional feature descriptor furthermore a single type of feature cannot be descriptive enough for different images when it is used for hashing thus how to combine multiple representations for learning effective hashing functions is an imminent task in this paper we present a novel unsupervised multiview alignment hashing approach based on regularized kernel nonnegative matrix factorization which can find a compact representation uncovering the hidden semantics and simultaneously respecting the joint probability distribution of data in particular we aim to seek a matrix factorization to effectively fuse the multiple information sources meanwhile discarding the feature redundancy since the raised problem is regarded as nonconvex and discrete our objective function is then optimized via an alternate way with relaxation and converges to a locally optimal solution after finding the low dimensional representation the hashing functions are finally obtained through multivariable logistic regression the proposed method is systematically evaluated on three data sets 1 caltech 256 2 cifar 10 and 3 cifar 20 and the results show that our method significantly outperforms the state of the art multiview hashing techniques

low rank matrix factorization with multiple hypergraph regularizer this paper presents a novel low rank matrix factorization method named multihmmf which incorporates multiple hypergraph manifold regularization to the low rank matrix factorization in order to effectively exploit high order information among the data samples the hypergraph is introduced to model the local structure of the intrinsic manifold specifically multiple hypergraph regularization terms are separately constructed to consider the local invariance the optimal intrinsic manifold is constructed by linearly combining multiple hypergraph manifolds then the regularization term is incorporated into a truncated singular value decomposition framework resulting in a unified objective function so that matrix factorization is changed into an optimization problem alternating optimization is used to solve the optimization problem with the result that the low dimensional representation of data space is obtained the experimental results of image clustering demonstrate that the proposed method outperforms state of the art data representation methods we propose a novel low rank matrix factorization method we incorporate multiple hypergraph manifold regularization to the matrix factorization we adopt alternating optimization to solve the optimization problem

relevance preserving projection and ranking for web image search reranking an image search reranking isr technique aims at refining text based search results by mining images visual content feature extraction and ranking function design are two key steps in isr inspired by the idea of hypersphere in one class classification this paper proposes a feature extraction algorithm named hypersphere based relevance preserving projection hrpp and a ranking function called hypersphere based rank h rank specifically an hrpp is a spectral embedding algorithm to transform an original high dimensional feature space into an intrinsically low dimensional hypersphere space by preserving the manifold structure and a relevance relationship among the images an h rank is a simple but effective ranking algorithm to sort the images by their distances to the hypersphere center moreover to capture the user s intent with minimum human interaction a reversed k nearest neighbor knn algorithm is proposed which harvests enough pseudorelevant images by requiring that the user gives only one click on the initially searched images the hrpp method with reversed knn is named one click based hrpp oc hrpp finally an oc hrpp algorithm and the h rank algorithm form a new isr method h reranking extensive experimental results on three large real world data sets show that the proposed algorithms are effective moreover the fact that only one relevant image is required to be labeled makes it has a strong practical significance

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

markov fields on branching planes we investigate ising models indexed by the sites of a branching plane mathbb t which is the product of a regular tree mathbb t and the line there are three parameter regimes corresponding to 1 a unique gibbs distribution 2 nonunique gibbs distributions with treelike structure the free boundary condition field is not a mixture of the plus and minus b c fields 3 nonunique gibbs distributions with planelike structure the free b c field is a mixture of the plus and minus b c fields

k local hyperplane distance nearest neighbor classifier oriented local discriminant analysis k local hyperplane distance nearest neighbor hknn classifier is an improved k nearest neighbor knn algorithm that has been successfully applied to pattern classification this paper embeds the decision rule of hknn classifier into the discriminant analysis model to develop a new feature extractor the obtained feature extractor is called k local hyperplane distance nearest neighbor classifier oriented local discriminant analysis holda in which a regularization item is imposed on the original hknn algorithm to obtain a more reliable distance metric based on this distance metric the homo class and hetero class local scatters are characterized in holda by maximizing the ratio of the hetero class local scatter to the homo class local scatter we obtain a subspace which is suitable for feature extraction and classification in general this paper provides a framework for building a feature extractor from the decision rule of a classifier by this means the feature extractor and classifier can be seamlessly integrated experimental results on four databases demonstrate that the integrated pattern recognition system is effective

multi label image categorization with sparse factor representation the goal of multilabel classification is to reveal the underlying label correlations to boost the accuracy of classification tasks most of the existing multilabel classifiers attempt to exhaustively explore dependency between correlated labels it increases the risk of involving unnecessary label dependencies which are detrimental to classification performance actually not all the label correlations are indispensable to multilabel model negligible or fragile label correlations cannot be generalized well to the testing data especially if there exists label correlation discrepancy between training and testing sets to minimize such negative effect in the multilabel model we propose to learn a sparse structure of label dependency the underlying philosophy is that as long as the multilabel dependency cannot be well explained the principle of parsimony should be applied to the modeling process of the label correlations the obtained sparse label dependency structure discards the outlying correlations between labels which makes the learned model more generalizable to future samples experiments on real world data sets show the competitive results compared with existing algorithms

efficient isometric multi manifold learning based on the self organizing method geodesic distance as an essential measurement for data similarity has been successfully used in manifold learning however many geodesic based isometric manifold learning algorithms such as the isometric feature mapping isomap and geonlm fail to work on data that distribute on clusters or multiple manifolds this limits their applications because practical data sets generally distribute on multiple manifolds in this paper we propose a new isometric multi manifold learning method called multi manifold proximity embedding mpe which can be efficiently optimized using the gradient descent method or the self organizing method compared with the previous methods the proposed method has two steps which can isometrically learn data distributed on several manifolds and is more accurate in preserving both the intra manifold and the inter manifold geodesic distances the effectiveness of the proposed method in recovering the nonlinear data structure and clustering is demonstrated through experiments on both synthetically and real data sets

generalization performance of magnitude preserving semi supervised ranking with graph based regularization semi supervised ranking is a relatively new and important learning problem inspired by many applications we propose a novel graph based regularized algorithm which learns the ranking function in the semi supervised learning framework it can exploit geometry of the data while preserving the magnitude of the preferences the least squares ranking loss is adopted and the optimal solution of our model has an explicit form we establish error analysis of our proposed algorithm and demonstrate the relationship between predictive performance and intrinsic properties of the graph the experiments on three datasets for recommendation task and two quantitative structure activity relationship datasets show that our method is effective and comparable to some other state of the art algorithms for ranking

graph based semisupervised learning graph based learning provides a useful approach for modeling data in classification problems in this modeling scenario the relationship between labeled and unlabeled data impacts the construction and performance of classifiers and therefore a semisupervised learning framework is adopted we propose a graph classifier based on kernel smoothing a regularization framework is also introduced and it is shown that the proposed classifier optimizes certain loss functions its performance is assessed on several synthetic and real benchmark data sets with good results especially in settings where only a small fraction of the data are labeled

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

unsupervised image categorization by hypergraph partition we present a framework for unsupervised image categorization in which images containing specific objects are taken as vertices in a hypergraph and the task of image clustering is formulated as the problem of hypergraph partition first a novel method is proposed to select the region of interest roi of each image and then hyperedges are constructed based on shape and appearance features extracted from the rois each vertex image and its k nearest neighbors based on shape or appearance descriptors form two kinds of hyperedges the weight of a hyperedge is computed as the sum of the pairwise affinities within the hyperedge through all of the hyperedges not only the local grouping relationships among the images are described but also the merits of the shape and appearance characteristics are integrated together to enhance the clustering performance finally a generalized spectral clustering technique is used to solve the hypergraph partition problem we compare the proposed method to several methods and its effectiveness is demonstrated by extensive experiments on three image databases

daml domain adaptation metric learning the state of the art metric learning algorithms cannot perform well for domain adaptation settings such as cross domain face recognition image annotation etc because labeled data in the source domain and unlabeled ones in the target domain are drawn from different but related distributions in this paper we propose the domain adaptation metric learning daml by introducing a data dependent regularization to the conventional metric learning in the reproducing kernel hilbert space rkhs this data dependent regularization resolves the distribution difference by minimizing the empirical maximum mean discrepancy between source and target domain data in rkhs theoretically by using the empirical rademacher complexity we prove risk bounds for the nearest neighbor classifier that uses the metric learned by daml practically learning the metric in rkhs does not scale up well fortunately we can prove that learning daml in rkhs is equivalent to learning daml in the space spanned by principal components of the kernel principle component analysis kpca thus we can apply kpca to select most important principal components to significantly reduce the time cost of daml we perform extensive experiments over four well known face recognition datasets and a large scale web image annotation dataset for the cross domain face recognition and image annotation tasks under various settings and the results demonstrate the effectiveness of daml

manifold regularized discriminative nonnegative matrix factorization with fast gradient descent nonnegative matrix factorization nmf has become a popular data representation method and has been widely used in image processing and pattern recognition problems this is because the learned bases can be interpreted as a natural parts based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole for practical classification tasks however nmf ignores both the local geometry of data and the discriminative information of different classes in addition existing research results show that the learned basis is unnecessarily parts based because there is neither explicit nor implicit constraint to ensure the representation parts based in this paper we introduce the manifold regularization and the margin maximization to nmf and obtain the manifold regularized discriminative nmf md nmf to overcome the aforementioned problems the multiplicative update rule mur can be applied to optimizing md nmf but it converges slowly in this paper we propose a fast gradient descent fgd to optimize md nmf fgd contains a newton method that searches the optimal step length and thus fgd converges much faster than mur in addition fgd includes mur as a special case and can be applied to optimizing nmf and its variants for a problem with 165 samples in r1600 fgd converges in 28 s while mur requires 282 s we also apply fgd in a variant of md nmf and experimental results confirm its efficiency experimental results on several face image datasets suggest the effectiveness of md nmf

hypergraph modelling for geometric model fitting in this paper we propose a novel hypergraph based method called hf to fit and segment multi structural data the proposed hf formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph model in the hypergraph model vertices represent data points and hyperedges denote model hypotheses the hypergraph with large and data determined degrees of hyperedges can express the complex relationships between model hypotheses and data points in addition we develop a robust hypergraph partition algorithm to detect sub hypergraphs for model fitting hf can effectively and efficiently estimate the number of and the parameters of model instances in multi structural data heavily corrupted with outliers simultaneously experimental results show the advantages of the proposed method over previous methods on both synthetic data and real images highlightswe propose a novel hypergraph based method to fit and segment multi structural data the proposed method includes a hypergraph model with large degrees of hyperedges the proposed method includes a robust hypergraph partition algorithm experimental results show that the proposed method is superior to some state of the art fitting methods

web image search re ranking with click based similarity and typicality in image search re ranking besides the well known semantic gap intent gap which is the gap between the representation of users query demand and the real intent of the users is becoming a major problem restricting the development of image retrieval to reduce human effects in this paper we use image click through data which can be viewed as the implicit feedback from users to help overcome the intention gap and further improve the image search performance generally the hypothesis visually similar images should be close in a ranking list and the strategy images with higher relevance should be ranked higher than others are widely accepted to obtain satisfying search results thus image similarity and the level of relevance typicality are determinate factors correspondingly however when measuring image similarity and typicality conventional re ranking approaches only consider visual information and initial ranks of images while overlooking the influence of click through data this paper presents a novel re ranking approach named spectral clustering re ranking with click based similarity and typicality first to learn an appropriate similarity measurement we propose click based multi feature similarity learning algorithm which conducts metric learning based on click based triplets selection and integrates multiple features into a unified similarity space via multiple kernel learning then based on the learnt click based image similarity measure we conduct spectral clustering to group visually and semantically similar images into same clusters and get the final re rank list by calculating click based clusters typicality and within clusters click based image typicality in descending order our experiments conducted on two real world query image data sets with diverse representative queries show that our proposed re ranking approach can significantly improve initial search results and outperform several existing re ranking approaches

semi supervised linear discriminant analysis for dimension reduction and classification when facing high dimensional data dimension reduction is necessary before classification among dimension reduction methods linear discriminant analysis lda is a popular one that has been widely used lda aims to maximize the ratio of the between class scatter and total data scatter in projected space and the label of each data is necessary however in real applications the labeled data are scarce and unlabeled data are in large quantity so lda is hard to be used under such case in this paper we propose a novel method named semi supervised linear discriminant analysis slda which can use limited number of labeled data and a quantity of the unlabeled ones for training so that lda can accommodate to the situation of a few labeled data available assuming that f represents the calculated class indicator matrix of the training data and y denotes the true label of the labeled data the objective function contains two parts one is the criterion of lda which is a function of projection w and a class indicator matrix f the other is the difference between the true data label and calculated label of these labeled data as far as we know there is no closed form solution to the objective function to solve such problem we develop an iterative algorithm which calculates the class indicator matrix and the projection alternatively the convergence of the proposed iterative algorithm is proved and confirmed by experiments the experimental results on eight datasets show that the performance of slda is superior to that of traditional lda and some state of the art semi supervised algorithms highlightsa semi supervised variant of lda named semi supervised lda is proposed our method can use limited number of labeled data and a quantity of the unlabeled ones for training we develop an iterative algorithm which calculates the class indicator matrix and the projection alternatively

multimodal graph based reranking for web image search this paper introduces a web image search reranking approach that explores multiple modalities in a graph based learning scheme different from the conventional methods that usually adopt a single modality or integrate multiple modalities into a long feature vector our approach can effectively integrate the learning of relevance scores weights of modalities and the distance metric and its scaling for each modality into a unified scheme in this way the effects of different modalities can be adaptively modulated and better reranking performance can be achieved we conduct experiments on a large dataset that contains more than 1000 queries and 1 million images to evaluate our approach experimental results demonstrate that the proposed reranking approach is more robust than using each individual modality and it also performs better than many existing methods

new lower bounds on the self avoiding walk connective constant we give an elementary new method for obtaining rigorous lower bounds on the connective constant for self avoiding walks on the hypercubic lattice d the method is based on loop erasure and restoration and does not require exact enumeration data our bounds are best for highd and in fact agree with the first four terms of the 1 d expansion for the connective constant the bounds are the best to date for dimensionsd 3 but do not produce good results in two dimensions ford 3 4 5 and 6 respectively our lower bound is within 2 4 0 43 0 12 and 0 044 of the value estimated by series extrapolation

robust bilinear factorization with missing and grossly corrupted observations recovering low rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics machine learning computer vision as well as signal and image processing in theory this problem can be solved by the natural convex joint mixed relaxations i e l 1 norm and trace norm under certain conditions however all current provable algorithms suffer from superlinear per iteration cost which severely limits their applicability to large scale problems in this paper we propose a scalable provable and structured robust bilinear factorization rbf method to recover low rank and sparse matrices from missing and grossly corrupted data i e robust matrix completion rmc or incomplete and grossly corrupted measurements i e compressive principal component pursuit cpcp specifically we first present two small scale matrix trace norm regularized bilinear factorization models for rmc and cpcp problems in which repetitively calculating svd of a large scale matrix is replaced by updating two much smaller factor matrices then we apply the alternating direction method of multipliers admm to efficiently solve the rmc problems finally we provide the convergence analysis of our algorithm and extend it to address general cpcp problems experimental results verified both the efficiency and effectiveness of our method compared with the state of the art methods

the number and size of branched polymers in high dimensions we consider two models of branched polymers lattice trees on thed dimensional hypercubic lattice i the nearest neighbor model in sufficiently high dimensions and ii a spread out or long range model ford 8 in which trees are constructed from bonds of length less than or equal to a large parameterl we prove that for either model the critical exponent for the number of branched polymers exists and equals 5 2 and that the critical exponentv for the radius of gyration exists and equals 1 4 this improves our earlier results for the corresponding generating functions the proof uses the lace expansion together with an analysis involving fractional derivatives which has been applied previously to the self avoiding walk in a similar context

semisupervised multiview distance metric learning for cartoon synthesis in image processing cartoon character classification retrieval and synthesis are critical so that cartoonists can effectively and efficiently make cartoons by reusing existing cartoon data to successfully achieve these tasks it is essential to extract visual features that comprehensively represent cartoon characters and to construct an accurate distance metric to precisely measure the dissimilarities between cartoon characters in this paper we introduce three visual features color histogram shape context and skeleton to characterize the color shape and action respectively of a cartoon character these three features are complementary to each other and each feature set is regarded as a single view however it is improper to concatenate these three features into a long vector because they have different physical properties and simply concatenating them into a high dimensional feature vector will suffer from the so called curse of dimensionality hence we propose a semisupervised multiview distance metric learning ssm dml ssm dml learns the multiview distance metrics from multiple feature sets and from the labels of unlabeled cartoon characters simultaneously under the umbrella of graph based semisupervised learning ssm dml discovers complementary characteristics of different feature sets through an alternating optimization based iterative algorithm therefore ssm dml can simultaneously accomplish cartoon character classification and dissimilarity measurement on the basis of ssm dml we develop a novel system that composes the modules of multiview cartoon character classification multiview graph based cartoon synthesis and multiview retrieval based cartoon synthesis experimental evaluations based on the three modules suggest the effectiveness of ssm dml in cartoon applications

mean field critical behaviour for percolation in high dimensions the triangle condition for percolation states that sum limits x y tau 0 x tau 0 y cdot tau y 0 is finite at the critical point where x y is the probability that the sitesx andy are connected we use an expansion related to the lace expansion for a self avoiding walk to prove that the triangle condition is satisfied in two situations i for nearest neighbour independent bond percolation on thed dimensional hypercubic lattice ifd is sufficiently large and ii in more than six dimensions for a class of spread out models of independent bond percolation which are believed to be in the same universality class as the nearest neighbour model the class of models in ii includes the case where the bond occupation probability is constant for bonds of length less than some large number and is zero otherwise in the course of the proof an infrared bound is obtained the triangle condition is known to imply that various critical exponents take their mean field bethe lattice values gamma beta 1 delta delta t 2 t underset raise0 3em hbox smash scriptscriptstyle geqslant 2 and that the percolation density is continuous at the critical point we also prove thatv2 in i and ii wherev2 is the critical exponent for the correlation length

fusing mathcal r r features and local features with context aware kernels for action recognition the performance of action recognition in video sequences depends significantly on the representation of actions and the similarity measurement between the representations in this paper we combine two kinds of features extracted from the spatio temporal interest points with context aware kernels for action recognition for the action representation local cuboid features extracted around interest points are very popular using a bag of visual words bovw model such representations however ignore potentially valuable information about the global spatio temporal distribution of interest points we propose a new global feature to capture the detailed geometrical distribution of interest points it is calculated by using the 3d mathcal r r transform which is defined as an extended 3d discrete radon transform followed by the application of a two directional two dimensional principal component analysis for the similarity measurement we model a video set as an optimized probabilistic hypergraph and propose a context aware kernel to measure high order relationships among videos the context aware kernel is more robust to the noise and outliers in the data than the traditional context free kernel which just considers the pairwise relationships between videos the hyperedges of the hypergraph are constructed based on a learnt mahalanobis distance metric any disturbing information from other classes is excluded from each hyperedge finally a multiple kernel learning algorithm is designed by integrating the l 2 l2 norm regularization into a linear svm classifier to fuse the mathcal r r feature and the bovw representation for action recognition experimental results on several datasets demonstrate the effectiveness of the proposed approach for action recognition

self avoiding walk in five or more dimensions i the critical behaviour we use the lace expansion to study the standard self avoiding walk in thed dimensional hypercubic lattice ford 5 we prove that the numbercn ofn step self avoiding walks satisfiescn a n where is the connective constant i e 1 and that the mean square displacement is asymptotically linear in the number of steps i e v 1 2 a bound is obtained forcn x the number ofn step self avoiding walks ending atx the correlation length is shown to diverge asymptotically like z 1 2 the critical two point function is shown to decay at least as fast as x 2 and its fourier transform is shown to be asymptotic to a multiple ofk 2 ask 0 i e 0 we also prove that the scaling limit is gaussian in the sense of convergence in distribution to brownian motion the infinite self avoiding walk is constructed in this paper we prove these results assuming convergence of the lace expansion the convergence of the lace expansion is proved in a companion paper

embedded local feature selection within mixture of experts a useful strategy to deal with complex classification scenarios is the divide and conquer approach the mixture of experts moe technique makes use of this strategy by jointly training a set of classifiers or experts that are specialized in different regions of the input space a global model or gate function complements the experts by learning a function that weighs their relevance in different parts of the input space local feature selection appears as an attractive alternative to improve the specialization of experts and gate function particularly in the case of high dimensional data in general subsets of dimensions or subspaces are usually more appropriate to classify instances located in different regions of the input space accordingly this work contributes with a regularized variant of moe that incorporates an embedded process for local feature selection using l 1 regularization experiments using artificial and real world datasets provide evidence that the proposed method improves the classical moe technique in terms of accuracy and sparseness of the solution furthermore our results indicate that the advantages of the proposed technique increase with the dimensionality of the data

a novel technique for subpixel image classification based on support vector machine this paper presents a novel support vector machine classifier designed for subpixel image classification pixel spectral unmixing the proposed classifier generalizes the properties of svms to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic this results in the definition of a fuzzy input fuzzy output support vector machine f2svm classifier that can 1 process fuzzy information given as input to the classification algorithm for modeling the subpixel information in the learning phase of the classifier and 2 provide a fuzzy modeling of the classification results allowing a relation many to one between classes and pixels the presented binary f2svm can address multicategory problems according to two strategies the fuzzy one against all foaa and the fuzzy one against one foao strategies these strategies generalize to the fuzzy case techniques based upon ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems the effectiveness of the proposed f2svm classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics experimental results confirm the validity of the proposed subpixel classification method