基于改进K-means的局部离群点检测方法

离群点检测任务是指检测与正常数据在特征属性上存在显著差异的异常数据。大多数基于聚类的离群点检测方法主要从全局角度对数据集中的离群点进行检测,而对局部离群点的检测性能较弱。基于此,本文通过引入快速搜索和发现密度峰值方法改进K-means聚类算法,提出了一种名为KLOD(local outlier detection based on improved K-means and least-squares methods)的局部离群点检测方法,以实现对局部离群点的精确检测。首先,利用快速搜索和发现密度峰值方法计算数据点的局部密度和相对距离,并将二者相乘得到γ值。其次,将γ值降序排序,利用肘部法则选择γ值最大的k个数据点作为K-means聚类算法的初始聚类中心。然后,通过K-means聚类算法将数据集聚类成k个簇,计算数据点在每个维度上的目标函数值并进行升序排列。接着,确定数据点的每个维度的离散程度并选择适当的拟合函数和拟合点,通过最小二乘法对升序排列的每个簇的每1维目标函数值进行函数拟合并求导,以获取变化率。最后,结合信息熵,将每个数据点的每个维度目标函数值乘以相应的变化率进行加权,得到最终的异常得分,并将异常值得分较高的top-n个数据点视为离群点。通过人工数据集和UCI数据集,对KLOD、LOF和KNN方法在准确度上进行仿真实验对比。结果表明KLOD方法相较于KNN和LOF方法具有更高的准确度。本文提出的KLOD方法能够有效改善K-means聚类算法的聚类效果,并且在局部离群点检测方面具有较好的精度和性能。

A novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise,minimum mean square variance criterion and least mean square adaptive filter

Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.

A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.

Noise cancellation of a multi-reference full-wave magnetic resonance sounding signal based on a modified sigmoid variable step size least mean square algorithm

Nano-volt magnetic resonance sounding(MRS) signals are sufficiently weak so that during the actual measurement, they are affected by environmental electromagnetic noise, leading to inaccuracy of the extracted characteristic parameters and hindering effective inverse interpretation. Considering the complexity and non-homogeneous spatial distribution of environmental noise and based on the theory of adaptive noise cancellation, a model system for noise cancellation using multi-reference coils was constructed to receive MRS signals. The feasibility of this system with theoretical calculation and experiments was analyzed and a modified sigmoid variable step size least mean square(SVSLMS) algorithm for noise cancellation was presented. The simulation results show that, the multi-reference coil method performs better than the single one on both signal-to-noise ratio(SNR) improvement and signal waveform optimization after filtering, under the condition of different noise correlations in the reference coils and primary detecting coils and different SNRs. In particular, when the noise correlation is poor and the SNR<0, the SNR can be improved by more than 8 dB after filtering with multi-reference coils. And the average fitting errors for initial amplitude and relaxation time are within 5%. Compared with the normalized least mean square(NLMS) algorithm and multichannel Wiener filter and processing field test data, the effectiveness of the proposed method is verified.

Revisiting Akaike’s Final Prediction Error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.

Degree Splitting of Root Square Mean Graphs

Let be an injective function. For a vertex labeling f, the induced edge labeling is defined by, or;then, the edge labels are distinct and are from . Then f is called a root square mean labeling of G. In this paper, we prove root square mean labeling of some degree splitting graphs.

Mean Square Heun’s Method Convergent for Solving Random Differential Initial Value Problems of First Order

This paper deals with the construction of Heun’s method of random initial value problems. Sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several illustrative examples.

A Quantized Kernel Least Mean Square Scheme with Entropy-Guided Learning for Intelligent Data Analysis

Quantized kernel least mean square(QKLMS) algorithm is an effective nonlinear adaptive online learning algorithm with good performance in constraining the growth of network size through the use of quantization for input space. It can serve as a powerful tool to perform complex computing for network service and application. With the purpose of compressing the input to further improve learning performance, this article proposes a novel QKLMS with entropy-guided learning, called EQ-KLMS. Under the consecutive square entropy learning framework, the basic idea of entropy-guided learning technique is to measure the uncertainty of the input vectors used for QKLMS, and delete those data with larger uncertainty, which are insignificant or easy to cause learning errors. Then, the dataset is compressed. Consequently, by using square entropy, the learning performance of proposed EQ-KLMS is improved with high precision and low computational cost. The proposed EQ-KLMS is validated using a weather-related dataset, and the results demonstrate the desirable performance of our scheme.

Separate Least Mean Square Based Equalizer with Joint Optimization for Multi-CAP Visible Light Communication

Visible light communication(VLC) is expected to be a potential candidate of the key technologies in the sixth generation(6G) wireless communication system to support Internet of Things(IoT) applications. In this work, a separate least mean square(S-LMS) equalizer is proposed to compensate lowpass frequency response in VLC system. Joint optimization is employed to realize the proposed S-LMS equalizer with pre-part and post-part by introducing Lagrangian. For verification, the performance of VLC system based on multi-band carrier-less amplitude and phase(m-CAP) modulation with S-LMS equalizer is investigated and compared with that without equalizer,with LMS equalizer and with recursive least squares(RLS)-Volterra equalizer. Results indicate the proposed equalizer shows significant improved bit error ratio(BER) performance under the same conditions. Compared to the RLS-Volterra equalizer, SLMS equalizer achieves better performance under low data rate or high signal noise ratio(SNR) conditions with obviously lower computational complexity.

Low Complexity Minimum Mean Square Error Channel Estimation for Adaptive Coding and Modulation Systems

Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmission.Earlier analysis of methods of pilot-aided channel estimation for ACM systems were relatively little.In this paper,we investigate the performance of CSI prediction using the Minimum Mean Square Error(MMSE)channel estimator for an ACM system.To solve the two problems of MMSE:high computational operations and oversimplified assumption,we then propose the Low-Complexity schemes(LC-MMSE and Recursion LC-MMSE(R-LC-MMSE)).Computational complexity and Mean Square Error(MSE) are presented to evaluate the efficiency of the proposed algorithm.Both analysis and numerical results show that LC-MMSE performs close to the wellknown MMSE estimator with much lower complexity and R-LC-MMSE improves the application of MMSE estimation to specific circumstances.

Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs

Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and mathematical sciences. In this paper we use three finite difference schemes in order to approximate the solution of stochastic parabolic partial differential equations. The conditions of the mean square convergence of the numerical solution are studied. Some case studies are discussed.

Mean Square Containment Control of Multi-agent Systems with Transmission Noises

为有传播噪音的多代理人系统的抑制控制问题被考虑。由于噪音的存在，腐烂的获得功能被介绍稀释噪音。动态地交换拓扑学并且随机交换拓扑学被考虑。通讯图和控制获得功能上的足够的条件被导出保证吝啬的方形的抑制。一些数字例子被提供验证结果。

Calculation of Significant Wave Height Using the Linear Mean Square Estimation Method

Significant wave height is an important criterion in designing coastal and offshore structures.Based on the orthogonality principle, the linear mean square estimation method is applied to calculate significant wave height in this paper.Twenty-eight-year time series of wave data collected from three ocean buoys near San Francisco along the California coast are analyzed.It is proved theoretically that the computation error will be reduced by using as many measured data as possible for the calculation of significant wave height.Measured significant wave height at one buoy location is compared with the calculated value based on the data from two other adjacent buoys.The results indicate that the linear mean square estimation method can be well applied to the calculation and prediction of significant wave height in coastal regions.

Amplitude phase control for electro-hydraulic servo system based on normalized least-mean-square adaptive filtering algorithm

The electro-hydraulic servo system was studied to cancel the amplitude attenuation and phase delay of its sinusoidal response,by developing a network using normalized least-mean-square (LMS) adaptive filtering algorithm.The command input was corrected by weights to generate the desired input for the algorithm,and the feedback was brought into the feedback correction,whose output was the weighted feedback.The weights of the normalized LMS adaptive filtering algorithm were updated on-line according to the estimation error between the desired input and the weighted feedback.Thus,the updated weights were copied to the input correction.The estimation error was forced to zero by the normalized LMS adaptive filtering algorithm such that the weighted feedback was equal to the desired input,making the feedback track the command.The above concept was used as a basis for the development of amplitude phase control.The method has good real-time performance without estimating the system model.The simulation and experiment results show that the proposed amplitude phase control can efficiently cancel the amplitude attenuation and phase delay with high precision.

Application of Linear Mean-Square Estimation in Ocean Engineering

The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-square estimation method, a new way to extend short-term data to long-term ones is developed. The long-term data about concerning sea areas can be constructed via a series of long-term data obtained from neighbor oceanographic stations, through relevance analysis of different data series. It is effective to cover the insufficiency of time series prediction method＇s overdependence upon the length of data series, as well as the limitation of variable numbers adopted in multiple linear regression model. The storm surge data collected from three oceanographic stations located in Shandong Peninsula are taken as examples to analyze the number-selection effect of reference oceanographic stations（adjacent to the concerning sea area） and the correlation coefficients between sea sites which are selected for reference and for engineering projects construction respectively. By comparing the N-year return-period values which are calculated from observed raw data and processed data which are extended from finite data series by means of the linear mean-square estimation method, one can draw a conclusion that this method can give considerably good estimation in practical ocean engineering, in spite of different extreme value distributions about raw and processed data.

Random Crank-Nicolson Scheme for Random Heat Equation in Mean Square Sense

The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.

Mean-Square Exponential Input-to-State Stability of Numerical Solutions for Stochastic Control Systems

这份报纸处理随机的控制系统(SCS ) 的数字解决方案的吝啬平方的指数的 input-to-state 稳定性(expbe ) 。第一，一个有限时间的强壮的集中条件成立为，这被显示出随机 ? SCS 上的方法。那么，如果并且仅当，我们能看到 SCS 的吝啬平方的 expbe 成立的随机 ? 方法(为足够地小的步尺寸) 在有限时间的强壮的集中条件下面被保存。为有片面 Lipschitz 飘移的 SCS 的一个班，第二，它被证明那二含蓄的 Euler 方法(为任何步尺寸) 能继承 SCS 的吝啬平方的 expbe 性质。最后，数字例子证实在这研究介绍的定理的正确性。

A new method of lung sounds filtering using modulated least mean square—Adaptive noise cancellation

Advanced processing of lung sound (LS) recording is a significant means to separate heart sounds (HS) and combined low frequency noise from instruments (NI), with saving its characteristics. This paper proposes a new method of LS filtering which separates HS and NI simultaneously. It focuses on the application of least mean squares (LMS) algorithm with adaptive noise cancelling (ANC) technique. The second step of the new method is to modulate the reference input r1(n) of LMS-ANC to acquiesce combining HS and NI signals. The obtained signal is removed from primary signal (original lung sound recording-LS). The original signal is recorded from subjects and derived HS from it and it is modified by a band pass filter. NI is simulated by generating approximately periodic white gaussian noise (WGN) signal. The LMS-ANC designed algorithm is controlled in order to determine the optimum values of the order L and the coefficient convergence μ. The output results are measured using power special density (PSD), which has shown the effectiveness of our suggested method. The result also has shown visual difference PSD (to) normal and abnormal LS recording. The results show that the method is a good technique for heart sound and noise reduction from lung sounds recordings simultaneously with saving LS characteristics.

ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.