The proposed method is able to deal with intensity inhomogeneity as a Gaussian kernel function has been used in the energy formulation . The kernel function is used to assign weights to the intensity values during energy formulation . Different scale parameters are used for the kernel function for background and foreground regions . The key measure is Shannon 's entropy estimated via the inertia provided by the contribution of each object in data . As a result , the proposed method uses kernel mapping function to map data before performing entropy principal component analysis . Then data could be reduced into lower dimension of valuable extracted features . As the special kernel methods , the important characteristics of both HFSR and centered-ELM are that rigorous Mercer 's condition for kernel functions is not required and that they can inherently be used to propagate the prominent advantages of ELM into MLFN . Except for randomly assigned weights adopted in both ELM and HFSR , HFSR also exploits another randomness , i.e. , randomly selected examplars from the training set for kernel activation functions . Through forward layer-by-layer data transformation , we can extend HFSR and Centered-ELM to MLFN . It is shown that the best activation function is represented by a kernel expansion in the training set , that can be effectively approximated over an opportune set of points modeling 1-D clusters . The idea can be naturally extended to recurrent networks , where the expressiveness of kernel-based activation functions turns out to be a crucial ingredient to capture long-term dependencies . We give experimental evidence of this property by a set of challenging experiments , where we compare the results with neural architectures based on state of the art LSTM cells . CMSM ( Constraint Mutual Subspace Method ) constructs a class subspace for each person and makes the relation between class subspaces by projecting them onto a generalized difference subspace so that the canonical angles between subspaces are enlarged to approach to the orthogonal relation . GDA ( Generalized Discriminant Analysis ) adopts kernel function operator to make it easy to extend and generalize the classical Linear Discriminant Analysis to a non linear one . Both CMSM and GDA are effective to recognize human faces , however , CMSM constructs a subspace from several face images and GDA needs only one face image to perform recognition . We present a new method that we call generalized discriminant analysis ( GDA ) to deal with nonlinear discriminant analysis using kernel function operator . The underlying theory is close to the support vector machines ( SVM ) insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space . We report the first visualization and explanation of neural network kernel activation maps during H&E staining and destaining of RGB images by cGANs . High similarities between kernel activation maps of computational and H&E stained images ( Mean-Squared Errors < 0.0005 ) provide additional mathematical and mechanistic validation of the staining system . Our neural network framework thus is automated , explainable and performs high precision H&E staining and destaining of low cost native RGB images , and is computer vision and physician authenticated for rapid and accurate tumor diagnoses . To address this issue , we propose a KerneL dEnsity-bAsed Probability cleaning method ( KLEAP ) to remove cross-reads within a sliding window . The method estimates the density of each tag using a kernel-based function . The reader corresponding to the micro-cluster with the largest density will be regarded as the position that the tagged object should locate in current window , and the readings derived from other readers will be treated as the cross-reads . The algorithm called evolutionary KPCA-LSSVM is the combination of genetic algorithm ( GA ) , kernel principal component analysis ( KPCA ) and Least Squares Support Vector Machine ( LSSVM ) , which can obtain better fault recognition rate . Firstly , kernel function concept is introduced , and then GA is used to select the kernel parameter in order to improve the performances of nonlinear feature extraction and fault classification of KPCA-LSSVM method . Secondly , KPCA is used to extract the nonlinear principal features of loopers by adopting the optimal kernel trick to map nonlinearly the data into a feature space and employing the PCA procedure . The work that carried out in this paper is to develop a model that can predict better accuracy of churn . We used the existing models of SVM and kernel function of it and collaborated with the artificial neural networks in prediction . The results proved to be outstanding when both the models integrated with each other . However , the approach used fixed convolutional features , and can not jointly learn the kernel classifier and convolutional filters . showed how to learn a kernel function in an unsupervised manner . There have been other attempts to replace the fully connected layers . The first convolutional layer filters the 224 ⇥ 224 ⇥ 3 input image with 96 kernels of size 11 ⇥ 11 ⇥ 3 with a stride of 4 pixels ( this is the distance between the receptive field centers of neighboring 3We can not describe this network in detail due to space constraints , but it is specified precisely by the code and parameter files provided here : http: // code.google.com / p / cuda - convnet / . neurons in a kernel map ) . The second convolutional layer takes as input the ( response - normalized and pooled ) output of the first convolutional layer and filters it with 256 kernels of size 5 ⇥ 5 ⇥ 48 . The first one is the use of supervision to better approximate the kernel for the prediction task . The second consists in leveraging the kernel interpretation of our convolutional neural networks to better understand the theoretical properties of the feature spaces that these networks produce . subsubsection : Acknowledgments The approximation is reasonable only if we can effectively cover the region of interest with densely spaced { Z i } ; it requires a nontrivial amount of computation even for the very simple 1 - dimensional toy problem of Example 1 . One advantage of this estimator , though , is that finding its derivative with respect to the input points or the kernel parameterization is almost free once we have computed the estimate , as long as our solver has computed the dual variables µ corresponding to the constraints in [ reference ] . We just need to exploit the envelope theorem and then differentiate the KKT conditions , as done for instance in [ reference ] . ( MMD ) gretton2006kernel : Asymptotically , for a universal kernel such as the Gaussian kernel , is if and only if . Equivalently , minimizing MMD can be viewed as matching all of the moments of and . Rectified linear unit ( ReLU ) is a widely used activation function for deep convolutional neural networks . In this paper , we propose a novel activation function called flexible rectified linear unit ( FReLU ) . FReLU improves the flexibility of ReLU by a learnable rectified point . Unlike the tanh function which is smooth , the ReLU yields networks that are piecewise linear functions with a limited number of facets . This paper presents a new activation function , the Piecewise Linear Unit ( PLU ) that is a hybrid of tanh and ReLU and shown to outperform the ReLU on a variety of tasks while avoiding the vanishing gradients issue of the tanh . The purpose of kernel adaptive filtering ( KAF ) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems . However , the growth of the weighted networks for KAF based on existing kernel functions leads to high computational complexity . In the traditional Multiple Model Adaptive Estimation ( MMAE ) algorithm , the extended Kalman filter has theoretical limitations , and the establishment of accurate aircraft mathematical model is almost impossible . In this paper , the Kernel Adaptive Filter ( KAF ) is introduced to replace the Kalman filter , a new multi-model adaptive estimation fault diagnosis method is proposed . Based on the kernel methods , the complex nonlinear system is mapped to the high-dimensional feature space , then the adaptive filter is designed in the high-dimensional feature space without the need to know the system model in advance . Accurate remaining useful life ( RUL ) prediction under the noisy environment is a big challenge for the health management of modern industrial systems since the extraction of the accurate data structure from heavily corrupted data is difficult . In recent years , the kernel adaptive filter ( KAF ) has been widely adopted to solve the robust regression problem due to its low-complexity and high-approximation capability and robustness while the applications in battery RUL prediction are still few and far between . Thus , this paper is concerned with long-term RUL prediction using the KAF method . In particular , instead of using fixed point-wise functions ( e.g. , the rectified linear unit ) , several authors have proposed ways of learning these functions directly from the data in a non-parametric fashion . In this paper we focus on the kernel activation function ( KAF ) , a recently proposed framework wherein each function is modeled as a one-dimensional kernel model , whose weights are adapted through standard backpropagation-based optimization . One drawback of KAFs is the need to select a single kernel function and its eventual hyper-parameters . The protection scheme uses already available neutral grounding signals in the existing subharmonic injection protection to obtain a Kalman adaptive filter ( KAF ) for real-time stator insulation parameter estimation . The KAF estimator yields a method of continuous tracking of stator insulation condition during healthy operations . This information is then used for real-time stator ground fault detection as well as fault location . In this method , the kernel parameters are all adaptive and data-driven , although they should be given or estimated by cross-validation . In terms of the Gaussian KAF , every input sample or signal has its own width and center , which are updated at each iteration based on the proposed least-square-type rules to minimize the estimation error . In particular , the proposed update rule keeps the width in the manifold of the positive numbers . First , the KLMP algorithm is proposed by the gradient decent method to improve the robustness of the traditional kernel least mean square ( KLMS ) . Second , the recursion idea and the kernel method are utilized to develop a recursive KAF , namely KRLP , to improve the robustness of the traditional kernel recursive least squares ( KRLS ) . Simulation results show that the proposed algorithms display notable robustness in CTSP when the training data contain different levels of noises , and can perform better in terms of testing MSE than other algorithms . Understanding the behavior of the anatomical KAF system during gait initiation and termination may aid in the design of prosthetic components , i.e. mechanical devices that replace complete anatomical structures . Prostheses that intend to mimic the overall behavior of physiological KAF systems ( biomimetic designs ) could be manufactured using approaches that are much simpler than attempting to reconstruct the complexity of the lower limb . This kernelized recurrent system , the kernel adaptive ARMA ( KAARMA ) algorithm , brings together the theories of adaptive signal processing and recurrent neural networks ( RNNs ) , extending the current theory of kernel adaptive filtering ( KAF ) using the representer theorem to include feedback . Compared with classical feedforward KAF methods , the KAARMA algorithm provides general nonlinear solutions for complex dynamical systems in a state-space representation , with a deferred teacher signal , by propagating forward the hidden states . We demonstrate its capabilities to provide exact solutions with compact structures by solving a set of benchmark nondeterministic polynomial-complete problems involving grammatical inference . Short term prediction of air pollution is gaining increasing attention in the research community , due to its social and economical impact . In this paper we study the application of a Kernel Adaptive Filtering ( KAF ) algorithm to the problem of predicting PM10 data in the Italian province of Ancona , and we show how this predictor is able to achieve a significant low error with the inclusion of chemical data correlated with the PM10 such as NO2 . We describe our experiences with a very high-level parallel composition language ( called GLU ) that enables rapid construction of parallel applications using sequential building blocks ( extracted from existing sequential applications ) and their execution on diverse parallel computer systems . GLU is sufficiently rich to succinctly express different forms of parallelism -- from function parallelism to data parallelism and from pipeline parallelism to tree parallelism . Describes a system called GLU for large-grain parallel processing . GLU provides for ease of programming , scalable performance , and resilient execution . GLU is a hybrid system that combines the powerful abstract concepts of declarative systems with the practical concrete aspects of procedural systems . In the GLU programming model , a program is declarative at the higher levels and procedural at lower levels . The GLU abstract architecture for executing GLU programs is based on the demand-driven dataflow execution model . This third edition covers OpenGL Version 1.2 , including its newest features : 3D texture mapping ; multitexturing ; mipmapped texture level-of-detail control ; new pixel storage formats , including packed and reversed ( BGRA ) formats ; rescaling vertex normals ; and specular lighting after texturing . In addition , this book documents the newest routines in the OpenGL Utility Library ( GLU 1.3 ) and added functionality in the OpenGL extension to the X Window System ( GLX 1.3 ) . The comprehensive reference section documents each set of related OpenGL commands . Our algorithm constructs an intermediate “ raw offset curve ” as input to the tessellator routines in the OpenGL Utility library ( GLU ) , which calculates the winding number for each connected region . By construction , the invalid loops of our raw offset curve bound areas with non-positive winding numbers and thus can be removed by using the positive winding rule implemented in the GLU tessellator . The proposed algorithm takes O((n + k)logn ) time and O(n + k ) space , where n is the number of vertices in the input polygon and k is the number of self-intersections in the raw offset curve . This paper proposes a new location update scheme for subscribers on an area where a large number of fast-moving users need send update information frequently . The group location update ( GLU ) scheme in which a group location update is performed by a leader mobile terminal ( LMT ) instead of individual update by every normal mobile terminal ( NMT ) has been proposed . Mobile terminals ( MTs ) relatively near spontaneously form a group and select a LMT to collect location information of NMTs and report in groups . * Relevant parameters * The effects of functions * Possible errors generated by functions * Associated effects Reference pages for the OpenGL Utility Library ( GLU ) and the OpenGL extension to the X Window System ( GLX ) are included in this manual . The first edition of the OpenGL Reference Manual was written by Kurt Akeley , Kevin P. Smith , Jackie Neider , and Mark Segal of Silicon Graphics , Inc. ; and Sally Browning of SABL Productions . Started at CDS in 2002 , the work around Web Services isin a full exploitation phase . Several services are now available via SOAP : the Sesame name resolver for Simbad-NED-VizieR , a GLU tag resolver , aUCD resolver , the UCD tag list , Aladin image Access , VizieR catalogueaccess , etc . A portal is available to publish all information about howto use CDS XML Webservices and also hints on how to start to useXML Web Services ( tutorial , links , etc . ) . The introduction of GLU and temporal attention-based localization mechanisms plays an important role for both AT and SED tasks . In this paper , we propose a novel region based attention method to further boost the representation power of the existing GLU based CRNN . Specifically , we insert a feature selection ( FS ) structure after each GLU to create what we term a GLU-F. block , to exploit channel relationships . The specification of relations or links between data are an important part of the metadata , and we use GLU ( Generateur de Liens Uniformes = uniform link generator ) expressions to describe the links to external databases or services . The basic principles of the GLU system initiated at CDS , as well as some tools based on the GLU protocol , are briefly described . Finally , the on-going developments , especially related to data mining purposes , are presented . Near-sensor image processing ( NSIP ) is a new approach to low-level image processing in which the ability to perform global operations is crucial . We define a 2-D global logic unit ( GLU ) , which consists of simple logical circuits arranged in a regular net , and describe how to perform powerful segmentation and feature-extracting operations using this net . Typical segmentation operations performed by the net are hole filling , smallest circumscribing rectangle , thresholding with hysteresis , and arbitrary propagation patterns . and takes as input X ∈ R k×d which is a concatenation of k input elements embedded in d dimensions and maps them to a single output element Y ∈ R 2d that has twice the dimensionality of the input elements ; subsequent layers operate over the k output elements of the previous layer . We choose gated linear units ( GLU ; [ reference ] as non - linearity which implement a simple gating mechanism over the output of the convolu - where A , B ∈ R d are the inputs to the non - linearity , ⊗ is the point - wise multiplication and the output v ( This ensures that the variance of a normally distributed input is retained . For layers which are followed by a GLU activation , we propose a weight initialization scheme by adapting the derivations in [ reference ][ reference ][ reference ] . If the GLU inputs are distributed with mean 0 and have sufficiently small variance , then we can approximate the output variance with 1 / 4 of the input variance ( Appendix A.1 ) . Hence , we initialize the weights so that the input to the GLU activations have 4 times the variance of the layer input . In this paper , we propose an air quality prediction model to infer air pollutant concentrations , such as CO , NOx , NO2 . The idea is to design a sophisticate piecewise linear model by using a gated linear network . A top k% winner-take-all autoencoder is first built to generate a set of binary sequences as the gate control signals , so as to perform the input space partitioning . A gated linear network is able to mimic the functionality of a pre-trained neural network with a compound activation function R(x ) = x * S(x ) . An SVM can then be formulated to further implicitly optimize the gated linear network , in which a quasi-linear kernel is composed by using the gate signal S(x ) generated from the pre-trained neural network . Then the gated linear model is formulated into a linear regression form with the gate signals included . Secondly , a Laplacian regularized least squares ( LapRLS ) formulation is applied to optimize the linear regression form of the gated linear model . In this way , the gate signals are integrated into the kernel function , which is defined as inner product of the regression vectors . All embeddings are initialized from a normal distribution with mean 0 and standard deviation 0.1 . For layers whose output is not directly fed to a gated linear unit , we initialize weights from N ( 0 , 1 / n l ) where n l is the number of input connections to each neuron . Each block contains a 1 - D convolution that takes as input feature vectors and outputs another vector ; subsequent layers operate over the output elements of the previous layer . The output of the convolution is then fed into a gated linear unit dauphin2017icml . In the decoder network , we rely on causal convolution which rely only on states from the previous time steps . SummaryIn this paper , we consider estimators of the finite dimensional parameter θ0 in the single-index regression model defined by : E(Y|X)=E(Y|Xθ0 ) . We use semiparametric weighted M-estimators defined as maximizing a pseudo-likelihood based on the linear exponential family and which have been shown to be asymptotically efficient . We discuss the choice of the pseudo-likelihood and the practical efficiency of these estimators , using computational arguments . Despite their closer resemblance to the human cortex and their hypothetical improved performance , CA adoption as a deep learning approach remains limited in energy aware environments due to their high computational training complexity . Motivated to reduce CA supervised training complexity in limited hardware resources environments , we propose in this paper a piecewise linear or polygonal weight update rule for a supervised training of CA based on a linearization of the exponential function . As shown by our simulation results on 12 publicly available databases and our developed error-bound proofs , the proposed rule reduces CA training time by a factor of 3 at the expense of a 0.5 % degradation in accuracy . Our algorithms work by connecting statistical discrepancy to combinatorial discrepancy ; roughly speaking , we show that in order to maximize a convex discrepancy function over a class of shapes , one needs only maximize a linear discrepancy function over the same set of shapes . We derive general discrepancy functions for data generated from a one- parameter exponential family . This generalizes the widely-used Kulldorff scan statistic for data from a Poisson distribution . Since the important runoff generation mechanism occurs chiefly in lowland areas of a catchment or a simulating grid unit , it is not necessary to accurately capture the distribution where the TI values are less than the mean TI value ( corresponding to upland areas ) . As a special case of the three-parameter gamma distribution , the two- parameter exponential function is used to fit only the part of the actual discrete CDF where TI is larger than its mean value so that it performs better than the previous gamma distribution does . In this exponential function , two significant parameters , the maximum fractional saturated area ( Fmax ) and the exponential coefficient ( Cs ) should be determined by topographic characteristics . This paper introduces a new algorithm to estimate and perform inferences on a recently proposed and developed semiparametric generalized linear model ( glm ) . Rather than selecting a particular parametric exponential family model , such as the Poisson distribution , this semiparametric glm assumes that the response is drawn from the more general exponential tilt family . The regression coefficients and unspecified reference distribution are estimated by maximizing a semiparametric likelihood . In this paper we present a novel image prior-isolate edges prior to predict a sharp ` vision ' of degraded image edges , and utilize the two images to solve for the OTF . In this prior , the isolate edges of the image gradients are modeled by parametric exponential functions . We transform the estimated OTF to blur kernel and modify it using a maximum-a-posteriori model . We first define a measure of discrimination of an arbitrary conditional probability model on a set of labeled training data . We consider maximizing discrimination on a parametric family of exponential models that arises naturally in the maximum entropy framework . We show that this optimization problem is globally convex in R/sup n/ , and is moreover piecewise linear on R/sup n/. We propose a solution that involves solving a series of linear programming problems . section : Exponential Linear Units ( ELUs ) The exponential linear unit ( ELU ) with is The ELU hyperparameter controls the value to which an ELU saturates for negative net inputs ( see Fig . [ reference ] ) . In this paper , we propose learning a parameterization of ELU in order to learn the proper activation shape at each layer in the CNNs . Our results on the MNIST , CIFAR-10/100 and ImageNet datasets using the NiN , Overfeat , All-CNN and ResNet networks indicate that our proposed Parametric ELU ( PELU ) has better performances than the non-parametric ELU . We have observed as much as a 7.28 % relative error improvement on ImageNet with the NiN network , with only 0.0003 % parameter increase . The development of Rectified linear units ( ReLU ) has revolutionized the use of supervised deep learning methods for speech recognition . Recently there has been a great deal of research interest in the development of activation functions Leaky-ReLU ( LReLU ) , Parametric-ReLU ( PReLU ) , Exponential Linear units ( ELU ) and Parametric-ELU ( PELU ) . This work is aimed at studying the influence of various activation functions on speech recognition system .
The proposed method is able to deal with intensity inhomogeneity as a Gaussian kernel function has been used in the energy formulation . The kernel function is used to assign weights to the intensity values during energy formulation . Different scale parameters are used for the kernel function for background and foreground regions .
The key measure is Shannon 's entropy estimated via the inertia provided by the contribution of each object in data . As a result , the proposed method uses kernel mapping function to map data before performing entropy principal component analysis . Then data could be reduced into lower dimension of valuable extracted features .
As the special kernel methods , the important characteristics of both HFSR and centered-ELM are that rigorous Mercer 's condition for kernel functions is not required and that they can inherently be used to propagate the prominent advantages of ELM into MLFN . Except for randomly assigned weights adopted in both ELM and HFSR , HFSR also exploits another randomness , i.e. , randomly selected examplars from the training set for kernel activation functions . Through forward layer-by-layer data transformation , we can extend HFSR and Centered-ELM to MLFN .
It is shown that the best activation function is represented by a kernel expansion in the training set , that can be effectively approximated over an opportune set of points modeling 1-D clusters . The idea can be naturally extended to recurrent networks , where the expressiveness of kernel-based activation functions turns out to be a crucial ingredient to capture long-term dependencies . We give experimental evidence of this property by a set of challenging experiments , where we compare the results with neural architectures based on state of the art LSTM cells .
CMSM ( Constraint Mutual Subspace Method ) constructs a class subspace for each person and makes the relation between class subspaces by projecting them onto a generalized difference subspace so that the canonical angles between subspaces are enlarged to approach to the orthogonal relation . GDA ( Generalized Discriminant Analysis ) adopts kernel function operator to make it easy to extend and generalize the classical Linear Discriminant Analysis to a non linear one . Both CMSM and GDA are effective to recognize human faces , however , CMSM constructs a subspace from several face images and GDA needs only one face image to perform recognition .
We present a new method that we call generalized discriminant analysis ( GDA ) to deal with nonlinear discriminant analysis using kernel function operator . The underlying theory is close to the support vector machines ( SVM ) insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space .
We report the first visualization and explanation of neural network kernel activation maps during H&E staining and destaining of RGB images by cGANs . High similarities between kernel activation maps of computational and H&E stained images ( Mean-Squared Errors < 0.0005 ) provide additional mathematical and mechanistic validation of the staining system . Our neural network framework thus is automated , explainable and performs high precision H&E staining and destaining of low cost native RGB images , and is computer vision and physician authenticated for rapid and accurate tumor diagnoses .
To address this issue , we propose a KerneL dEnsity-bAsed Probability cleaning method ( KLEAP ) to remove cross-reads within a sliding window . The method estimates the density of each tag using a kernel-based function . The reader corresponding to the micro-cluster with the largest density will be regarded as the position that the tagged object should locate in current window , and the readings derived from other readers will be treated as the cross-reads .
The algorithm called evolutionary KPCA-LSSVM is the combination of genetic algorithm ( GA ) , kernel principal component analysis ( KPCA ) and Least Squares Support Vector Machine ( LSSVM ) , which can obtain better fault recognition rate . Firstly , kernel function concept is introduced , and then GA is used to select the kernel parameter in order to improve the performances of nonlinear feature extraction and fault classification of KPCA-LSSVM method . Secondly , KPCA is used to extract the nonlinear principal features of loopers by adopting the optimal kernel trick to map nonlinearly the data into a feature space and employing the PCA procedure .
The work that carried out in this paper is to develop a model that can predict better accuracy of churn . We used the existing models of SVM and kernel function of it and collaborated with the artificial neural networks in prediction . The results proved to be outstanding when both the models integrated with each other .
However , the approach used fixed convolutional features , and can not jointly learn the kernel classifier and convolutional filters . showed how to learn a kernel function in an unsupervised manner . There have been other attempts to replace the fully connected layers .
The first convolutional layer filters the 224 ⇥ 224 ⇥ 3 input image with 96 kernels of size 11 ⇥ 11 ⇥ 3 with a stride of 4 pixels ( this is the distance between the receptive field centers of neighboring 3We can not describe this network in detail due to space constraints , but it is specified precisely by the code and parameter files provided here : http: // code.google.com / p / cuda - convnet / . neurons in a kernel map ) . The second convolutional layer takes as input the ( response - normalized and pooled ) output of the first convolutional layer and filters it with 256 kernels of size 5 ⇥ 5 ⇥ 48 .
The first one is the use of supervision to better approximate the kernel for the prediction task . The second consists in leveraging the kernel interpretation of our convolutional neural networks to better understand the theoretical properties of the feature spaces that these networks produce . subsubsection : Acknowledgments
The approximation is reasonable only if we can effectively cover the region of interest with densely spaced { Z i } ; it requires a nontrivial amount of computation even for the very simple 1 - dimensional toy problem of Example 1 . One advantage of this estimator , though , is that finding its derivative with respect to the input points or the kernel parameterization is almost free once we have computed the estimate , as long as our solver has computed the dual variables µ corresponding to the constraints in [ reference ] . We just need to exploit the envelope theorem and then differentiate the KKT conditions , as done for instance in [ reference ] .
( MMD ) gretton2006kernel : Asymptotically , for a universal kernel such as the Gaussian kernel , is if and only if . Equivalently , minimizing MMD can be viewed as matching all of the moments of and .
Rectified linear unit ( ReLU ) is a widely used activation function for deep convolutional neural networks . In this paper , we propose a novel activation function called flexible rectified linear unit ( FReLU ) . FReLU improves the flexibility of ReLU by a learnable rectified point .
Unlike the tanh function which is smooth , the ReLU yields networks that are piecewise linear functions with a limited number of facets . This paper presents a new activation function , the Piecewise Linear Unit ( PLU ) that is a hybrid of tanh and ReLU and shown to outperform the ReLU on a variety of tasks while avoiding the vanishing gradients issue of the tanh .
The purpose of kernel adaptive filtering ( KAF ) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems . However , the growth of the weighted networks for KAF based on existing kernel functions leads to high computational complexity .
In the traditional Multiple Model Adaptive Estimation ( MMAE ) algorithm , the extended Kalman filter has theoretical limitations , and the establishment of accurate aircraft mathematical model is almost impossible . In this paper , the Kernel Adaptive Filter ( KAF ) is introduced to replace the Kalman filter , a new multi-model adaptive estimation fault diagnosis method is proposed . Based on the kernel methods , the complex nonlinear system is mapped to the high-dimensional feature space , then the adaptive filter is designed in the high-dimensional feature space without the need to know the system model in advance .
Accurate remaining useful life ( RUL ) prediction under the noisy environment is a big challenge for the health management of modern industrial systems since the extraction of the accurate data structure from heavily corrupted data is difficult . In recent years , the kernel adaptive filter ( KAF ) has been widely adopted to solve the robust regression problem due to its low-complexity and high-approximation capability and robustness while the applications in battery RUL prediction are still few and far between . Thus , this paper is concerned with long-term RUL prediction using the KAF method .
In particular , instead of using fixed point-wise functions ( e.g. , the rectified linear unit ) , several authors have proposed ways of learning these functions directly from the data in a non-parametric fashion . In this paper we focus on the kernel activation function ( KAF ) , a recently proposed framework wherein each function is modeled as a one-dimensional kernel model , whose weights are adapted through standard backpropagation-based optimization . One drawback of KAFs is the need to select a single kernel function and its eventual hyper-parameters .
The protection scheme uses already available neutral grounding signals in the existing subharmonic injection protection to obtain a Kalman adaptive filter ( KAF ) for real-time stator insulation parameter estimation . The KAF estimator yields a method of continuous tracking of stator insulation condition during healthy operations . This information is then used for real-time stator ground fault detection as well as fault location .
In this method , the kernel parameters are all adaptive and data-driven , although they should be given or estimated by cross-validation . In terms of the Gaussian KAF , every input sample or signal has its own width and center , which are updated at each iteration based on the proposed least-square-type rules to minimize the estimation error . In particular , the proposed update rule keeps the width in the manifold of the positive numbers .
First , the KLMP algorithm is proposed by the gradient decent method to improve the robustness of the traditional kernel least mean square ( KLMS ) . Second , the recursion idea and the kernel method are utilized to develop a recursive KAF , namely KRLP , to improve the robustness of the traditional kernel recursive least squares ( KRLS ) . Simulation results show that the proposed algorithms display notable robustness in CTSP when the training data contain different levels of noises , and can perform better in terms of testing MSE than other algorithms .
Understanding the behavior of the anatomical KAF system during gait initiation and termination may aid in the design of prosthetic components , i.e. mechanical devices that replace complete anatomical structures . Prostheses that intend to mimic the overall behavior of physiological KAF systems ( biomimetic designs ) could be manufactured using approaches that are much simpler than attempting to reconstruct the complexity of the lower limb .
This kernelized recurrent system , the kernel adaptive ARMA ( KAARMA ) algorithm , brings together the theories of adaptive signal processing and recurrent neural networks ( RNNs ) , extending the current theory of kernel adaptive filtering ( KAF ) using the representer theorem to include feedback . Compared with classical feedforward KAF methods , the KAARMA algorithm provides general nonlinear solutions for complex dynamical systems in a state-space representation , with a deferred teacher signal , by propagating forward the hidden states . We demonstrate its capabilities to provide exact solutions with compact structures by solving a set of benchmark nondeterministic polynomial-complete problems involving grammatical inference .
Short term prediction of air pollution is gaining increasing attention in the research community , due to its social and economical impact . In this paper we study the application of a Kernel Adaptive Filtering ( KAF ) algorithm to the problem of predicting PM10 data in the Italian province of Ancona , and we show how this predictor is able to achieve a significant low error with the inclusion of chemical data correlated with the PM10 such as NO2 .
We describe our experiences with a very high-level parallel composition language ( called GLU ) that enables rapid construction of parallel applications using sequential building blocks ( extracted from existing sequential applications ) and their execution on diverse parallel computer systems . GLU is sufficiently rich to succinctly express different forms of parallelism -- from function parallelism to data parallelism and from pipeline parallelism to tree parallelism .
Describes a system called GLU for large-grain parallel processing . GLU provides for ease of programming , scalable performance , and resilient execution . GLU is a hybrid system that combines the powerful abstract concepts of declarative systems with the practical concrete aspects of procedural systems . In the GLU programming model , a program is declarative at the higher levels and procedural at lower levels . The GLU abstract architecture for executing GLU programs is based on the demand-driven dataflow execution model .
This third edition covers OpenGL Version 1.2 , including its newest features : 3D texture mapping ; multitexturing ; mipmapped texture level-of-detail control ; new pixel storage formats , including packed and reversed ( BGRA ) formats ; rescaling vertex normals ; and specular lighting after texturing . In addition , this book documents the newest routines in the OpenGL Utility Library ( GLU 1.3 ) and added functionality in the OpenGL extension to the X Window System ( GLX 1.3 ) . The comprehensive reference section documents each set of related OpenGL commands .
Our algorithm constructs an intermediate “ raw offset curve ” as input to the tessellator routines in the OpenGL Utility library ( GLU ) , which calculates the winding number for each connected region . By construction , the invalid loops of our raw offset curve bound areas with non-positive winding numbers and thus can be removed by using the positive winding rule implemented in the GLU tessellator . The proposed algorithm takes O((n + k)logn ) time and O(n + k ) space , where n is the number of vertices in the input polygon and k is the number of self-intersections in the raw offset curve .
This paper proposes a new location update scheme for subscribers on an area where a large number of fast-moving users need send update information frequently . The group location update ( GLU ) scheme in which a group location update is performed by a leader mobile terminal ( LMT ) instead of individual update by every normal mobile terminal ( NMT ) has been proposed . Mobile terminals ( MTs ) relatively near spontaneously form a group and select a LMT to collect location information of NMTs and report in groups .
* Relevant parameters * The effects of functions * Possible errors generated by functions * Associated effects Reference pages for the OpenGL Utility Library ( GLU ) and the OpenGL extension to the X Window System ( GLX ) are included in this manual . The first edition of the OpenGL Reference Manual was written by Kurt Akeley , Kevin P. Smith , Jackie Neider , and Mark Segal of Silicon Graphics , Inc. ; and Sally Browning of SABL Productions .
Started at CDS in 2002 , the work around Web Services isin a full exploitation phase . Several services are now available via SOAP : the Sesame name resolver for Simbad-NED-VizieR , a GLU tag resolver , aUCD resolver , the UCD tag list , Aladin image Access , VizieR catalogueaccess , etc . A portal is available to publish all information about howto use CDS XML Webservices and also hints on how to start to useXML Web Services ( tutorial , links , etc . ) .
The introduction of GLU and temporal attention-based localization mechanisms plays an important role for both AT and SED tasks . In this paper , we propose a novel region based attention method to further boost the representation power of the existing GLU based CRNN . Specifically , we insert a feature selection ( FS ) structure after each GLU to create what we term a GLU-F. block , to exploit channel relationships .
The specification of relations or links between data are an important part of the metadata , and we use GLU ( Generateur de Liens Uniformes = uniform link generator ) expressions to describe the links to external databases or services . The basic principles of the GLU system initiated at CDS , as well as some tools based on the GLU protocol , are briefly described . Finally , the on-going developments , especially related to data mining purposes , are presented .
Near-sensor image processing ( NSIP ) is a new approach to low-level image processing in which the ability to perform global operations is crucial . We define a 2-D global logic unit ( GLU ) , which consists of simple logical circuits arranged in a regular net , and describe how to perform powerful segmentation and feature-extracting operations using this net . Typical segmentation operations performed by the net are hole filling , smallest circumscribing rectangle , thresholding with hysteresis , and arbitrary propagation patterns .
and takes as input X ∈ R k×d which is a concatenation of k input elements embedded in d dimensions and maps them to a single output element Y ∈ R 2d that has twice the dimensionality of the input elements ; subsequent layers operate over the k output elements of the previous layer . We choose gated linear units ( GLU ; [ reference ] as non - linearity which implement a simple gating mechanism over the output of the convolu - where A , B ∈ R d are the inputs to the non - linearity , ⊗ is the point - wise multiplication and the output v (
This ensures that the variance of a normally distributed input is retained . For layers which are followed by a GLU activation , we propose a weight initialization scheme by adapting the derivations in [ reference ][ reference ][ reference ] . If the GLU inputs are distributed with mean 0 and have sufficiently small variance , then we can approximate the output variance with 1 / 4 of the input variance ( Appendix A.1 ) . Hence , we initialize the weights so that the input to the GLU activations have 4 times the variance of the layer input .
In this paper , we propose an air quality prediction model to infer air pollutant concentrations , such as CO , NOx , NO2 . The idea is to design a sophisticate piecewise linear model by using a gated linear network . A top k% winner-take-all autoencoder is first built to generate a set of binary sequences as the gate control signals , so as to perform the input space partitioning .
A gated linear network is able to mimic the functionality of a pre-trained neural network with a compound activation function R(x ) = x * S(x ) . An SVM can then be formulated to further implicitly optimize the gated linear network , in which a quasi-linear kernel is composed by using the gate signal S(x ) generated from the pre-trained neural network .
Then the gated linear model is formulated into a linear regression form with the gate signals included . Secondly , a Laplacian regularized least squares ( LapRLS ) formulation is applied to optimize the linear regression form of the gated linear model . In this way , the gate signals are integrated into the kernel function , which is defined as inner product of the regression vectors .
All embeddings are initialized from a normal distribution with mean 0 and standard deviation 0.1 . For layers whose output is not directly fed to a gated linear unit , we initialize weights from N ( 0 , 1 / n l ) where n l is the number of input connections to each neuron .
Each block contains a 1 - D convolution that takes as input feature vectors and outputs another vector ; subsequent layers operate over the output elements of the previous layer . The output of the convolution is then fed into a gated linear unit dauphin2017icml . In the decoder network , we rely on causal convolution which rely only on states from the previous time steps .
SummaryIn this paper , we consider estimators of the finite dimensional parameter θ0 in the single-index regression model defined by : E(Y|X)=E(Y|Xθ0 ) . We use semiparametric weighted M-estimators defined as maximizing a pseudo-likelihood based on the linear exponential family and which have been shown to be asymptotically efficient . We discuss the choice of the pseudo-likelihood and the practical efficiency of these estimators , using computational arguments .
Despite their closer resemblance to the human cortex and their hypothetical improved performance , CA adoption as a deep learning approach remains limited in energy aware environments due to their high computational training complexity . Motivated to reduce CA supervised training complexity in limited hardware resources environments , we propose in this paper a piecewise linear or polygonal weight update rule for a supervised training of CA based on a linearization of the exponential function . As shown by our simulation results on 12 publicly available databases and our developed error-bound proofs , the proposed rule reduces CA training time by a factor of 3 at the expense of a 0.5 % degradation in accuracy .
Our algorithms work by connecting statistical discrepancy to combinatorial discrepancy ; roughly speaking , we show that in order to maximize a convex discrepancy function over a class of shapes , one needs only maximize a linear discrepancy function over the same set of shapes . We derive general discrepancy functions for data generated from a one- parameter exponential family . This generalizes the widely-used Kulldorff scan statistic for data from a Poisson distribution .
Since the important runoff generation mechanism occurs chiefly in lowland areas of a catchment or a simulating grid unit , it is not necessary to accurately capture the distribution where the TI values are less than the mean TI value ( corresponding to upland areas ) . As a special case of the three-parameter gamma distribution , the two- parameter exponential function is used to fit only the part of the actual discrete CDF where TI is larger than its mean value so that it performs better than the previous gamma distribution does . In this exponential function , two significant parameters , the maximum fractional saturated area ( Fmax ) and the exponential coefficient ( Cs ) should be determined by topographic characteristics .
This paper introduces a new algorithm to estimate and perform inferences on a recently proposed and developed semiparametric generalized linear model ( glm ) . Rather than selecting a particular parametric exponential family model , such as the Poisson distribution , this semiparametric glm assumes that the response is drawn from the more general exponential tilt family . The regression coefficients and unspecified reference distribution are estimated by maximizing a semiparametric likelihood .
In this paper we present a novel image prior-isolate edges prior to predict a sharp ` vision ' of degraded image edges , and utilize the two images to solve for the OTF . In this prior , the isolate edges of the image gradients are modeled by parametric exponential functions . We transform the estimated OTF to blur kernel and modify it using a maximum-a-posteriori model .
We first define a measure of discrimination of an arbitrary conditional probability model on a set of labeled training data . We consider maximizing discrimination on a parametric family of exponential models that arises naturally in the maximum entropy framework . We show that this optimization problem is globally convex in R/sup n/ , and is moreover piecewise linear on R/sup n/. We propose a solution that involves solving a series of linear programming problems .
section : Exponential Linear Units ( ELUs ) The exponential linear unit ( ELU ) with is The ELU hyperparameter controls the value to which an ELU saturates for negative net inputs ( see Fig . [ reference ] ) .
In this paper , we propose learning a parameterization of ELU in order to learn the proper activation shape at each layer in the CNNs . Our results on the MNIST , CIFAR-10/100 and ImageNet datasets using the NiN , Overfeat , All-CNN and ResNet networks indicate that our proposed Parametric ELU ( PELU ) has better performances than the non-parametric ELU . We have observed as much as a 7.28 % relative error improvement on ImageNet with the NiN network , with only 0.0003 % parameter increase .
The development of Rectified linear units ( ReLU ) has revolutionized the use of supervised deep learning methods for speech recognition . Recently there has been a great deal of research interest in the development of activation functions Leaky-ReLU ( LReLU ) , Parametric-ReLU ( PReLU ) , Exponential Linear units ( ELU ) and Parametric-ELU ( PELU ) . This work is aimed at studying the influence of various activation functions on speech recognition system .
A variable region scalable fitting energy approach for human Metaspread chromosome image segmentation Kernel entropy principal component analysis using Parzen estimator Least learning machine and its experimental studies on regression capability Learning Neuron Non-Linearities with Kernel-Based Deep Neural Networks Face Recognition Based on Complementary Matching of Single Image and Sequential Images Generalized Discriminant Analysis Using a Kernel Approach High Accuracy Tumor Diagnoses and Benchmarking of Hematoxylin and Eosin Stained Prostate Core Biopsy Images Generated by Explainable Deep Neural Networks KLEAP: an efficient cleaning method to remove cross-reads in RFID streams Application for fault diagnosis of loopers based on evolutionary KPCA-LSSVM A Hybrid Classification Approach for Customer Churn Prediction using Supervised Learning Methods: Banking Sector Deep Fried Convnets ImageNet classification with deep convolutional neural networks Convolutional Kernel Networks On gradient regularizers for MMD GANs The Variational Fair Autoencoder Flexible Rectified Linear Units for Improving Convolutional Neural Networks PLU: The Piecewise Linear Unit Activation Function A Reduced Gaussian Kernel Least-Mean-Square Algorithm for Nonlinear Adaptive Signal Processing Kernel Adaptive Filtering Multiple-model Actuator Fault Diagnostic For Multi-effectors Aircraft A Robust Hybrid Filtering Method for Accurate Battery Remaining Useful Life Prediction Multikernel activation functions: formulation and a case study Adaptive 100% Injection-Based Generator Stator Ground Fault Protection With Real-Time Fault Location Capability Dictionary Learning for Gaussian Kernel Adaptive Filtering with Variablekernel Center and Width Robust kernel adaptive filters based on mean p-power error for noisy chaotic time series prediction Roll-over shapes of the able-bodied knee-ankle-foot system during gait initiation, steady-state walking, and gait termination. The Kernel Adaptive Autoregressive-Moving-Average Algorithm PM 10 Forecasting Using Kernel Adaptive Filtering: An Italian Case Study An application experience with an implicitly parallel composition language GLU: a system for scalable and resilient large-grain parallel processing OpenGL Reference Manual: The Official Reference Document to OpenGL, Version 1.2 Polygon Offsetting by Computing Winding Numbers Group location update scheme and performance analysis for location management in mobile network OpenGL reference manual (2nd ed.): the official reference document to OpenGL, Version 1.1 Web Services and Related Works at CDS A Region Based Attention Method for Weakly Supervised Sound Event Detection and Classification The VizieR system, a unified interface to astronomical catalogs Global feature extraction operations for near-sensor image processing Convolutional Sequence to Sequence Learning Air Quality Forecasting Using SVR with Quasi-Linear Kernel A Metric Learning Method for Improving Neural Network Based Kernel Learning for SVM A Semi-supervised Classification Using Gated Linear Model Convolutional Sequence to Sequence Learning Classical Structured Prediction Losses for Sequence to Sequence Learning Are Efficient Estimators in Single-Index Models Really Efficient? A Computational Discussion A piecewise weight update rule for a supervised training of cortical algorithms The hunting of the bump: on maximizing statistical discrepancy A two-parameter exponential function approach to simply and accurately characterize spatial regime of topographic index for land-surface parameterizations Semiparametric Generalized Linear Models with the gldrm Package Deblurring atmospheric turbulence degraded images using an isolate edges prior Discriminative training via linear programming Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) Parametric Exponential Linear Unit for Deep Convolutional Neural Networks Investigative study of various activation functions for speech recognition
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IIH-MSP CIKM 2015 IEEE International Conference on Computer Vision (ICCV) CACM NIPS NeurIPS ICLR ASCC INNSBDDL ICASSP WIRN ICASSP ICML CITS SMC IJCNN ICML NAACL-HLT SODA IGARSS ICASSP ICLR NCC
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