Preservation of local linearity by neighborhood subspace scaling for solving the pre-image problem

An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the distance in feature space, indirect methods aimed at constructing approximate equivalent models have shown outstanding performance. In this paper, an indirect method for solving the pre-image problem is proposed. In the proposed algorithm, an inverse mapping process is constructed based on a novel framework that preserves local linearity. In this framework, a local nonlinear transformation is implicitly conducted by neighborhood subspace scaling transformation to preserve the local linearity between feature space and input space. By extending the inverse mapping process to test samples, we can obtain pre-images in input space. The proposed method is non-iterative,and can be used for any kernel functions. Experimental results based on image denoising using kernel principal component analysis(PCA) show that the proposed method outperforms the state-of-the-art methods for solving the pre-image problem.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

Fault Detection Based on Incremental Locally Linear Embedding for Satellite TX-I

A fault detection method based on incremental locally linear embedding(LLE)is presented to improve fault detecting accuracy for satellites with telemetry data.Since conventional LLE algorithm cannot handle incremental learning,an incremental LLE method is proposed to acquire low-dimensional feature embedded in high-dimensional space.Then,telemetry data of Satellite TX-I are analyzed.Therefore,fault detection are performed by analyzing feature information extracted from the telemetry data with the statistical indexes T2 and squared prediction error(SPE)and SPE.Simulation results verify the fault detection scheme.

Testing Linearity of Nonparametric Component in Partially Linear Model

In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.

KLT-based local linear prediction of chaotic time series

In the reconstructed phase space, based on the Karhunen-Loeve transformation （KLT）, the new local linear prediction method is proposed to predict chaotic time series. ＆ noise-free chaotic time series and a noise added chaotic time series are analyzed. The simulation results show that the KLT-based local linear prediction method can effectively make one-step and multi-step prediction for chaotic time series, and the one-step and multi-step prediction accuracies of the KLT-based local linear prediction method are superior to that of the traditional local linear prediction.

Preventing Pressure Oscillations Does Not Fix Local Linear Stability Issues of Entropy-Based Split-Form High-Order Schemes

Recently,it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the sim-ple density wave propagation example for the compressible Euler equations.The issue is related to missing local linear stability,i.e.,the stability of the discretization towards per-turbations added to a stable base flow.This is strongly related to an anti-diffusion mech-anism,that is inherent in entropy-conserving two-point fluxes,which are a key ingredi-ent for the high-order discontinuous Galerkin extension.In this paper,we investigate if pressure equilibrium preservation is a remedy to these recently found local linear stability issues of entropy-conservative/dissipative high-order split-form discontinuous Galerkin methods for the compressible Euler equations.Pressure equilibrium preservation describes the property of a discretization to keep pressure and velocity constant for pure density wave propagation.We present the full theoretical derivation,analysis,and show corresponding numerical results to underline our findings.In addition,we characterize numerical fluxes for the Euler equations that are entropy-conservative,kinetic-energy-preserving,pressure-equilibrium-preserving,and have a density flux that does not depend on the pressure.The source code to reproduce all numerical experiments presented in this article is available online(https://doi.org/10.5281/zenodo.4054366).

Noiseless Linear Amplification with General Local Unitary Operations

Noiseless linear amplification （NLA）, first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state ｜n） → gn｜n）, with g being the amplification gain. We here give a general frame- work for improving the NLA scheme with arbitrary general local unitary operations. We derive the improvement in the amplification gain in 0 1 photon subspace. In particular, we study if the local unitary is composed of sin- gle mode squeezing and coherent displacement operation. Finally, numerical simulations show that local unitary operation could give a further enhancement in the amplification gain as well as the success probability, making the NLA more feasible in future optic quantum communications.

The M-estimate of Local Linear Regression with Variable Window Breadth

In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.

Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator

In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.

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.

ESTIMATORS AND SOME BEHAVIORS FORA PARTIALLY LINEAR MODEL WITH CENSORED DATA

This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.

LLE-BASED CLASSIFICATION ALGORITHM FOR MMW RADAR TARGET RECOGNITION

In this paper,a new multiclass classification algorithm is proposed based on the idea of Locally Linear Embedding(LLE),to avoid the defect of traditional manifold learning algorithms,which can not deal with new sample points.The algorithm defines an error as a criterion by computing a sample's reconstruction weight using LLE.Furthermore,the existence and characteristics of low dimensional manifold in range-profile time-frequency information are explored using manifold learning algorithm,aiming at the problem of target recognition about high range resolution MilliMeter-Wave(MMW) radar.The new algorithm is applied to radar target recognition.The experiment results show the algorithm is efficient.Compared with other classification algorithms,our method improves the recognition precision and the result is not sensitive to input parameters.

Fast color transfer from multiple images

Color transfer between images uses the statistics information of image effectively. We present a novel approach of local color transfer between images based on the simple statistics and locally linear embedding. A sketching interface is proposed for quickly and easily specifying the color correspondences between target and source image. The user can specify the corre- spondences of local region using scribes, which more accurately transfers the target color to the source image while smoothly preserving the boundaries, and exhibits more natural output results. Our algorithm is not restricted to one-to-one image color transfer and can make use of more than one target images to transfer the color in different regions in the source image. Moreover, our algorithm does not require to choose the same color style and image size between source and target images. We propose the sub-sampling to reduce the computational load. Comparing with other approaches, our algorithm is much better in color blending in the input data. Our approach preserves the other color details in the source image. Various experimental results show that our approach specifies the correspondences of local color region in source and target images. And it expresses the intention of users and generates more actual and natural results of visual effect.

Novel algorithm for pose-invariant face recognition

By combining the AdaBoost modular locality preserving projection （AMLPP） algorithm and the locally linear regression （LLR） algorithm, a novel pose-invariant algorithm is proposed to realize high-accuracy face recognition under different poses. In the training stage of this algorithm, the AMLPP is employed to select the crucial frontal blocks and construct effective strong classifier. According to the selected frontal blocks and the corresponding non-frontal blocks, LLR is then applied to learn the linear mappings which will be used to convert the non-frontal blocks to visual frontal blocks. During the testing of the learned linear mappings, when a non-frontal face image is inputted, the non-frontal blocks corresponding to the selected frontal blocks are extracted and converted to the visual frontal blocks. The generated virtual frontal blocks are finally fed into the strong classifier constructed by AMLPP to realize accurate and efficient face recognition. Our algorithm is experimentally compared with other pose-invariant face recognition algorithms based on the Bosphorus database. The results show a significant improvement with our proposed algorithm.

Prediction of flyrock induced by mine blasting using a novel kernel-based extreme learning machine

Blasting is a common method of breaking rock in surface mines.Although the fragmentation with proper size is the main purpose,other undesirable effects such as flyrock are inevitable.This study is carried out to evaluate the capability of a novel kernel-based extreme learning machine algorithm,called kernel extreme learning machine(KELM),by which the flyrock distance(FRD) is predicted.Furthermore,the other three data-driven models including local weighted linear regression(LWLR),response surface methodology(RSM) and boosted regression tree(BRT) are also developed to validate the main model.A database gathered from three quarry sites in Malaysia is employed to construct the proposed models using 73 sets of spacing,burden,stemming length and powder factor data as inputs and FRD as target.Afterwards,the validity of the models is evaluated by comparing the corresponding values of some statistical metrics and validation tools.Finally,the results verify that the proposed KELM model on account of highest correlation coefficient(R) and lowest root mean square error(RMSE) is more computationally efficient,leading to better predictive capability compared to LWLR,RSM and BRT models for all data sets.

Testing Equality of Nonparametric Functions in Two Partially Linear Models

We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.

基于两部模型的组合惩罚似然估计方法研究及其应用

在统计学中,多借助零膨胀模型研究零膨胀数据潜在的模型结构及变量选择问题。然而,在多数情况下,响应变量的非零部分为定量数据,简单的零膨胀模型无法刻画这类数据的模型结构,对应的参数估计方法也不再适用。鉴于此,学者提出处理零膨胀半连续数据的两部模型。本文将组合惩罚似然估计方法引入两部模型,研究其变量选择问题。提出一种新的处理高维统计分析问题的惩罚似然估计方法:NCPM (New Combined Punishment Method),并将该方法应用于太原市降水量数据,分析其影响因素。模拟及实例分析结果均表明本文的方法行之有效,较传统的惩罚似然估计方法具有更高的预测精度。

LINEAR INDEPENDENCE OF THE INTEGER TRANS-LATES OF COMPACTLY SUPPORTED DISTRIBU-TIONS AND REFINABLE VECTORS

In this paper,the global and local linear independence of any compactly supported distributions by using time domain spaces,and of refinable vectors by invariant linear spaces are investigated.

Nonlinear fault detection based on locally linear embedding

In this paper, a new nonlinear fault detection technique based on locally linear embedding （LLE） is developed. LLE can efficiently compute the low-dimensional embedding of the data with the local neighborhood structure information preserved. In this method, a data-dependent kernel matrix which can reflect the nonlinear data structure is defined. Based on the kernel matrix, the Nystrrm formula makes the mapping extended to the testing data possible. With the kernel view of the LLE, two monitoring statistics are constructed. Together with the out of sample extensions, LLE is used for nonlinear fault detection. Simulation cases were studied to demonstrate the performance of the proposed method.

Adaptive Local Linear Quantile Regression

In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation （MSE） and mean absolute estimation （MAE） criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.