Lateral interaction by Laplacian‐based graph smoothing for deep neural networks

Lateral interaction in the biological brain is a key mechanism that underlies higher cognitive functions.Linear self‐organising map(SOM)introduces lateral interaction in a general form in which signals of any modality can be used.Some approaches directly incorporate SOM learning rules into neural networks,but incur complex operations and poor extendibility.The efficient way to implement lateral interaction in deep neural networks is not well established.The use of Laplacian Matrix‐based Smoothing(LS)regularisation is proposed for implementing lateral interaction in a concise form.The authors’derivation and experiments show that lateral interaction implemented by SOM model is a special case of LS‐regulated k‐means,and they both show the topology‐preserving capability.The authors also verify that LS‐regularisation can be used in conjunction with the end‐to‐end training paradigm in deep auto‐encoders.Additionally,the benefits of LS‐regularisation in relaxing the requirement of parameter initialisation in various models and improving the classification performance of prototype classifiers are evaluated.Furthermore,the topologically ordered structure introduced by LS‐regularisation in feature extractor can improve the generalisation performance on classification tasks.Overall,LS‐regularisation is an effective and efficient way to implement lateral interaction and can be easily extended to different models.

THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS

In this work,we study the linearized Landau equation with soft potentials and show that the smooth solution to the Cauchy problem with initial datum in L^(2)(ℝ^(3))enjoys an analytic regularization effect,and that the evolution of the analytic radius is the same as the heat equations.

An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH

In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.

An Empirical Study of Good-Turing Smoothing for Language Models on Different Size Corpora of Chinese

Data sparseness has been an inherited issue of statistical language models and smoothing method is usually used to resolve the zero count problems. In this paper, we studied empirically and analyzed the well-known smoothing methods of Good-Turing and advanced Good-Turing for language models on large sizes Chinese corpus. In the paper, ten models are generated sequentially on various size of corpus, from 30 M to 300 M Chinese words of CGW corpus. In our experiments, the smoothing methods;Good-Turing and Advanced Good-Turing smoothing are evaluated on inside testing and outside testing. Based on experiments results, we analyzed further the trends of perplexity of smoothing methods, which are useful for employing the effective smoothing methods to alleviate the issue of data sparseness on various sizes of language models. Finally, some helpful observations are described in detail.

EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.

ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H^1 -solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

Micro-Mechanism of Silicon-Based Waveguide Surface Smoothing in Hydrogen Annealing

The micro-mechanism of the silicon-based waveguide surface smoothing is investigated systematically to explore the effects of silicon-hydrogen bonds on high-temperature hydrogen annealing waveguides. The effect of silicon- hydrogen bonds on the surface migration movement of silicon atoms and the waveguide surface topography are revealed. The micro-migration from an upper state to a lower state of silicon atoms is driven by silicon- hydrogen bonding, which is the key to ameliorate the rough surface morphology of the silicon-based waveguide. The process of hydrogen annealing is experimentally validated based on the simulated parameters. The surface roughness declines from 1.523nm to 0.461 nm.

Research on Comparison and Evaluation Studies of Several Smoothing Denoising Method Based on γ-ray Spectrum Detector

The extraction of spectral parameters is very difficult because of the limited energy resolution for NaI( TI) gamma-ray detectors. For statistical fluctuation of radioactivity under complex environment,some smoothing filtering methods are proposed to solve the problem. These methods include adopting method of arithmetic moving average,center of gravity,least squares of polynomial,slide converter of discrete funcion convolution etc. The process of spectrum data is realized,and the results are assessed in H / FWHM( Peak High / Full Width at Half Maximum) and peak area based on the Matlab programming. The results indicate that different methods smoothed spectrum have respective superiority in different ergoregion,but the Gaussian function theory in discrete function convolution slide method is used to filter the complex γ-spectrum on Embedded system platform,and the statistical fluctuation of γ-spectrum is filtered well.

HAZARD REGRESSION WITH PENALIZED SPLINE:THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.

Visible and Near-Infrared Spectroscopy with Multi-Parameters Optimization of Savitzky-Golay Smoothing Applied to Rapid Analysis of Soil Cr Content of Pearl River Delta

Using visible and near-infrared (Vis-NIR) spectroscopy combined with partial least squares (PLS) regression, the rapid reagent-free analysis model for chromium (Cr) content in tideland reclamation soil in the Pearl River Delta, China was established. Based on Savitzky-Golay (SG) smoothing and PLS regression, a multi-parameters optimization platform (SG-PLS) covering 264 modes was constructed to select the appropriately spectral preprocessing mode. The optimal SG-PLS model was determined according to the prediction effect. The selected optimal parameters d, p, m and LV were 2, 6, 23 and 8, respectively. Using the validation samples that were not involved in modeling, the root mean square error (SEPV), relative root mean square error (R-SEPV) and correlation coefficients (RP, V) of prediction were 11.66 mg·kg-1, 10.7% and 0.722, respectively. The results indicated that the feasibility of using Vis-NIR spectroscopy combined with SG-PLS method to analyze soil Cr content. The constructed multi-parameters optimization platform with SG-PLS is expected to be applied to a wider field of analysis. The rapid detection method has important application values to large-scale agricultural production.

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

ANALYSIS ON CODE MULTIPATH MITIGATION BY PHASE-AIDED SMOOTHING

Multipath influence on code range under static condition is described firstly in this paper, and the problem that to what extent the phase-aided smoothing can mitigate multipath interference is detailed. Some problems regarding smoothing and mitigation are discussed. Suggestions based on the analysis has been made.

MODE SPACE SMOOTHING ALGORITHM TO ESTIMATE DOA OF COHERENT SIGNALS IMPINGING ON UNIFORM CIRCULAR ARRAY

A novel method to estimate DOA of coherent signals impinging on a uniform circular array( UCA) is presented in this paper. A virtual uniform linear array (VULA) is first derived by using spatial DFT technique, transforming the UCA from element space to phase mode space to obtain the properties of ordinary ULA, and then the well known spatial smoothing technique is applied to the VULA so that the lost rank of covariance matrix due to signal coherence can be retrieved. This method makes it feasible to use the simple MUSIC algorithm to estimate DOA of coherent signals impinging on a UCA without heavy computation burden. Simulation results strongly verify the effectiveness of the algorithm.

Template-based smoothing functions for data smoothing in Geodesy

This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid.The method employed here is the local L^2-seminorm minimization,through Euler-Lagrange method,for the Beltrami operator.The method results in a weighted average of the surrounding points in a te mplate based on the first order Taylor expansion of the unknown function under consideration.The coefficients of the weighted average are calculated and used to smooth the Geoid height data in Iran,derived from the EGM2008 geopotential model.

A Study on Precipitation Products with High Resolution in Anhui Province Based on Thin Plate Smoothing Spline

In order to achieve refined precipitation grid data with high accuracy and high spatial resolution,hourly precipitation grid dataset with 1 km spatial resolution in Anhui Province from May to September (in the rainy season) in 2016 and from August 2017 to July 2018 was established based on thin plate smoothing spline (TPS),which meets the needs of climate change research and meteorological disaster risk assessment.The interpolation errors were then analyzed.The grid precipitation product obtained based on thin plate smoothing spline,CLDAS-FAST and CLDAS-FRT were evaluated.The results show that the interpolated values of hourly precipitation by thin plate smoothing spline are close to the observed values in the rainy season of 2016.The errors are generally below 0.9 mm/h.However,the errors of precipitation in the mountainous areas of eastern Huaibei and western Anhui are above 1.2 mm/h.On monthly scale,the errors in June and July are the largest,and the proportion of absolute values of the errors ≥2 mm/h is up to 2.0% in June and 2.2% in July.The errors in September are the smallest,and the proportion of absolute values of the errors ≥2 mm/h is only 0.6%.The root mean square (RMSE) is only 0.37 mm/h,and the correlation coefficient (COR) is 0.93.The interpolation accuracy of CLDAS-FRT is the highest,with the smallest RMSE (0.65 mm/h) and mean error ( ME =0.01 mm/h),and the largest COR (0.81).The accuracy of the precipitation product obtained by thin plate smoothing spline interpolation is close to that of CLDAS-FAST.Its RMSE is up to 0.80 mm/h,and its ME is only -0.01 mm/h.Its COR is 0.73,but its bias (BIAS) is up to 1.06 mm/h.

A Smoothing Neural Network Algorithm for Absolute Value Equations

In this paper, we give a smoothing neural network algorithm for absolute value equations (AVE). By using smoothing function, we reformulate the AVE as a differentiable unconstrained optimization and we establish a steep descent method to solve it. We prove the stability and the equilibrium state of the neural network to be a solution of the AVE. The numerical tests show the efficient of the proposed algorithm.

A Smoothing Newton Method for the Box Constrained Variational Inequality Problems

The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function.The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.

A Smoothing SAA Method for a Stochastic Linear Complementarity Problem

Utilizing the well-known aggregation technique, we propose a smoothing sample average approximation （SAA） method for a stochastic linear complementarity problem, where the underlying functions are represented by expectations of stochastic functions. The method is proved to be convergent and the preliminary numerical results are reported.