( 3 ) The distance criterion generally provides a higher accuracy than the cosine criterion . The use of other p-norms ( p > 2 ) provides similar results to the Euclidean norm , nevertheless some methods perform better . ( 4 ) No spectral method can provide 100 % accuracy by itself . However , these methods suffer from the curse of dimensionality , i.e. , in large dimensions their complexity approaches $ O(N)$ per query data point . In the special case where the conditional probability distribution $ p(y|x)$ is a Gaussian centered at x , i.e. , $ p(y|x ) \propto N (x,\sigma)$ , the maximum likelihood classification reduces to the nearest neighbor search with the Euclidean norm . Sublinear methods based on locality sensitive hashing ( LSH ) have been introduced to solve an approximate version of the nearest neighbor search for high dimensional data . Abstract In this paper , we propose a modified Euclidean norm computation for breadth-first signal decoder ( BSIDE ) that reduces the computational complexity without sacrificing the performance . We exploit the reordered channel representation and rewrite the Euclidean norm computation in a simpler form , which results at significant reduction in number of operations required to decode the transmitted symbols . Also from the simulation results , it is observed that the reduction in complexity is 59 % for 2 × 2 and 75 % for the 4 × 4 multiple-input multiple output systems when compared to BSIDE . PFCM addresses the noise sensitivity defect of Fuzzy c-means ( FCM ) and overcomes the coincident cluster problem of possibilistic c-means ( PCM ) . Here we propose a new model called Kernel-based hybrid c-means clustering ( KPFCM ) where PFCM is extended by adopting a Kernel induced metric in the data space to replace the original Euclidean norm metric . Use of Kernel function makes it possible to cluster data that is linearly non-separable in the original space into homogeneous groups in the transformed high dimensional space . The main difficulty was the unfavorable influence of large amplitude impulses on the operation of nonlinear alignment ( or time-warping ) . When the classical definition of the alignment costs was replaced by the Euclidean norm based one , and when additionally the ordered weighted averaging was used to diminish the role of large noise impulses , the method appeared rather effective . Not only was it robust against this type of noise but also allowed for effective suppression of the usual Gaussian noise . The goal of this work is energy disaggregation . A recent work showed that instead of employing the usual Euclidean norm cost function for dictionary learning , better results can be achieved by learning the dictionaries in a robust fashion by employing an l1-norm cost function ; this is because energy data is corrupted by large but sparse outliers . In this work we propose to improve the robust dictionary learning approach by imposing low-rank penalty on the learned coefficients . This paper proposes a distributed model to compute a score that measures the quality of each feature with respect to multiple labels on Apache Spark . We propose two different approaches that study how to aggregate the mutual information of multiple labels : Euclidean Norm Maximization ( ENM ) and Geometric Mean Maximization ( GMM ) . The former selects the features with the largest L 2 -norm whereas the latter selects the features with the largest geometric mean . Then , the information IMFs and the mixed components after thresholding were selected to give the optimal signal reconstruction . Static and dynamic signal tests of the fiber optic gyroscope ( FOG ) were carried out to illustrate the performance of the proposed method , and compared with other traditional EMD denoising methods , such as the Euclidean norm measure method ( EMD-l2-norm ) and the sliding average filtering method ( EMD-SA ) . The results of the analysis of both the static and dynamic signal tests indicate the effectiveness of the proposed method . Next , a new method of optimizing a subtask criterion , defined using the infinity-norm , to perform additional tasks such as obstacle avoidance or joint limit avoidance is introduced . Simulations illustrating these methods and comparing the results with the Euclidean norm solutions are presented . It is well known that Hopfield neural networks without delays exhibit no oscillations and possess global stability ( i.e. , all trajectories tend to some equilibrium ) . In the present paper we show that if the bound /spl tau//spl beta//spl par/T/sub 2//spl par/ 0 , interconnection matrix T/sub 2/ associated with delays , and gain of the neurons given by /spl beta/ , will exhibit similar qualitative properties as the original Hopfield neural network without delays ( /spl par/T/sub 2//spl par/ denotes the matrix norm induced by the Euclidean vector norm ) . The envelopes are parameterized along principal axes of model inertia . As a distance measure among , we experimented with theEuclidean norm as well as a distance measure based on elastic matching by using the dynamic programming technique . Experiments showed that our approach could identify models having similar shapes fainy well . The mini - batch size is 100 . The autoencoder is trained with a Euclidean cost function for reconstruction . On the MNIST dataset we use the sigmoid activation function in the last layer of the autoencoder and on the TFD dataset we use the linear activation function . In this paper , we proposed an accelerated predictor-corrector iterated Tikhonov regularization . This method combined the classical iterated Tikhonov regularization with modified Euler method , which could improve computational efficiency without sacrificing numerical accuracy . The convergence rate of the accelerated regularization was investigated theoretically when the right-hand side was corrupted by noise . When the regularization matrix is the identity , iterated Tikhonov regularization can yield computed approximate solutions of higher quality than ( standard ) Tikhonov regularization . This paper provides an analysis of iterated Tikhonov regularization with a regularization matrix different from the identity . Computed examples illustrate the performance of this method . In this work we derive a new on-line parametric model for time series forecasting based on Vapnik-Chervonenkis ( VC ) theory . Using the strong connection between support vector machines ( SVM ) and Regularization theory ( RT ) , we propose a regularization operator in order to obtain a suitable expansion of radial basis functions ( RBFs ) with the corresponding expressions for updating neural parameters . This operator seeks for the " flattest " function in a feature space , minimizing the risk functional . The image is modeled as a graph and local spectral analysis is performed to identify noisy and noise free pixels . On the set of noise free pixels , a topology adapted graph regularization is performed . Experimental results show the benefits of the proposed approach regarding the standard VMF when noise proportion is high . For the diagonal or near diagonal entries corresponding to the integrals over a singular or near-singular element where the kernels are singular or near singular , we develop a systematic singularity treatment technique , known as the local correction scheme , based on the linear approximation of elements . The scheme differs from the singularity regularization or subtraction technique used in the boundary element method ( BEM ) . It applies the series expansion of scalar Green 's function to the kernels and derives analytical solutions for the strongly singular integrals under the Cauchy principal value like ( CPV-like ) sense . This two-step architecture is capable of extracting more reliable motion information from the initially estimated rain-free frame at the first stage for better frame alignment and motion modeling at the second stage . Furthermore , to keep the motion consistency between frames that facilitates a frame-consistent deraining model at the second stage , a dual-level flow based regularization is proposed at both coarse flow and fine pixel levels . To better train and evaluate the proposed video deraining network , a novel rain synthesis model is developed to produce more visually authentic paired training and evaluation videos . In this paper , we discuss the nonsmooth second-order regularization , suggested by Lysaker , Lundervold and Tai , and its application in image denoising . A function space Thi臼s inf扣orn 丑m丑lation is c ∞ompressed into the directional total variation regularization term based on the width of stroke . By linear combination of minimization regularization and data fidelity ten丑 , the high-resolution images are reconstructed . Compared with the related document image super resolution method , the proposed method has been improved in the visual image quality and character recognition accuracy . One consequence is that the proposed estimator can fit any consistent partial ranking over a subset of the items represented as a directed acyclic graph ( DAG ) , generalizing standard techniques that can only fit preference scores . Despite this generality , for supervision representing total or blockwise total orders , the computational complexity of our algorithm is within a log factor of the standard algorithms for nuclear norm regularization based estimates for matrix completion . We further show promising empirical results for a novel and challenging application of collaboratively ranking of the associations between brain-regions and cognitive neuroscience terms . However , the previous works for this subject are usually based on independent and identical distributed ( i.i.d ) samples . In this paper , we go beyond this restriction by investigating the generalization ability of magnitude-preserving regularization ranking ( MPRank ) with dependent samples . For the MPRank , we establish its upper bound for the excess ranking risk which demonstrates the satisfactory learning rate can be reached for dependent samples . We re-formulated the joint optimization problem as a network-wide resource allocation problem with cardinality constraints . A reweighted heuristic l1-norm regularization method is used to obtain a sparse solution to the re-formulated problem . The cell association scheme is then derived from the sparsity pattern of the solution , which guarantees a single BS association for each user . ( 1 ) First , we implement the multiclass version of the intersection-over-union ( IoU ) loss function that contributes to handling highly imbalanced datasets and preventing overfitting . ( 2 ) Thereafter , we propose a novel deep learning architecture integrating the deep atrous network architecture with the stochastic depth approach for speeding up the learning process , and impose a regularization effect . ( 3 ) Finally , we introduce an early fusion deep layer that combines image-based and LiDAR-derived features . How to design faster and more accurate image classification algorithms has become our research interests . In this paper , we proposed a new model called stochastic depth networks with deep energy model ( SADIE ) , and the model improved stochastic depth neural network with deep energy model to provide attributes of images and analysis their characteristics . The approach we adopted is to perform pre-processing such as image segmentation and denoising , and then normalize the data . This paper also describes a simple way to estimate " reasonable bounds " – linearly increasing the learning rate of the network for a few epochs . In addition , cyclical learning rates are demonstrated on the CIFAR-10 and CIFAR-100 datasets with ResNets , Stochastic Depth networks , and DenseNets , and the ImageNet dataset with the AlexNet and GoogLeNet architectures . These are practical tools for everyone who trains neural networks . In this paper , we studied the application of the recently proposed deep networks with stochastic depth ( DNSD ) to train deeper acoustic models for speech recognition . By randomly dropping a subset of layers during training , the studied stochastic depth training method helps reduce the training time substantially , yet the networks trained are much deeper since all the layers are kept during testing . We investigated this approach on the TIMIT data set . It has long been known that an ensemble of multiple neural networks generally yields better predictions than a single network in the ensemble . This effect has also been indirectly exploited when training a single network through dropout [ reference ] , dropconnect [ reference ] , or stochastic depth [ reference ] regularization methods , and in swapout networks [ reference ] , where training always focuses on a particular subset of the network , and thus the complete network can be seen as an implicit ensemble of such trained sub - networks . We extend this idea by forming ensemble predictions during training , using the outputs of a single network on different training epochs and under different regularization and input augmentation conditions . However , for our PyramidNet , the results in Figure [ reference ] implies that increasing the model capacity of the input - side layers would lead to a better performance improvement than using a conventional way of multiplicative scaling of feature map dimension . We also note that , although the use of regularization methods such as dropout or stochastic depth could further improve the performance of our model , we did not involve those methods to ensure a fair comparison with other models . subsection : ImageNet This paper also presents a consistent shape metric used to match the GANs . The performed qualitative and quantitative experiments show that the proposed GAN matching method provides accurate displacement fields enabling us to perform image rigid registration , even for data from different modalities , that outperforms the classical block matching algorithm with respect to robustness and accuracy criteria . HighlightsNovel image rigid registration method based on a block matching strategy .
( 3 ) The distance criterion generally provides a higher accuracy than the cosine criterion . The use of other p-norms ( p > 2 ) provides similar results to the Euclidean norm , nevertheless some methods perform better . ( 4 ) No spectral method can provide 100 % accuracy by itself .
However , these methods suffer from the curse of dimensionality , i.e. , in large dimensions their complexity approaches $ O(N)$ per query data point . In the special case where the conditional probability distribution $ p(y|x)$ is a Gaussian centered at x , i.e. , $ p(y|x ) \propto N (x,\sigma)$ , the maximum likelihood classification reduces to the nearest neighbor search with the Euclidean norm . Sublinear methods based on locality sensitive hashing ( LSH ) have been introduced to solve an approximate version of the nearest neighbor search for high dimensional data .
Abstract In this paper , we propose a modified Euclidean norm computation for breadth-first signal decoder ( BSIDE ) that reduces the computational complexity without sacrificing the performance . We exploit the reordered channel representation and rewrite the Euclidean norm computation in a simpler form , which results at significant reduction in number of operations required to decode the transmitted symbols . Also from the simulation results , it is observed that the reduction in complexity is 59 % for 2 × 2 and 75 % for the 4 × 4 multiple-input multiple output systems when compared to BSIDE .
PFCM addresses the noise sensitivity defect of Fuzzy c-means ( FCM ) and overcomes the coincident cluster problem of possibilistic c-means ( PCM ) . Here we propose a new model called Kernel-based hybrid c-means clustering ( KPFCM ) where PFCM is extended by adopting a Kernel induced metric in the data space to replace the original Euclidean norm metric . Use of Kernel function makes it possible to cluster data that is linearly non-separable in the original space into homogeneous groups in the transformed high dimensional space .
The main difficulty was the unfavorable influence of large amplitude impulses on the operation of nonlinear alignment ( or time-warping ) . When the classical definition of the alignment costs was replaced by the Euclidean norm based one , and when additionally the ordered weighted averaging was used to diminish the role of large noise impulses , the method appeared rather effective . Not only was it robust against this type of noise but also allowed for effective suppression of the usual Gaussian noise .
The goal of this work is energy disaggregation . A recent work showed that instead of employing the usual Euclidean norm cost function for dictionary learning , better results can be achieved by learning the dictionaries in a robust fashion by employing an l1-norm cost function ; this is because energy data is corrupted by large but sparse outliers . In this work we propose to improve the robust dictionary learning approach by imposing low-rank penalty on the learned coefficients .
This paper proposes a distributed model to compute a score that measures the quality of each feature with respect to multiple labels on Apache Spark . We propose two different approaches that study how to aggregate the mutual information of multiple labels : Euclidean Norm Maximization ( ENM ) and Geometric Mean Maximization ( GMM ) . The former selects the features with the largest L 2 -norm whereas the latter selects the features with the largest geometric mean .
Then , the information IMFs and the mixed components after thresholding were selected to give the optimal signal reconstruction . Static and dynamic signal tests of the fiber optic gyroscope ( FOG ) were carried out to illustrate the performance of the proposed method , and compared with other traditional EMD denoising methods , such as the Euclidean norm measure method ( EMD-l2-norm ) and the sliding average filtering method ( EMD-SA ) . The results of the analysis of both the static and dynamic signal tests indicate the effectiveness of the proposed method .
Next , a new method of optimizing a subtask criterion , defined using the infinity-norm , to perform additional tasks such as obstacle avoidance or joint limit avoidance is introduced . Simulations illustrating these methods and comparing the results with the Euclidean norm solutions are presented .
It is well known that Hopfield neural networks without delays exhibit no oscillations and possess global stability ( i.e. , all trajectories tend to some equilibrium ) . In the present paper we show that if the bound /spl tau//spl beta//spl par/T/sub 2//spl par/ 0 , interconnection matrix T/sub 2/ associated with delays , and gain of the neurons given by /spl beta/ , will exhibit similar qualitative properties as the original Hopfield neural network without delays ( /spl par/T/sub 2//spl par/ denotes the matrix norm induced by the Euclidean vector norm ) .
The envelopes are parameterized along principal axes of model inertia . As a distance measure among , we experimented with theEuclidean norm as well as a distance measure based on elastic matching by using the dynamic programming technique . Experiments showed that our approach could identify models having similar shapes fainy well .
The mini - batch size is 100 . The autoencoder is trained with a Euclidean cost function for reconstruction . On the MNIST dataset we use the sigmoid activation function in the last layer of the autoencoder and on the TFD dataset we use the linear activation function .
In this paper , we proposed an accelerated predictor-corrector iterated Tikhonov regularization . This method combined the classical iterated Tikhonov regularization with modified Euler method , which could improve computational efficiency without sacrificing numerical accuracy . The convergence rate of the accelerated regularization was investigated theoretically when the right-hand side was corrupted by noise .
When the regularization matrix is the identity , iterated Tikhonov regularization can yield computed approximate solutions of higher quality than ( standard ) Tikhonov regularization . This paper provides an analysis of iterated Tikhonov regularization with a regularization matrix different from the identity . Computed examples illustrate the performance of this method .
In this work we derive a new on-line parametric model for time series forecasting based on Vapnik-Chervonenkis ( VC ) theory . Using the strong connection between support vector machines ( SVM ) and Regularization theory ( RT ) , we propose a regularization operator in order to obtain a suitable expansion of radial basis functions ( RBFs ) with the corresponding expressions for updating neural parameters . This operator seeks for the " flattest " function in a feature space , minimizing the risk functional .
The image is modeled as a graph and local spectral analysis is performed to identify noisy and noise free pixels . On the set of noise free pixels , a topology adapted graph regularization is performed . Experimental results show the benefits of the proposed approach regarding the standard VMF when noise proportion is high .
For the diagonal or near diagonal entries corresponding to the integrals over a singular or near-singular element where the kernels are singular or near singular , we develop a systematic singularity treatment technique , known as the local correction scheme , based on the linear approximation of elements . The scheme differs from the singularity regularization or subtraction technique used in the boundary element method ( BEM ) . It applies the series expansion of scalar Green 's function to the kernels and derives analytical solutions for the strongly singular integrals under the Cauchy principal value like ( CPV-like ) sense .
This two-step architecture is capable of extracting more reliable motion information from the initially estimated rain-free frame at the first stage for better frame alignment and motion modeling at the second stage . Furthermore , to keep the motion consistency between frames that facilitates a frame-consistent deraining model at the second stage , a dual-level flow based regularization is proposed at both coarse flow and fine pixel levels . To better train and evaluate the proposed video deraining network , a novel rain synthesis model is developed to produce more visually authentic paired training and evaluation videos .
In this paper , we discuss the nonsmooth second-order regularization , suggested by Lysaker , Lundervold and Tai , and its application in image denoising . A function space
Thi臼s inf扣orn 丑m丑lation is c ∞ompressed into the directional total variation regularization term based on the width of stroke . By linear combination of minimization regularization and data fidelity ten丑 , the high-resolution images are reconstructed . Compared with the related document image super resolution method , the proposed method has been improved in the visual image quality and character recognition accuracy .
One consequence is that the proposed estimator can fit any consistent partial ranking over a subset of the items represented as a directed acyclic graph ( DAG ) , generalizing standard techniques that can only fit preference scores . Despite this generality , for supervision representing total or blockwise total orders , the computational complexity of our algorithm is within a log factor of the standard algorithms for nuclear norm regularization based estimates for matrix completion . We further show promising empirical results for a novel and challenging application of collaboratively ranking of the associations between brain-regions and cognitive neuroscience terms .
However , the previous works for this subject are usually based on independent and identical distributed ( i.i.d ) samples . In this paper , we go beyond this restriction by investigating the generalization ability of magnitude-preserving regularization ranking ( MPRank ) with dependent samples . For the MPRank , we establish its upper bound for the excess ranking risk which demonstrates the satisfactory learning rate can be reached for dependent samples .
We re-formulated the joint optimization problem as a network-wide resource allocation problem with cardinality constraints . A reweighted heuristic l1-norm regularization method is used to obtain a sparse solution to the re-formulated problem . The cell association scheme is then derived from the sparsity pattern of the solution , which guarantees a single BS association for each user .
( 1 ) First , we implement the multiclass version of the intersection-over-union ( IoU ) loss function that contributes to handling highly imbalanced datasets and preventing overfitting . ( 2 ) Thereafter , we propose a novel deep learning architecture integrating the deep atrous network architecture with the stochastic depth approach for speeding up the learning process , and impose a regularization effect . ( 3 ) Finally , we introduce an early fusion deep layer that combines image-based and LiDAR-derived features .
How to design faster and more accurate image classification algorithms has become our research interests . In this paper , we proposed a new model called stochastic depth networks with deep energy model ( SADIE ) , and the model improved stochastic depth neural network with deep energy model to provide attributes of images and analysis their characteristics . The approach we adopted is to perform pre-processing such as image segmentation and denoising , and then normalize the data .
This paper also describes a simple way to estimate " reasonable bounds " – linearly increasing the learning rate of the network for a few epochs . In addition , cyclical learning rates are demonstrated on the CIFAR-10 and CIFAR-100 datasets with ResNets , Stochastic Depth networks , and DenseNets , and the ImageNet dataset with the AlexNet and GoogLeNet architectures . These are practical tools for everyone who trains neural networks .
In this paper , we studied the application of the recently proposed deep networks with stochastic depth ( DNSD ) to train deeper acoustic models for speech recognition . By randomly dropping a subset of layers during training , the studied stochastic depth training method helps reduce the training time substantially , yet the networks trained are much deeper since all the layers are kept during testing . We investigated this approach on the TIMIT data set .
It has long been known that an ensemble of multiple neural networks generally yields better predictions than a single network in the ensemble . This effect has also been indirectly exploited when training a single network through dropout [ reference ] , dropconnect [ reference ] , or stochastic depth [ reference ] regularization methods , and in swapout networks [ reference ] , where training always focuses on a particular subset of the network , and thus the complete network can be seen as an implicit ensemble of such trained sub - networks . We extend this idea by forming ensemble predictions during training , using the outputs of a single network on different training epochs and under different regularization and input augmentation conditions .
However , for our PyramidNet , the results in Figure [ reference ] implies that increasing the model capacity of the input - side layers would lead to a better performance improvement than using a conventional way of multiplicative scaling of feature map dimension . We also note that , although the use of regularization methods such as dropout or stochastic depth could further improve the performance of our model , we did not involve those methods to ensure a fair comparison with other models . subsection : ImageNet
This paper also presents a consistent shape metric used to match the GANs . The performed qualitative and quantitative experiments show that the proposed GAN matching method provides accurate displacement fields enabling us to perform image rigid registration , even for data from different modalities , that outperforms the classical block matching algorithm with respect to robustness and accuracy criteria . HighlightsNovel image rigid registration method based on a block matching strategy .
Numerical Analysis and Comparison of spectral Decomposition Methods in Biometric Applications Tree-wise Distribution Sensitive hashing: Efficient Maximum likelihood Classification by joint dimensionality reduction in known probabilistic settings A Modified Euclidean Norm Computation for Complexity Reduction in MIMO Decoder A new Kernelized hybrid c-mean clustering model with optimized parameters Averaging of Nonlinearly Aligned Evoked Potentials in Impulsive Noise Environment Nuclear norm regularized robust dictionary learning for energy disaggregation Distributed multi-label feature selection using individual mutual information measures A Gyroscope Signal Denoising Method Based on Empirical Mode Decomposition and Signal Reconstruction Minimum effort inverse kinematics for redundant manipulators Qualitative Analysis of Hopfield Neural Nets with Delays: Global and Local Results Computer Graphics. Shape-Similarity Search of 3D Models by Using Moment Envelopes. Adversarial Autoencoders A predictor-corrector iterated Tikhonov regularization for linear ill-posed inverse problems Iterated Tikhonov regularization with a general penalty term On-line support vector machines and optimization strategies Impulse noise removal by spectral clustering and regularization on graphs Nyström method for elastic wave scattering by three-dimensional obstacles Frame-Consistent Recurrent Video Deraining With Dual-Level Flow Semismooth Newton method for minimization of the LLT model 基于定向双边全变差正则化的文档图像超分辨率算法研究 (Research of Document Image Super Resolution Algorithm Based on Directional Bilateral Total Variation Regularization) Preference Completion from Partial Rankings Learning rate of magnitude-preserving regularization ranking with dependent samples QoS Constrained Optimization of Cell Association and Resource Allocation for Load Balancing in Downlink Heterogeneous Cellular Networks Land Cover Segmentation of Airborne LiDAR Data Using Stochastic Atrous Network An Image Classification Method Based on Deep Neural Network with Energy Model Cyclical Learning Rates for Training Neural Networks Deep networks with stochastic depth for acoustic modelling Temporal Ensembling for Semi-Supervised Learning Deep Pyramidal Residual Networks Rigid image registration by General Adaptive Neighborhood matching
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