The edges connecting the nodes indicate that these nodes represent the same landmark or place , even though places and landmarks encoded by the nodes may exhibit different appearances in the long-term periods . Then , a graph embedding is learned to preserve the locality in the feature descriptor space , i.e. , finding a projection such that the same landmark and place have the identical representation in the new projected descriptor space , no matter in what scenarios they are recorded . We formulate the embedding learning as an optimization problem and implement a new solver that provides a theoretical convergence guarantee . By utilizing a multi-layer classifier , a scheduling strategy can be learned in a supervised manner based on the graph embedding results for each node . We also propose an unsupervised manner to train the graph embedding based method to further reinforce the scalability and generalizability and develop a K-nearest neighbor graph representation method to reduce the computational complexity . Extensive simulation demonstrates that the proposed method is near-optimal compared with the existing state-of-art methods but is with only hundreds of training samples . ABSTRACT Recently , graph embedding-based methods have drawn increasing attention for dimensionality reduction ( DR ) of hyperspectral image ( HSI ) classification . Graph construction is a critical step for those DR methods . Graph-based embedding methods receive much attention due to the use of graph and manifold information . However , conventional graph-based embedding methods may not always be effective if the data have high dimensions and have complex distributions . First , the similarity matrix only considers local distance measurement in the original space , which can not reflect a wide variety of data structures . This paper proposes a novel discriminant semi-supervised feature extraction method for generic classification and recognition tasks . This method , called inductive flexible semi-supervised feature extraction , is a graph-based embedding method that seeks a linear subspace close to a non-linear one . It is based on a criterion that simultaneously exploits the discrimination information provided by the labeled samples , maintains the graph-based smoothness associated with all samples , regularizes the complexity of the linear transform , and minimizes the discrepancy between the unknown linear regression and the unknown non-linear projection . 3 ) the LoNGAE model can be trained end - to - end in a single stage for multi - task learning of link prediction and semi - supervised node classification . On the other hand , training SDNE requires multiple steps that are difficult to jointly optimize : i ) pre - training via a deep belief network ; and ii ) utilizing a separate downstream classifier on top of node embeddings for LPNC . Lastly , GCNs are a recent class of algorithms based on convolutional encoders for learning node embeddings . subsection : Datasets and Baselines We evaluate our proposed autoencoder models on nine graph - structured datasets , spanning multiple application domains , from which previous graph embedding methods have achieved strong results for LPNC . The datasets are summarized in Table [ reference ] and include networks for Protein interactions , Metabolic pathways , military Conflict between countries , the U.S. PowerGrid , collaboration between users on the BlogCatalog social website , and publication citations from the Cora , Citeseer , Pubmed , Arxiv - GRQC databases . Interestingly , we also observe that Graph2Seq - PGE ( pooling - based graph embedding ) performs better than Graph2Seq - NGE ( node - based graph embedding ) . One potential reason is that the node - based graph embedding method artificially added a super node in graph which changes the original graph topology and brings unnecessary noise into the graph . figureA running example of the NLG task . In this paper , we propose a new nonlinear dimensionality reduction method by combining Locally Linear Embedding ( LLE ) with Laplacian Eigenmaps , and apply it to hyperspectral data . LLE projects high dimensional data into a low-dimensional Euclidean space while preserving local topological structures . A multi-matcher system is proposed where each matcher is trained using features extracted from a single sub-window of the whole 2D image . The features are extracted by the convolution of each sub-window with a bank of Gabor Filters , then their dimensionality is reduced by Laplacian EigenMaps . The best matchers , corresponding to the most discriminative sub-windows , are selected by running the Sequential Forward Floating Selection ( SFFS ) . This has large ramifications in improved acquisition of nuclear magnetic resonance spectra , for which we give several examples . The second part of this thesis studies the Laplacian Eigenmaps ( LE ) algorithm and its uses in data fusion . In particular , we build a natural approximate inversion algorithm for LE embeddings using L regularization and MDS embedding techniques . We are exploring the novel technique of Laplacian Eigenmaps ( LE ) [ 1 ] as a means of improving the clustering-based segmentation of multivariate images . A computationally efficient scheme , taking advantage of the ability of LE-algorithm to learn the actual manifold of the multivariate data , is introduced . Based on the proposed DM-EVD , a deviation based methodology is then proposed to include more dimension reduction methods . In this work , the incorporation of Laplacian Eigen-map and Principal Component Analysis ( PCA ) are explored , and the latter algorithm is named as PCA-Dev and is validated in the case study . To show the successful application of the proposed methodology , case studies from diverse fields are presented and investigated in this work . Large-Scale Web Graph Embedding via Laplacian Eigenmap Approximation . The Web as a graph can be embedded in a low-dimensional space where its geometry can be visualized and studied in order to mine interesting patterns such as web communities . The framework is based on an information theoretic criterion , which favors objects that reduce the uncertainty of the visualization . We present a concrete application of the proposed framework to the Laplacian eigenmap visualization method . We demonstrate experimentally that the proposed framework yields the desired visualization with fewer user interactions than existing methods . Connectivity measurements , i.e. , whether or not two sensors can communicate , can be used to calculate localization in networks of inexpensive wireless sensors . We show that a Laplacian eigenmaps-based algorithm , combined with an adaptive neighbor weighting method , can provide an accurate , low complexity solution . Laplacian eigenmaps is a manifold learning method which optimizes using eigen-decomposition , thus is non-iterative and finds the global optimum . We preserve the significance of a color sequence during decolorization by mapping the colors from a source image to a grid in the CIELAB color space . We then identify the most significant hues , and thin the corresponding cells of the grid to approximate a curve in the color space , eliminating outliers using a weighted Laplacian eigenmap . This curve is then mapped to a monotonic sequence of gray levels . Most existing graph embedding algorithms do not scale for networks of this size . For example , the time complexity of classical graph embedding algorithms such as MDS , IsoMap , Laplacian eigenmap are at least quadratic to the number of vertices , which is too expensive for networks with millions of nodes . Although a few very recent studies approach the embedding of large - scale networks , these methods either use an indirect approach that is not designed for networks ( e.g. , ) or lack a clear objective function tailored for network embedding ( e.g. , ) . section : Related Work Our work is related to classical methods of graph embedding or dimension reduction in general , such as multidimensional scaling ( MDS ) , IsoMap , LLE and Laplacian Eigenmap . These approaches typically first construct the affinity graph using the feature vectors of the data points , e.g. , the K - nearest neighbor graph of data , and then embed the affinity graph into a low dimensional space . In addition , since spectral synchronization couples with graph alignment , providing rough shape graph correspondences could facilitate good prediction . Based on these , we use voxel functions that is computed from laplacian eigenbases as the input to SpecTN : Specifically , is a volumetric reparameterization of the graph laplacian eigenbases , defined voxel - wise in 3D volumetric space . The volumetric reparameterization is conducted by converting graph vertex function into voxel function in a straightforward manner – we simply assign a vertex function value to the voxel where the vertex lies . We compare and evaluate an extensive number of different model selection criteria for this purpose and examine which factors can affect their performance . We conclude that SSC , GIC , MCAIC and CAIC have a better performance ( for this particular application ) compared to the other criteria . The class of simple HK ( S-HK ) schemes includes the TIN scheme and schemes that involve various levels of interference decoding and cancellation at each receiver . For the 2-user GIC , simple HK schemes are sufficient to achieve all known sum capacity results — sum capacity under mixed , strong and noisy interference conditions . We derive channel conditions under which simple HK schemes achieve sum capacity for general K-user Gaussian ICs . In this paper , a cooperative power control scheme is proposed for two-user Gaussian interference channel ( GIC ) to mitigate the interference and improve the sum-rate . In the proposed scheme , codewords are divided into several segments . In this presentation , a CMOS custom Integrated Circuit featuring a multi-stage Universal Switched-Capacitor ( SC ) Filter is Introduced . The network is based on the Generalized Immittance Converter ( GIC ) configuration , known for its excellent passive and active sensitivities . CMOS switches were used for elements relocation and are digitally controlled to select and realized different filter topologies . In this paper , we develop a new upper-bounding technique that utilizes a new type of genie signal and applies < italic > time sharing</italic > to genie signals at < inline-formula > < tex-math notation="LaTeX">$K$ < /tex-math></inline-formula > receivers . Based on this technique , we derive new upper bounds on the sum capacity of the three-user GIC with constant , complex channel coefficients and then generalize to the < inline-formula > < tex-math notation="LaTeX">$K$ < /tex-math></inline-formula>-user case to better understand sum-rate behavior at finite SNR . We also provide closed-form expressions of our upper bounds on the capacity of the < inline-formula > < tex-math notation="LaTeX">$K$ < /tex-math></inline-formula>-user symmetric GIC easily computable for < italic > any</italic > < inline-formula > < tex-math notation="LaTeX">$K$ < /tex-math></inline-formula>. From the perspectives of our results , some sum-rate behavior at finite SNR is in line with the insights given by the known DoF results , while some others are not . The test model had the same geometry , conductor surface finish and insulators as the 242 kV commercial system currently offered by ABB . The results from the tests were used to establish the dielectric design parameters for the 420 kV GIC system as well as the satisfactory ratios of SFS in N2 , ( SFfl2 ) . 1 . ~troduction EdF is evaluating the various possibilities of reducing the environmental impact of its grid . A simple modification of Antoniou 's generalised impedance converter ( GIC ) was presented recently by Wangenheim . An equally simple alternative modification of the Antoniou GIC circuit is highlighted here . One advantage this approach has is that it allows us to separate the estimation of the marginal distribution from the estimation of the joint distribution of underlying bidder values . The third chapter is an empirical study of the municipal GIC auctions , motivated by the theoretical frameworks developed in the first two chapters . This study deals with the operation of the wind power generation system ( WPGS ) having active filter capabilities using the grid-interfacing converter ( GIC ) control approach . A novel current decomposition technique based on enhanced instantaneous power theory ( EIPT ) is suggested for controlling the GIC to realise an improved power quality ( PQ ) in WPGS and to provide the requisite reactive power support . Cost-effective task scheduling is an important operation in green infrastructure-as-a-service clouds ( GICs ) as the energy consumed by users ’ tasks is drastic . The irregular task arrival forces private GIC to adopt hybrid clouds to outsource some tasks to dynamic and reliable virtual machines ( VMs ) of public external clouds . However , temporal differences in revenue , electricity prices , wind and solar energy , and VM running prices of public external clouds make it difficult to dispatch all tasks in a cost-effective way while satisfying users ’ specified response time constraints . In contrast , screen readers allow for deep engagement with content ( when content is accessible ) , and provide fine-grained navigation & control , but at the cost of increased complexity , and reduced walk-up-and-use convenience . In this demonstration , we showcase VERSE , a system that combines the positive aspects of VAs and screen readers , and allows other devices ( e.g. , smart watches ) to serve as optional input accelerators . Together , these features allow people with visual impairments to deeply engage with web content through voice interaction . The results show that SVDS pulses simultaneously reduce integrated RF power and peak RF by about 30 % on average compared to CVDS pulses for a square pattern ( $ 80\times80 $ mm2 ) with flip angles of 30 ° , 90 ° , and 180 ° . Compared with the VERSE method under the same peak RF constraints , the SVDS method reduces integrated RF power by an average of 20 % for small tip excitations for profiles of slice , rectangular , square , and circle , and has slightly reduced excitation accuracy slightly ( about 0.6 % , from 6.8 % to 7.4 % ) . The SVERSE method shortens the duration of the VERSE pulse by 12.8 % at large ti p angle ( 180 ° ) . A Variable Rate Selective Excitation ( VERSE ) is a type of Radio Frequency ( RF ) pulse that reduces the Specific Absorption Rate ( SAR ) of molecules in a specimen . As high levels of SAR lead to increased patient temperatures during Magnetic Resonance Imaging ( MRI ) procedures , we develop a selective VERSE pulse that is designed to minimize SAR while preserving its duration and slice profile ; called the generalized VERSE ( gVERSE ) . After the formulation of a rigorous mathematical model , the nonlinear gVERSE optimization problem is solved via an optimal control approach . It is most commonly used to reduce the peak magnitude and specific absorption rate ( SAR ) of RF pulses by reshaping pulses and gradient waveforms to reduce RF magnitude while preserving excitation profiles . In this work , a general time-optimal VERSE algorithm for multidimensional and parallel transmit pulses is presented . Time optimality is achieved by translating peak RF limits to gradient upper bounds in excitation k-space . The limits are fed into a time-optimal gradient waveform design technique . Effective SAR reduction is achieved by reducing peak RF subject to a fixed pulse length . The presented method is different from other VERSE techniques in that it provides a noniterative time-optimal multidimensional solution , which drastically simplifies VERSE designs . Examples are given for 1D and 2D single channel and 2D parallel transmit pulses . Yet , as we show , the objectives used in past works implicitly utilize similarity measures among graph nodes . In this paper , we carry the similarity orientation of previous works to its logical conclusion ; we propose VERtex Similarity Embeddings ( VERSE ) , a simple , versatile , and memory-efficient method that derives graph embeddings explicitly calibrated to preserve the distributions of a selected vertex-to-vertex similarity measure . VERSE learns such embeddings by training a single-layer neural network .
The edges connecting the nodes indicate that these nodes represent the same landmark or place , even though places and landmarks encoded by the nodes may exhibit different appearances in the long-term periods . Then , a graph embedding is learned to preserve the locality in the feature descriptor space , i.e. , finding a projection such that the same landmark and place have the identical representation in the new projected descriptor space , no matter in what scenarios they are recorded . We formulate the embedding learning as an optimization problem and implement a new solver that provides a theoretical convergence guarantee .
By utilizing a multi-layer classifier , a scheduling strategy can be learned in a supervised manner based on the graph embedding results for each node . We also propose an unsupervised manner to train the graph embedding based method to further reinforce the scalability and generalizability and develop a K-nearest neighbor graph representation method to reduce the computational complexity . Extensive simulation demonstrates that the proposed method is near-optimal compared with the existing state-of-art methods but is with only hundreds of training samples .
ABSTRACT Recently , graph embedding-based methods have drawn increasing attention for dimensionality reduction ( DR ) of hyperspectral image ( HSI ) classification . Graph construction is a critical step for those DR methods .
Graph-based embedding methods receive much attention due to the use of graph and manifold information . However , conventional graph-based embedding methods may not always be effective if the data have high dimensions and have complex distributions . First , the similarity matrix only considers local distance measurement in the original space , which can not reflect a wide variety of data structures .
This paper proposes a novel discriminant semi-supervised feature extraction method for generic classification and recognition tasks . This method , called inductive flexible semi-supervised feature extraction , is a graph-based embedding method that seeks a linear subspace close to a non-linear one . It is based on a criterion that simultaneously exploits the discrimination information provided by the labeled samples , maintains the graph-based smoothness associated with all samples , regularizes the complexity of the linear transform , and minimizes the discrepancy between the unknown linear regression and the unknown non-linear projection .
3 ) the LoNGAE model can be trained end - to - end in a single stage for multi - task learning of link prediction and semi - supervised node classification . On the other hand , training SDNE requires multiple steps that are difficult to jointly optimize : i ) pre - training via a deep belief network ; and ii ) utilizing a separate downstream classifier on top of node embeddings for LPNC . Lastly , GCNs are a recent class of algorithms based on convolutional encoders for learning node embeddings .
subsection : Datasets and Baselines We evaluate our proposed autoencoder models on nine graph - structured datasets , spanning multiple application domains , from which previous graph embedding methods have achieved strong results for LPNC . The datasets are summarized in Table [ reference ] and include networks for Protein interactions , Metabolic pathways , military Conflict between countries , the U.S. PowerGrid , collaboration between users on the BlogCatalog social website , and publication citations from the Cora , Citeseer , Pubmed , Arxiv - GRQC databases .
Interestingly , we also observe that Graph2Seq - PGE ( pooling - based graph embedding ) performs better than Graph2Seq - NGE ( node - based graph embedding ) . One potential reason is that the node - based graph embedding method artificially added a super node in graph which changes the original graph topology and brings unnecessary noise into the graph . figureA running example of the NLG task .
In this paper , we propose a new nonlinear dimensionality reduction method by combining Locally Linear Embedding ( LLE ) with Laplacian Eigenmaps , and apply it to hyperspectral data . LLE projects high dimensional data into a low-dimensional Euclidean space while preserving local topological structures .
A multi-matcher system is proposed where each matcher is trained using features extracted from a single sub-window of the whole 2D image . The features are extracted by the convolution of each sub-window with a bank of Gabor Filters , then their dimensionality is reduced by Laplacian EigenMaps . The best matchers , corresponding to the most discriminative sub-windows , are selected by running the Sequential Forward Floating Selection ( SFFS ) .
This has large ramifications in improved acquisition of nuclear magnetic resonance spectra , for which we give several examples . The second part of this thesis studies the Laplacian Eigenmaps ( LE ) algorithm and its uses in data fusion . In particular , we build a natural approximate inversion algorithm for LE embeddings using L regularization and MDS embedding techniques .
We are exploring the novel technique of Laplacian Eigenmaps ( LE ) [ 1 ] as a means of improving the clustering-based segmentation of multivariate images . A computationally efficient scheme , taking advantage of the ability of LE-algorithm to learn the actual manifold of the multivariate data , is introduced .
Based on the proposed DM-EVD , a deviation based methodology is then proposed to include more dimension reduction methods . In this work , the incorporation of Laplacian Eigen-map and Principal Component Analysis ( PCA ) are explored , and the latter algorithm is named as PCA-Dev and is validated in the case study . To show the successful application of the proposed methodology , case studies from diverse fields are presented and investigated in this work .
Large-Scale Web Graph Embedding via Laplacian Eigenmap Approximation . The Web as a graph can be embedded in a low-dimensional space where its geometry can be visualized and studied in order to mine interesting patterns such as web communities .
The framework is based on an information theoretic criterion , which favors objects that reduce the uncertainty of the visualization . We present a concrete application of the proposed framework to the Laplacian eigenmap visualization method . We demonstrate experimentally that the proposed framework yields the desired visualization with fewer user interactions than existing methods .
Connectivity measurements , i.e. , whether or not two sensors can communicate , can be used to calculate localization in networks of inexpensive wireless sensors . We show that a Laplacian eigenmaps-based algorithm , combined with an adaptive neighbor weighting method , can provide an accurate , low complexity solution . Laplacian eigenmaps is a manifold learning method which optimizes using eigen-decomposition , thus is non-iterative and finds the global optimum .
We preserve the significance of a color sequence during decolorization by mapping the colors from a source image to a grid in the CIELAB color space . We then identify the most significant hues , and thin the corresponding cells of the grid to approximate a curve in the color space , eliminating outliers using a weighted Laplacian eigenmap . This curve is then mapped to a monotonic sequence of gray levels .
Most existing graph embedding algorithms do not scale for networks of this size . For example , the time complexity of classical graph embedding algorithms such as MDS , IsoMap , Laplacian eigenmap are at least quadratic to the number of vertices , which is too expensive for networks with millions of nodes . Although a few very recent studies approach the embedding of large - scale networks , these methods either use an indirect approach that is not designed for networks ( e.g. , ) or lack a clear objective function tailored for network embedding ( e.g. , ) .
section : Related Work Our work is related to classical methods of graph embedding or dimension reduction in general , such as multidimensional scaling ( MDS ) , IsoMap , LLE and Laplacian Eigenmap . These approaches typically first construct the affinity graph using the feature vectors of the data points , e.g. , the K - nearest neighbor graph of data , and then embed the affinity graph into a low dimensional space .
In addition , since spectral synchronization couples with graph alignment , providing rough shape graph correspondences could facilitate good prediction . Based on these , we use voxel functions that is computed from laplacian eigenbases as the input to SpecTN : Specifically , is a volumetric reparameterization of the graph laplacian eigenbases , defined voxel - wise in 3D volumetric space . The volumetric reparameterization is conducted by converting graph vertex function into voxel function in a straightforward manner – we simply assign a vertex function value to the voxel where the vertex lies .
We compare and evaluate an extensive number of different model selection criteria for this purpose and examine which factors can affect their performance . We conclude that SSC , GIC , MCAIC and CAIC have a better performance ( for this particular application ) compared to the other criteria .
The class of simple HK ( S-HK ) schemes includes the TIN scheme and schemes that involve various levels of interference decoding and cancellation at each receiver . For the 2-user GIC , simple HK schemes are sufficient to achieve all known sum capacity results — sum capacity under mixed , strong and noisy interference conditions . We derive channel conditions under which simple HK schemes achieve sum capacity for general K-user Gaussian ICs .
In this paper , a cooperative power control scheme is proposed for two-user Gaussian interference channel ( GIC ) to mitigate the interference and improve the sum-rate . In the proposed scheme , codewords are divided into several segments .
In this presentation , a CMOS custom Integrated Circuit featuring a multi-stage Universal Switched-Capacitor ( SC ) Filter is Introduced . The network is based on the Generalized Immittance Converter ( GIC ) configuration , known for its excellent passive and active sensitivities . CMOS switches were used for elements relocation and are digitally controlled to select and realized different filter topologies .
In this paper , we develop a new upper-bounding technique that utilizes a new type of genie signal and applies < italic > time sharing</italic > to genie signals at < inline-formula > < tex-math notation="LaTeX">$K$ < /tex-math></inline-formula > receivers . Based on this technique , we derive new upper bounds on the sum capacity of the three-user GIC with constant , complex channel coefficients and then generalize to the < inline-formula > < tex-math notation="LaTeX">$K$ < /tex-math></inline-formula>-user case to better understand sum-rate behavior at finite SNR . We also provide closed-form expressions of our upper bounds on the capacity of the < inline-formula > < tex-math notation="LaTeX">$K$ < /tex-math></inline-formula>-user symmetric GIC easily computable for < italic > any</italic > < inline-formula > < tex-math notation="LaTeX">$K$ < /tex-math></inline-formula>. From the perspectives of our results , some sum-rate behavior at finite SNR is in line with the insights given by the known DoF results , while some others are not .
The test model had the same geometry , conductor surface finish and insulators as the 242 kV commercial system currently offered by ABB . The results from the tests were used to establish the dielectric design parameters for the 420 kV GIC system as well as the satisfactory ratios of SFS in N2 , ( SFfl2 ) . 1 . ~troduction EdF is evaluating the various possibilities of reducing the environmental impact of its grid .
A simple modification of Antoniou 's generalised impedance converter ( GIC ) was presented recently by Wangenheim . An equally simple alternative modification of the Antoniou GIC circuit is highlighted here .
One advantage this approach has is that it allows us to separate the estimation of the marginal distribution from the estimation of the joint distribution of underlying bidder values . The third chapter is an empirical study of the municipal GIC auctions , motivated by the theoretical frameworks developed in the first two chapters .
This study deals with the operation of the wind power generation system ( WPGS ) having active filter capabilities using the grid-interfacing converter ( GIC ) control approach . A novel current decomposition technique based on enhanced instantaneous power theory ( EIPT ) is suggested for controlling the GIC to realise an improved power quality ( PQ ) in WPGS and to provide the requisite reactive power support .
Cost-effective task scheduling is an important operation in green infrastructure-as-a-service clouds ( GICs ) as the energy consumed by users ’ tasks is drastic . The irregular task arrival forces private GIC to adopt hybrid clouds to outsource some tasks to dynamic and reliable virtual machines ( VMs ) of public external clouds . However , temporal differences in revenue , electricity prices , wind and solar energy , and VM running prices of public external clouds make it difficult to dispatch all tasks in a cost-effective way while satisfying users ’ specified response time constraints .
In contrast , screen readers allow for deep engagement with content ( when content is accessible ) , and provide fine-grained navigation & control , but at the cost of increased complexity , and reduced walk-up-and-use convenience . In this demonstration , we showcase VERSE , a system that combines the positive aspects of VAs and screen readers , and allows other devices ( e.g. , smart watches ) to serve as optional input accelerators . Together , these features allow people with visual impairments to deeply engage with web content through voice interaction .
The results show that SVDS pulses simultaneously reduce integrated RF power and peak RF by about 30 % on average compared to CVDS pulses for a square pattern ( $ 80\times80 $ mm2 ) with flip angles of 30 ° , 90 ° , and 180 ° . Compared with the VERSE method under the same peak RF constraints , the SVDS method reduces integrated RF power by an average of 20 % for small tip excitations for profiles of slice , rectangular , square , and circle , and has slightly reduced excitation accuracy slightly ( about 0.6 % , from 6.8 % to 7.4 % ) . The SVERSE method shortens the duration of the VERSE pulse by 12.8 % at large ti p angle ( 180 ° ) .
A Variable Rate Selective Excitation ( VERSE ) is a type of Radio Frequency ( RF ) pulse that reduces the Specific Absorption Rate ( SAR ) of molecules in a specimen . As high levels of SAR lead to increased patient temperatures during Magnetic Resonance Imaging ( MRI ) procedures , we develop a selective VERSE pulse that is designed to minimize SAR while preserving its duration and slice profile ; called the generalized VERSE ( gVERSE ) . After the formulation of a rigorous mathematical model , the nonlinear gVERSE optimization problem is solved via an optimal control approach .
It is most commonly used to reduce the peak magnitude and specific absorption rate ( SAR ) of RF pulses by reshaping pulses and gradient waveforms to reduce RF magnitude while preserving excitation profiles . In this work , a general time-optimal VERSE algorithm for multidimensional and parallel transmit pulses is presented . Time optimality is achieved by translating peak RF limits to gradient upper bounds in excitation k-space . The limits are fed into a time-optimal gradient waveform design technique . Effective SAR reduction is achieved by reducing peak RF subject to a fixed pulse length . The presented method is different from other VERSE techniques in that it provides a noniterative time-optimal multidimensional solution , which drastically simplifies VERSE designs . Examples are given for 1D and 2D single channel and 2D parallel transmit pulses .
Yet , as we show , the objectives used in past works implicitly utilize similarity measures among graph nodes . In this paper , we carry the similarity orientation of previous works to its logical conclusion ; we propose VERtex Similarity Embeddings ( VERSE ) , a simple , versatile , and memory-efficient method that derives graph embeddings explicitly calibrated to preserve the distributions of a selected vertex-to-vertex similarity measure . VERSE learns such embeddings by training a single-layer neural network .
Learning of Holism-Landmark Graph Embedding for Place Recognition in Long-Term Autonomy Graph Embedding based Wireless Link Scheduling with Few Training Samples Spatial-spectral neighbour graph for dimensionality reduction of hyperspectral image classification Locality Sensitive Discriminative Unsupervised Dimensionality Reduction Inductive and flexible feature extraction for semi-supervised pattern categorization Learning to Make Predictions on Graphs with Autoencoders Graph2Seq: Graph to Sequence Learning with Attention-based Neural Networks A new nonlinear dimensionality reduction method with application to hyperspectral image analysis A multi-matcher for ear authentication Exploiting Data-Dependent Structure for Improving Sensor Acquisition and Integration Multivariate image segmentation using Laplacian Eigenmaps A deviation based assessment methodology for multiple machine health patterns classification and fault detection Mani-Web: Large-Scale Web Graph Embedding via Laplacian Eigenmap Approximation Active Learning for Interactive Visualization Adaptive neighborhoods for manifold learning-based sensor localization Color Sequence Preserving Decolorization LINE: Large-scale Information Network Embedding SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation Detecting cylinders in 3D range data using model selection criteria On the Optimality of Interference Decoding Schemes for K-User Gaussian Interference Channels A Cooperative Power Control Scheme for Two-User Gaussian Interference Channel A VLSI implementation of a universal programmable low sensitivity sampled data filter Capacity Bounds for the $K$ -User Gaussian Interference Channel Lightning Impulse Withstand Performance of a Practical GIC With 5 and 10 Percent SFm2 Mixtures Alternative modification of the classical GIC structure Three Essays on Collusion in English Auctions: Theory and Application Integration of wind power generation through an enhanced instantaneous power theory Multiqueue Scheduling of Heterogeneous Tasks With Bounded Response Time in Hybrid Green IaaS Clouds Bridging Screen Readers and Voice Assistants for Enhanced Eyes-Free Web Search Squeezed Trajectory Design for Peak RF and Integrated RF Power Reduction in Parallel Transmission MRI The gVERSE RF Pulse: An Optimal Approach to MRI Pulse Design Time-optimal design for multidimensional and parallel transmit variable-rate selective excitation. VERSE: Versatile Graph Embeddings from Similarity Measures
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