Recently , graph embedding emerges as an effective approach for graph analysis tasks such as node classification and link prediction . The goal of network embedding is to find low dimensional representation of graph nodes that preserves the graph structure . Modern graph embedding procedures can efficiently process graphs with millions of nodes . In this paper , we propose GEMSEC - a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding . GEMSEC is a general extension of earlier work in the domain of sequence-based graph embedding . Therefore , AGEDP not only greatly enhances the intraclass compactness and interclass separability , but also adaptively performs neighbor parameter selection which considers the fact that local manifold structure of each sample is generally different . Experiments on AR and COIL-20 datasets demonstrate the effectiveness of the proposed method for face recognition and object categorization , and especially under the interference of occlusion , noise and poses , it is superior to other graph embedding based methods with three different classifiers : nearest neighbor classifier , sparse representation classifier and linear regression classifier . Abstract There have been increasing interests in user identity linkage ( UIL ) across social networks since it supports many applications such as cross-net recommendation , link prediction , and network fusion . Existing graph embedding based techniques can not sufficiently model the higher-order structural properties in UIL . Moreover , the very limited supervisory anchor pairs ( SAP ) , which are crucial for the task of UIL across social networks , are not utilized effectively . Graph-based embedding methods are very useful for reducing the dimension of high-dimensional data and for extracting their relevant features . In this paper , we introduce a novel nonlinear method called Flexible Discriminant graph-based Embedding with feature selection ( FDEFS ) . It integrates two interesting properties : ( i ) being entirely parameter-free and ( ii ) the mapped data are uncorrelated . The proposed method has been integrated in the framework of three graph-based embedding techniques : Locality Preserving Projections ( LPP ) , Orthogonal Locality Preserving Projections ( OLPP ) , and supervised LPP ( SLPP ) . Recognition tasks on six public face databases show an improvement over the results of LPP , OLPP , and SLPP . This paper studies the problem of embedding very large information networks into low - dimensional vector spaces , which is useful in many tasks such as visualization , node classification , and link prediction . Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes . In this paper , we propose a novel network embedding method called the “ LINE , ” which is suitable for arbitrary types of information networks : undirected , directed , and / or weighted . Semi - supervised embedding method learns embeddings in a neural network , but our approach is different from this method in that instead of imposing regularization , we use the embeddings to predict the context in the graph . Graph embedding methods encode the graph structure into embeddings ; however , different from our approach , these methods are purely unsupervised and do not leverage label information for a specific task . Moreover , these methods are transductive and can not be directly generalized to instances unseen at training time . In our work here , we also capture the relation between any two words in WordNet through relation embedding . Specifically , we employed TransE DBLP : conf / nips / BordesUGWY13 , a widely used graph embedding methods , to capture relation embedding between any two words . We used two typical approaches to obtaining the relation embedding . In this paper , we introduce unsupervised generative neural networks for performing stain-color normalization . For color normalization in stained hematoxylin and eosin ( H&E ) images , we present three methods based on three frameworks for deep generative models : variational auto-encoder ( VAE ) , generative adversarial networks ( GAN ) and deep convolutional Gaussian mixture models ( DCGMM ) . Our contribution is defining the color normalization as a learning generative model that is able to generate various color copies of the input image through a nonlinear parametric transformation . These rectified Gaussian units allow spike-and-slab type sparsity , while retaining the differentiability necessary for efficient stochastic gradient variational inference . To learn the parameters of the new model , we approximate the posterior of the latent variables with a variational auto-encoder . Rather than making the usual mean-field assumption however , the encoder parameterizes a new type of structured variational approximation that retains the prior dependencies of the generative model . However , the high rate of false positive/negative interactions in PINs prevents accurately detecting complexes directly from the raw PINs . In this paper , we propose a denoising approach for protein complex detection by using variational graph auto-encoder . First , we embed a PIN to vector space by a stacked graph convolutional network ( GCN ) , then decide which interactions in the PIN are credible . In this paper , we propose an efficient learning based sub-pixel image compression algorithm . Our framework builds upon the previous variational auto-encoder architecture and reduces the computational complexity significantly . Specifically , we propose an end-to-end optimized image compression framework to utilize the powerful non-linear representation ability of neural networks . This framework follows the widely used variational auto-encoder architecture and is optimized based on the rate-distortion balance . More importantly , a sub-pixel image compression framework is exploited to reduce the spatial resolution of image and improve the inference speed . In this paper , we interpret source separation as a style transfer problem . We present a variational auto-encoder network that exploits the commonality across the domain of mixtures and the domain of clean sounds and learns a shared latent representation across the two domains . Using these cycle-consistent variational auto-encoders , we learn a mapping from the mixture domain to the domain of clean sounds and perform source separation without explicitly supervising with paired training examples . Our pooling operation effectively encodes the correspondence between coarser and finer meshes in the hierarchy . We then present a variational auto-encoder ( VAE ) structure with the edge contraction pooling and graph-based convolutions , to explore probability latent spaces of 3D surfaces and perform 3D shape generation . Our network requires far fewer parameters than the original mesh VAE and thus can handle denser models thanks to our new pooling operation and convolutional kernels . Moreover , the vanilla approach of simply concatenating multiple short sentences , possibly synthesized from a classical image captioning system , does n’t embrace the intricacies of paragraphs : coherent sentences , globally consistent structure , and diversity . To address those challenges , we propose to augment paragraph generation techniques with “ coherence vectors , ” “ global topic vectors , ” and modeling of the inherent ambiguity of associating paragraphs with images , via a variational auto-encoder formulation . We demonstrate the effectiveness of the developed approach on two datasets , outperforming existing state-of-the-art techniques on both . We present ` Bits Back with ANS ' ( BB-ANS ) , a scheme to perform lossless compression with latent variable models at a near optimal rate . We demonstrate this scheme by using it to compress the MNIST dataset with a variational auto-encoder model ( VAE ) , achieving compression rates superior to standard methods with only a simple VAE . Given that the scheme is highly amenable to parallelization , we conclude that with a sufficiently high quality generative model this scheme could be used to achieve substantial improvements in compression rate with acceptable running time . Motivated by this , in this paper , we learn a feature space using the shape information which is a strong prior shared among different datasets and robust to the appearance variation of input data . The shape feature is captured using a Variational Auto-Encoder ( VAE ) network that trained with only the ground truth masks . During testing , the segmentation results with bad shapes shall not fit the shape prior well , resulting in large loss values . Assuming that the invariant features are now called we enrich the generative story by similarly providing two distinct ( independent ) sources for ; a discrete ( in case of classification ) variable which denotes the label of the data point and a continuous latent variable which encodes the variation on that is not explained by ( dependent noise ) . The process now can be formally defined as : Similarly to the unsupervised case we use a variational auto - encoder and jointly optimize the variational and model parameters . The lower bound now becomes : where we assume that the posterior is factorized as , and where : with again being an appropriate probability distribution for the data we are modelling . We introduce a simple recurrent variational auto - encoder architecture that significantly improves image modeling . The system represents the state - of - the - art in latent variable models for both the ImageNet and Omniglot datasets . In this paper we propose a method that is able to transform an image into a progression of increasingly detailed representations , ranging from global conceptual aspects to low level details ( see Figures [ reference ] & [ reference ] ) . At the same time , our model greatly improves latent variable image modeling compared to earlier implementations of deep variational auto - encoders . Furthermore , it has the advantage of being a simple homogeneous architecture not requiring complex design choices , which is similar to the recurrent structure of DRAW ( ) . Last , it provides an important insight into building good variational auto - encoder models of images : the use of multiple layers of stochastic variables that are all ‘ close ’ to the pixels significantly improves performance . The system ’s ability to stratify information enables it to perform high quality lossy compression , by storing only a subset of latent variables , starting with the high level ones , and generating the remainder during decompression ( see Figure [ reference ] ) . Numerous techniques exist for unsupervised learning in deep networks , e.g. sparse auto - encoders and sparse coding , denoising auto - encoders , deconvolutional networks , restricted Boltzmann machines , deep Boltzmann machines , generative adversarial networks and variational auto - encoders . In this paper we focus on the class of models in the variational auto - encoding framework . Since we are also interested in compression , we present them from an information - theoretic perspective . Thus , sharp reconstructions should not be a property of high - precision values in the network , but should rather be the result of an iterative feedback mechanism that is robust to network parameter change . Such a mechanism is provided by the DRAW algorithm , which is a recurrent type of variational auto - encoder . At each time step , DRAW maintains a provisionary reconstruction , takes in information about a given image , stores it in latent variables and updates the reconstruction . We also report the likelihood for a ( non - recurrent ) variational auto - encoder and standard DRAW . For the variational auto - encoder we tested architectures with multiple layers , both deterministic and stochastic but with standard functional forms , and this was the best result that we obtained . Convolutional DRAW performs significantly better . The motivation for using the auto - encoder branch is to add additional guidance and regularization to the encoder part , since the training dataset size is limited . We follow the variational auto - encoder ( VAE ) approach to better cluster / group the features of the encoder endpoint . We describe the building parts of our networks in the next subsections ( see also Figure [ reference ] ) The architecture is sketched in Fig . [ reference ] , alongside a feedforward variational auto - encoder . subsection : Network Architecture The choice of the decoder depends on the task . For link prediction , the bilinear inner product is used in the context of the variational graph autoencoder ( VGAE ) . For semi - supervised node classification , the softmax activation function is employed . Effective solutions to the DGP problem have the potential to accelerate the therapeutic development pipeline at early stages via efficient prioritization of candidate genes for various diseases . In this work , we introduce the variational graph auto-encoder ( VGAE ) as a promising unsupervised approach for learning powerful latent embeddings in disease-gene networks that can be used for the DGP problem , the first approach using a generative model involving graph neural networks ( GNNs ) . In addition to introducing the VGAE as a promising approach to the DGP problem , we further propose an extension ( constrained-VGAE or C-VGAE ) which adapts the learning algorithm for link prediction between two distinct node types in heterogeneous graphs . Being an extension of VAE model , VGAE , also suffers from over-pruning in principal . In this paper we look at over-pruning in VGAE and observe that the generative capacity of VGAE is limited because of the way VGAE deals with this issue . We then propose epitomic variational graph autoencoder ( EVGAE ) , a generative variational framework for graph datasets to overcome over-pruning . We introduce the variational graph auto-encoder ( VGAE ) , a framework for unsupervised learning on graph-structured data based on the variational auto-encoder ( VAE ) . This model makes use of latent variables and is capable of learning interpretable latent representations for undirected graphs . Variational Graph Autoencoder ( VGAE ) has recently gained traction for learning representations on graphs . Its inception has allowed models to achieve state-of-the-art performance for challenging tasks such as link prediction , rating prediction , and node clustering . Fixing the auto-encoder enables a fairer assessment on the size of a nodes receptive field in building representations . Furthermore a by-product of fixing the auto-encoder design often results in substantially smaller networks than their VGAE counterparts especially as we increase the number of feature propagations . A comparative downstream evaluation on link prediction tasks show comparable state of the art performance to similar VGAE arrangements despite considerable simplification . The choice of the decoder depends on the task . For link prediction , the bilinear inner product is used in the context of the variational graph autoencoder ( VGAE ) . For semi - supervised node classification , the softmax activation function is employed . Table [ reference ] shows the efficacy of the MTGAE model for MTL when compared against recent state - of - the - art task - specific link prediction and node classification models , which require the complete adjacency matrix as input . For link prediction , MTGAE significantly outperforms the best VGAE model on Cora and Citeseer . For node classification , MTGAE is the best performing model on the Citeseer and Pubmed datasets , which have very low node label rates . However , these methods have obvious drawbacks of poor performance and expensive computation for largescale networks . In this work , we propose a novel solution to identify SH spanner based on graph embedding learning . Considering the special topological nature of SH spanner in the network , we design a deep embedding learning method for detecting SH spanner . In order to pursue aligned representation , conventional approaches tend to construct and optimize a linear projection or train a complex architecture of deep layers , yet it is difficult to compromise between accuracy and efficiency on modeling multimodal data . This paper proposes a novel graph-embedding learning framework implemented by neural networks . The learned embedding directly approximates the cross-modal aligned representation to perform cross-modal retrieval and image classification combining text information . Moreover , a heuristic negative sample selection scheme is adopted to make the classification more effective . In applications to tracking , the graph-embedding-based learning is incorporated into a Bayesian inference framework cascaded with hierarchical motion estimation , which significantly improves the accuracy and efficiency of the localization . Furthermore , an incremental updating technique for the graphs is developed to capture the changes in both appearance and illumination . Graph embedding-based learning methods have been widely employed to reduce the dimensionality of high-dimensional data , while how to construct adjacency graphs to discover the essential structure of the data is the key problem in these methods . In this paper , we present a novel algorithm called graph discriminant embedding ( GDE ) for feature extraction and recognition . Algorithmically , the proposed approach consists in computing a mapping based on pairwise dissimilarity where learning a linear decision function is amenable . Our experimental results show that the Wasserstein distance embedding performs better than kernel mean embeddings and computing Wasserstein distance is far more tractable than estimating pairwise Kullback-Leibler divergence of empirical distributions . Algorithmically , the proposed approach is very simple as it consists in computing a mapping based on pairwise Wasserstein distances and then learning a linear decision function . Our experimental results show that this Wasserstein distance embedding performs better than kernel mean embeddings and computing Wasserstein distance is far more tractable than estimating pairwise Kullback-Leibler divergence of empirical distributions . We examine empirically the representational capacity of our learned Wasserstein embeddings , showing that they can embed a wide variety of metric structures with smaller distortion than an equivalent Euclidean embedding . We also investigate an application to word embedding , demonstrating a unique advantage of Wasserstein embeddings : We can visualize the high-dimensional embedding directly , since it is a probability distribution on a low-dimensional space . This obviates the need for dimensionality reduction techniques like t-SNE for visualization . For the generalised minimum spanning tree problem , we analyse the two approaches presented by Hu and Raidl ( 2012 ) with respect to the number of clusters that distinguish each other by the chosen representation of possible solutions . Our results show that a ( 1 + 1 ) evolutionary algorithm working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem , whereas the problem can be solved in fixed-parameter time with the global structure representation . We present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other ’s hard instances very efficiently . VII . On the global structure of models for reflective truth . PART D : LEVELS OF TRUTH AND PROOF THEORY . Specifically , we first build the spatial pyramid representation to capture context information of objects at different scales . Guided by the task-specific information , we combine the dense global structure representation and local texture patterns at each spatial location effectively using the spatial attention mechanism . In this way , the network is enforced to focus on the discriminative regions with context information for domain adaption . The final descriptions ( global feature graphs ) are based on the quasi-convexity ( concavity ) structures incorporating quantized directional features of closed boundaries of cross-sections along several directions . The global feature graphs have the following properties : ( 1 ) They provide a characterization of global , structural , qualitative properties of the object ; ( 2 ) The graphs are composed of a few components ( nodes and edges ) with rich features , and give compact descriptions of the objects ; ( 3 ) The global feature graph representations are robust and qualitative in that they are not affected by geometrical , quantitative properties of the shape such as curvatures , length , and position ; ( 4 ) The representation has clear and rigorous properties . Furthermore , we present some theoretical basis for object recognition using the global features graphs . Graph convolutional network is utilized to perform graph representation encoding . Unlike traditional clustering approaches relying on hand-crafted criteria , our method learns to cluster graph-structured data by maximizing mutual information between the global-graph representation and local-graph representations . The learnt graph embeddings can preserve global information in all locations of local-graphs such as pseudo labels for image clustering tasks . This paper proposes a novel framework to identify and localize salient regions in a crowd scene , by transforming low-level features extracted from crowd motion field into a global similarity structure . The global similarity structure representation allows the discovery of the intrinsic manifold of the motion dynamics , which could not be captured by the low-level representation . Ranking is then performed on the global similarity structure to identify a set of extrem a. In this paper , we investigate the problem of retrieving candidate lists for matching partial fingerprints by exploiting global topological features . Specifically , we propose an analytical approach for reconstructing the global topology representation from a partial fingerprint . First , we present an inverse orientation model for describing the reconstruction problem . In particular , lung cancer diagnosis would benefit from segmentations reaching most distal airways . We present a method that combines descriptors of bronchi local appearance and graph global structural analysis to fine-tune thresholds on the descriptors adapted for each bronchial level . We have compared our method to the top performers of the EXACT09 challenge and to a commercial software for biopsy planning evaluated in an own-collected data-base of high resolution CT scans acquired under different breathing conditions . In this paper , we present a review of the latest developments on this topic . We compare modern methods based on matrix factorization , including GraRep [ 5 ] , HOPE [ 22 ] , DeepWalk [ 23 ] , and node2vec [ 12 ] , in a collection of 12 real-world networks . We find that the performance of methods depends on the applications and the specific characteristics of the networks . In this paper , we present { GraRep } , a novel model for learning vertex representations of weighted graphs . This model learns low dimensional vectors to represent vertices appearing in a graph and , unlike existing work , integrates global structural information of the graph into the learning process . This paper proposes a drug-target interaction prediction method that can integrate information from different heterogeneous networks . This method constructs multiple drug and target similarity networks and applies the GraRep algorithm on the similarity networks after denoising in order to extract the features . Features obtained from heterogeneous networks are combined as a feature vector of DTIs , which is the input of Random Forest . We exclude other matrix factorization approaches which have already been shown to be inferior to DeepWalk . We also exclude a recent approach , GraRep , that generalizes LINE to incorporate information from network neighborhoods beyond 2 - hops , but is unable to efficiently scale to large networks . In contrast to the setup used in prior work for evaluating sampling - based feature learning algorithms , we generate an equal number of samples for each method and then evaluate the quality of the obtained features on the prediction task .
Recently , graph embedding emerges as an effective approach for graph analysis tasks such as node classification and link prediction . The goal of network embedding is to find low dimensional representation of graph nodes that preserves the graph structure .
Modern graph embedding procedures can efficiently process graphs with millions of nodes . In this paper , we propose GEMSEC - a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding . GEMSEC is a general extension of earlier work in the domain of sequence-based graph embedding .
Therefore , AGEDP not only greatly enhances the intraclass compactness and interclass separability , but also adaptively performs neighbor parameter selection which considers the fact that local manifold structure of each sample is generally different . Experiments on AR and COIL-20 datasets demonstrate the effectiveness of the proposed method for face recognition and object categorization , and especially under the interference of occlusion , noise and poses , it is superior to other graph embedding based methods with three different classifiers : nearest neighbor classifier , sparse representation classifier and linear regression classifier .
Abstract There have been increasing interests in user identity linkage ( UIL ) across social networks since it supports many applications such as cross-net recommendation , link prediction , and network fusion . Existing graph embedding based techniques can not sufficiently model the higher-order structural properties in UIL . Moreover , the very limited supervisory anchor pairs ( SAP ) , which are crucial for the task of UIL across social networks , are not utilized effectively .
Graph-based embedding methods are very useful for reducing the dimension of high-dimensional data and for extracting their relevant features . In this paper , we introduce a novel nonlinear method called Flexible Discriminant graph-based Embedding with feature selection ( FDEFS ) .
It integrates two interesting properties : ( i ) being entirely parameter-free and ( ii ) the mapped data are uncorrelated . The proposed method has been integrated in the framework of three graph-based embedding techniques : Locality Preserving Projections ( LPP ) , Orthogonal Locality Preserving Projections ( OLPP ) , and supervised LPP ( SLPP ) . Recognition tasks on six public face databases show an improvement over the results of LPP , OLPP , and SLPP .
This paper studies the problem of embedding very large information networks into low - dimensional vector spaces , which is useful in many tasks such as visualization , node classification , and link prediction . Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes . In this paper , we propose a novel network embedding method called the “ LINE , ” which is suitable for arbitrary types of information networks : undirected , directed , and / or weighted .
Semi - supervised embedding method learns embeddings in a neural network , but our approach is different from this method in that instead of imposing regularization , we use the embeddings to predict the context in the graph . Graph embedding methods encode the graph structure into embeddings ; however , different from our approach , these methods are purely unsupervised and do not leverage label information for a specific task . Moreover , these methods are transductive and can not be directly generalized to instances unseen at training time .
In our work here , we also capture the relation between any two words in WordNet through relation embedding . Specifically , we employed TransE DBLP : conf / nips / BordesUGWY13 , a widely used graph embedding methods , to capture relation embedding between any two words . We used two typical approaches to obtaining the relation embedding .
In this paper , we introduce unsupervised generative neural networks for performing stain-color normalization . For color normalization in stained hematoxylin and eosin ( H&E ) images , we present three methods based on three frameworks for deep generative models : variational auto-encoder ( VAE ) , generative adversarial networks ( GAN ) and deep convolutional Gaussian mixture models ( DCGMM ) . Our contribution is defining the color normalization as a learning generative model that is able to generate various color copies of the input image through a nonlinear parametric transformation .
These rectified Gaussian units allow spike-and-slab type sparsity , while retaining the differentiability necessary for efficient stochastic gradient variational inference . To learn the parameters of the new model , we approximate the posterior of the latent variables with a variational auto-encoder . Rather than making the usual mean-field assumption however , the encoder parameterizes a new type of structured variational approximation that retains the prior dependencies of the generative model .
However , the high rate of false positive/negative interactions in PINs prevents accurately detecting complexes directly from the raw PINs . In this paper , we propose a denoising approach for protein complex detection by using variational graph auto-encoder . First , we embed a PIN to vector space by a stacked graph convolutional network ( GCN ) , then decide which interactions in the PIN are credible .
In this paper , we propose an efficient learning based sub-pixel image compression algorithm . Our framework builds upon the previous variational auto-encoder architecture and reduces the computational complexity significantly . Specifically , we propose an end-to-end optimized image compression framework to utilize the powerful non-linear representation ability of neural networks . This framework follows the widely used variational auto-encoder architecture and is optimized based on the rate-distortion balance . More importantly , a sub-pixel image compression framework is exploited to reduce the spatial resolution of image and improve the inference speed .
In this paper , we interpret source separation as a style transfer problem . We present a variational auto-encoder network that exploits the commonality across the domain of mixtures and the domain of clean sounds and learns a shared latent representation across the two domains . Using these cycle-consistent variational auto-encoders , we learn a mapping from the mixture domain to the domain of clean sounds and perform source separation without explicitly supervising with paired training examples .
Our pooling operation effectively encodes the correspondence between coarser and finer meshes in the hierarchy . We then present a variational auto-encoder ( VAE ) structure with the edge contraction pooling and graph-based convolutions , to explore probability latent spaces of 3D surfaces and perform 3D shape generation . Our network requires far fewer parameters than the original mesh VAE and thus can handle denser models thanks to our new pooling operation and convolutional kernels .
Moreover , the vanilla approach of simply concatenating multiple short sentences , possibly synthesized from a classical image captioning system , does n’t embrace the intricacies of paragraphs : coherent sentences , globally consistent structure , and diversity . To address those challenges , we propose to augment paragraph generation techniques with “ coherence vectors , ” “ global topic vectors , ” and modeling of the inherent ambiguity of associating paragraphs with images , via a variational auto-encoder formulation . We demonstrate the effectiveness of the developed approach on two datasets , outperforming existing state-of-the-art techniques on both .
We present ` Bits Back with ANS ' ( BB-ANS ) , a scheme to perform lossless compression with latent variable models at a near optimal rate . We demonstrate this scheme by using it to compress the MNIST dataset with a variational auto-encoder model ( VAE ) , achieving compression rates superior to standard methods with only a simple VAE . Given that the scheme is highly amenable to parallelization , we conclude that with a sufficiently high quality generative model this scheme could be used to achieve substantial improvements in compression rate with acceptable running time .
Motivated by this , in this paper , we learn a feature space using the shape information which is a strong prior shared among different datasets and robust to the appearance variation of input data . The shape feature is captured using a Variational Auto-Encoder ( VAE ) network that trained with only the ground truth masks . During testing , the segmentation results with bad shapes shall not fit the shape prior well , resulting in large loss values .
Assuming that the invariant features are now called we enrich the generative story by similarly providing two distinct ( independent ) sources for ; a discrete ( in case of classification ) variable which denotes the label of the data point and a continuous latent variable which encodes the variation on that is not explained by ( dependent noise ) . The process now can be formally defined as : Similarly to the unsupervised case we use a variational auto - encoder and jointly optimize the variational and model parameters . The lower bound now becomes : where we assume that the posterior is factorized as , and where : with again being an appropriate probability distribution for the data we are modelling .
We introduce a simple recurrent variational auto - encoder architecture that significantly improves image modeling . The system represents the state - of - the - art in latent variable models for both the ImageNet and Omniglot datasets .
In this paper we propose a method that is able to transform an image into a progression of increasingly detailed representations , ranging from global conceptual aspects to low level details ( see Figures [ reference ] & [ reference ] ) . At the same time , our model greatly improves latent variable image modeling compared to earlier implementations of deep variational auto - encoders . Furthermore , it has the advantage of being a simple homogeneous architecture not requiring complex design choices , which is similar to the recurrent structure of DRAW ( ) . Last , it provides an important insight into building good variational auto - encoder models of images : the use of multiple layers of stochastic variables that are all ‘ close ’ to the pixels significantly improves performance . The system ’s ability to stratify information enables it to perform high quality lossy compression , by storing only a subset of latent variables , starting with the high level ones , and generating the remainder during decompression ( see Figure [ reference ] ) .
Numerous techniques exist for unsupervised learning in deep networks , e.g. sparse auto - encoders and sparse coding , denoising auto - encoders , deconvolutional networks , restricted Boltzmann machines , deep Boltzmann machines , generative adversarial networks and variational auto - encoders . In this paper we focus on the class of models in the variational auto - encoding framework . Since we are also interested in compression , we present them from an information - theoretic perspective .
Thus , sharp reconstructions should not be a property of high - precision values in the network , but should rather be the result of an iterative feedback mechanism that is robust to network parameter change . Such a mechanism is provided by the DRAW algorithm , which is a recurrent type of variational auto - encoder . At each time step , DRAW maintains a provisionary reconstruction , takes in information about a given image , stores it in latent variables and updates the reconstruction .
We also report the likelihood for a ( non - recurrent ) variational auto - encoder and standard DRAW . For the variational auto - encoder we tested architectures with multiple layers , both deterministic and stochastic but with standard functional forms , and this was the best result that we obtained . Convolutional DRAW performs significantly better .
The motivation for using the auto - encoder branch is to add additional guidance and regularization to the encoder part , since the training dataset size is limited . We follow the variational auto - encoder ( VAE ) approach to better cluster / group the features of the encoder endpoint . We describe the building parts of our networks in the next subsections ( see also Figure [ reference ] )
The architecture is sketched in Fig . [ reference ] , alongside a feedforward variational auto - encoder . subsection : Network Architecture
The choice of the decoder depends on the task . For link prediction , the bilinear inner product is used in the context of the variational graph autoencoder ( VGAE ) . For semi - supervised node classification , the softmax activation function is employed .
Effective solutions to the DGP problem have the potential to accelerate the therapeutic development pipeline at early stages via efficient prioritization of candidate genes for various diseases . In this work , we introduce the variational graph auto-encoder ( VGAE ) as a promising unsupervised approach for learning powerful latent embeddings in disease-gene networks that can be used for the DGP problem , the first approach using a generative model involving graph neural networks ( GNNs ) . In addition to introducing the VGAE as a promising approach to the DGP problem , we further propose an extension ( constrained-VGAE or C-VGAE ) which adapts the learning algorithm for link prediction between two distinct node types in heterogeneous graphs .
Being an extension of VAE model , VGAE , also suffers from over-pruning in principal . In this paper we look at over-pruning in VGAE and observe that the generative capacity of VGAE is limited because of the way VGAE deals with this issue . We then propose epitomic variational graph autoencoder ( EVGAE ) , a generative variational framework for graph datasets to overcome over-pruning .
We introduce the variational graph auto-encoder ( VGAE ) , a framework for unsupervised learning on graph-structured data based on the variational auto-encoder ( VAE ) . This model makes use of latent variables and is capable of learning interpretable latent representations for undirected graphs .
Variational Graph Autoencoder ( VGAE ) has recently gained traction for learning representations on graphs . Its inception has allowed models to achieve state-of-the-art performance for challenging tasks such as link prediction , rating prediction , and node clustering .
Fixing the auto-encoder enables a fairer assessment on the size of a nodes receptive field in building representations . Furthermore a by-product of fixing the auto-encoder design often results in substantially smaller networks than their VGAE counterparts especially as we increase the number of feature propagations . A comparative downstream evaluation on link prediction tasks show comparable state of the art performance to similar VGAE arrangements despite considerable simplification .
The choice of the decoder depends on the task . For link prediction , the bilinear inner product is used in the context of the variational graph autoencoder ( VGAE ) . For semi - supervised node classification , the softmax activation function is employed .
Table [ reference ] shows the efficacy of the MTGAE model for MTL when compared against recent state - of - the - art task - specific link prediction and node classification models , which require the complete adjacency matrix as input . For link prediction , MTGAE significantly outperforms the best VGAE model on Cora and Citeseer . For node classification , MTGAE is the best performing model on the Citeseer and Pubmed datasets , which have very low node label rates .
However , these methods have obvious drawbacks of poor performance and expensive computation for largescale networks . In this work , we propose a novel solution to identify SH spanner based on graph embedding learning . Considering the special topological nature of SH spanner in the network , we design a deep embedding learning method for detecting SH spanner .
In order to pursue aligned representation , conventional approaches tend to construct and optimize a linear projection or train a complex architecture of deep layers , yet it is difficult to compromise between accuracy and efficiency on modeling multimodal data . This paper proposes a novel graph-embedding learning framework implemented by neural networks . The learned embedding directly approximates the cross-modal aligned representation to perform cross-modal retrieval and image classification combining text information .
Moreover , a heuristic negative sample selection scheme is adopted to make the classification more effective . In applications to tracking , the graph-embedding-based learning is incorporated into a Bayesian inference framework cascaded with hierarchical motion estimation , which significantly improves the accuracy and efficiency of the localization . Furthermore , an incremental updating technique for the graphs is developed to capture the changes in both appearance and illumination .
Graph embedding-based learning methods have been widely employed to reduce the dimensionality of high-dimensional data , while how to construct adjacency graphs to discover the essential structure of the data is the key problem in these methods . In this paper , we present a novel algorithm called graph discriminant embedding ( GDE ) for feature extraction and recognition .
Algorithmically , the proposed approach consists in computing a mapping based on pairwise dissimilarity where learning a linear decision function is amenable . Our experimental results show that the Wasserstein distance embedding performs better than kernel mean embeddings and computing Wasserstein distance is far more tractable than estimating pairwise Kullback-Leibler divergence of empirical distributions .
Algorithmically , the proposed approach is very simple as it consists in computing a mapping based on pairwise Wasserstein distances and then learning a linear decision function . Our experimental results show that this Wasserstein distance embedding performs better than kernel mean embeddings and computing Wasserstein distance is far more tractable than estimating pairwise Kullback-Leibler divergence of empirical distributions .
We examine empirically the representational capacity of our learned Wasserstein embeddings , showing that they can embed a wide variety of metric structures with smaller distortion than an equivalent Euclidean embedding . We also investigate an application to word embedding , demonstrating a unique advantage of Wasserstein embeddings : We can visualize the high-dimensional embedding directly , since it is a probability distribution on a low-dimensional space . This obviates the need for dimensionality reduction techniques like t-SNE for visualization .
For the generalised minimum spanning tree problem , we analyse the two approaches presented by Hu and Raidl ( 2012 ) with respect to the number of clusters that distinguish each other by the chosen representation of possible solutions . Our results show that a ( 1 + 1 ) evolutionary algorithm working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem , whereas the problem can be solved in fixed-parameter time with the global structure representation . We present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other ’s hard instances very efficiently .
VII . On the global structure of models for reflective truth . PART D : LEVELS OF TRUTH AND PROOF THEORY .
Specifically , we first build the spatial pyramid representation to capture context information of objects at different scales . Guided by the task-specific information , we combine the dense global structure representation and local texture patterns at each spatial location effectively using the spatial attention mechanism . In this way , the network is enforced to focus on the discriminative regions with context information for domain adaption .
The final descriptions ( global feature graphs ) are based on the quasi-convexity ( concavity ) structures incorporating quantized directional features of closed boundaries of cross-sections along several directions . The global feature graphs have the following properties : ( 1 ) They provide a characterization of global , structural , qualitative properties of the object ; ( 2 ) The graphs are composed of a few components ( nodes and edges ) with rich features , and give compact descriptions of the objects ; ( 3 ) The global feature graph representations are robust and qualitative in that they are not affected by geometrical , quantitative properties of the shape such as curvatures , length , and position ; ( 4 ) The representation has clear and rigorous properties . Furthermore , we present some theoretical basis for object recognition using the global features graphs .
Graph convolutional network is utilized to perform graph representation encoding . Unlike traditional clustering approaches relying on hand-crafted criteria , our method learns to cluster graph-structured data by maximizing mutual information between the global-graph representation and local-graph representations . The learnt graph embeddings can preserve global information in all locations of local-graphs such as pseudo labels for image clustering tasks .
This paper proposes a novel framework to identify and localize salient regions in a crowd scene , by transforming low-level features extracted from crowd motion field into a global similarity structure . The global similarity structure representation allows the discovery of the intrinsic manifold of the motion dynamics , which could not be captured by the low-level representation . Ranking is then performed on the global similarity structure to identify a set of extrem a.
In this paper , we investigate the problem of retrieving candidate lists for matching partial fingerprints by exploiting global topological features . Specifically , we propose an analytical approach for reconstructing the global topology representation from a partial fingerprint . First , we present an inverse orientation model for describing the reconstruction problem .
In particular , lung cancer diagnosis would benefit from segmentations reaching most distal airways . We present a method that combines descriptors of bronchi local appearance and graph global structural analysis to fine-tune thresholds on the descriptors adapted for each bronchial level . We have compared our method to the top performers of the EXACT09 challenge and to a commercial software for biopsy planning evaluated in an own-collected data-base of high resolution CT scans acquired under different breathing conditions .
In this paper , we present a review of the latest developments on this topic . We compare modern methods based on matrix factorization , including GraRep [ 5 ] , HOPE [ 22 ] , DeepWalk [ 23 ] , and node2vec [ 12 ] , in a collection of 12 real-world networks . We find that the performance of methods depends on the applications and the specific characteristics of the networks .
In this paper , we present { GraRep } , a novel model for learning vertex representations of weighted graphs . This model learns low dimensional vectors to represent vertices appearing in a graph and , unlike existing work , integrates global structural information of the graph into the learning process .
This paper proposes a drug-target interaction prediction method that can integrate information from different heterogeneous networks . This method constructs multiple drug and target similarity networks and applies the GraRep algorithm on the similarity networks after denoising in order to extract the features . Features obtained from heterogeneous networks are combined as a feature vector of DTIs , which is the input of Random Forest .
We exclude other matrix factorization approaches which have already been shown to be inferior to DeepWalk . We also exclude a recent approach , GraRep , that generalizes LINE to incorporate information from network neighborhoods beyond 2 - hops , but is unable to efficiently scale to large networks . In contrast to the setup used in prior work for evaluating sampling - based feature learning algorithms , we generate an equal number of samples for each method and then evaluate the quality of the obtained features on the prediction task .
Multi-layered Graph Embedding with Graph Convolutional Networks GEMSEC: Graph Embedding with Self Clustering Adaptive Graph Embedding Discriminant Projections Deep multi-granularity graph embedding for user identity linkage across social networks Learning a discriminant graph-based embedding with feature selection for image categorization Enhanced and parameterless Locality Preserving Projections for face recognition LINE: Large-scale Information Network Embedding Revisiting Semi-Supervised Learning with Graph Embeddings Neural Natural Language Inference Models Enhanced with External Knowledge Histopathology stain-color normalization using deep generative models A Structured Variational Auto-encoder for Learning Deep Hierarchies of Sparse Features Denoising Protein-Protein interaction network via variational graph auto-encoder for protein complex detection. Efficient Learning Based Sub-pixel Image Compression A Style Transfer Approach to Source Separation Mesh Variational Autoencoders with Edge Contraction Pooling Diverse and Coherent Paragraph Generation from Images Practical Lossless Compression with Latent Variables using Bits Back Coding An Alarm System for Segmentation Algorithm Based on Shape Model The Variational Fair Autoencoder Towards Conceptual Compression 3D MRI brain tumor segmentation using autoencoder regularization DRAW: A Recurrent Neural Network For Image Generation Learning to Make Predictions on Graphs with Autoencoders Towards Probabilistic Generative Models Harnessing Graph Neural Networks for Disease-Gene Prediction Epitomic Variational Graph Autoencoder Variational Graph Auto-Encoders Optimizing Variational Graph Autoencoder for Community Detection with Dual Optimization Decoupling feature propagation from the design of graph auto-encoders Learning to Make Predictions on Graphs with Autoencoders Multi-Task Graph Autoencoders Identifying Structural Hole Spanners in Social Networks via Graph Embedding Learning Cross-Modal Aligned Representation With Graph Embedding Graph-Embedding-Based Learning for Robust Object Tracking Feature extraction based on graph discriminant embedding and its applications to face recognition Distance Measure Machines Wasserstein Distance Measure Machines Learning Embeddings into Entropic Wasserstein Spaces A Parameterised Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms Logical frameworks for truth and abstraction - an axiomatic study Spatial Attention Pyramid Network for Unsupervised Domain Adaptation A structural approach to representation of curved objects A Graph-based Image Clustering Method Using Mutual Information Maximization Crowd Saliency Detection via Global Similarity Structure Global Ridge Orientation Modeling for Partial Fingerprint Identification Segmentation of distal airways using structural analysis A Comparative Study of Network Embedding Based on Matrix Factorization GraRep: Learning Graph Representations with Global Structural Information Drug-Target Interaction Prediction Based on Heterogeneous Networks node2vec: Scalable Feature Learning for Networks
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WWW '15 ICML ACL CVPR Workshops ECCV (2) ICLR NIPS BrainLes@MICCAI ICML 2018 IEEE 5th International Conference on Data Science and Advanced Analytics (DSAA) 2018 IEEE 5th International Conference on Data Science and Advanced Analytics (DSAA) ArXiv COCOA ICLR (Poster) ROBIO ICPR DMBD CIKM KDD
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