Locally weighted regression with different kernel smoothers for software effort estimation

Rich multimedia content including images, audio and text are frequently used to describe the same semantics in E-Learning and Ebusiness web pages, instructive slides, multimedia cyclopedias, and so on. In this paper, we present a framework for cross-media retrieval, where the query example and the retrieved result(s) can be of different media types. We first construct Multimedia Correlation Space (MMCS) by exploring the semantic correlation of different multimedia modalities, during which multimedia content and co-occurrence information is utilized. We propose a novel ranking algorithm, namely ranking with Local Regression and Global Alignment (LRGA), which learns a robust Laplacian matrix for data ranking. In LRGA, for each data point, a local linear regression model is used to predict the ranking values of its neighboring points. We propose a unified objective function to globally align the local models from all the data points so that an optimal ranking value can be assigned to each data point. LRGA is insensitive to parameters, making it particularly suitable for data ranking. A relevance feedback algorithm is proposed to improve the retrieval performance. Comprehensive experiments have demonstrated the effectiveness of our methods.

Based on the nonlinear time series local prediction method and the relevance vector machine regression model, the local relevance vector machine prediction method is proposed and applied to predict the small scale traffic measurement data, and the BIC-based neighbor point selection method is used to choose the number of nearest-neighbor points for the local relevance vector machine regression model. We also compare the performance of the local relevance vector machine regression model with the feed-forward neural network optimized by particle swarm optimization for the same problem. Experimental results show that the local relevance vector machine prediction method whose neighboring points have been optimized can effectively predict the small scale traffic measurement data, can reproduce the statistical features of real small scale traffic measurements, and the prediction accuracy of the local relevance vector machine regression model is superior to that of the feedforward neural network optimized by PSO and the local linear prediction method.

Active learning for social image retrieval using Locally Regressive Optimal Design

Intracranial pressure dynamics: changes of bandwidth as an indicator of cerebrovascular tension

Spatial data analysis focuses on both attribute and locational information. Local analyses deal with differences across space whereas global analyses deal with similarities across space. This paper addresses an experimental comparative study to analyse the spatial data by some weighted local regression models. Five local regression models have been developed and their estimation capacities have been evaluated. The experimental studies showed that integration of objective function based fuzzy clustering to geostatistics provides some accurate and general models structures. In particular, the estimation performance of the model established by combining the extended fuzzy clustering algorithm and standard regional dependence function is higher than that of the other regression models. Finally, it could be suggested that the hybrid regression models developed by combining soft computing and geostatistics could be used in spatial data analysis.

Nonparametric regression modelling for data applies the relationship between predictor and response variables without considering any particular trend. The main principle of nonparametric regression is estimating an unknown smooth function. Local polynomial regression is one of several methods for estimating smooth functions used in nonparametric regression models. There are two parameters in the local polynomial regression model the smoothing parameter and the polynomial degree parameter. Generalized Cross Validation is a classical method used to determine optimal smoothing parameter in nonparametric regression. The smoothing parameter that gives the minimum value of Generalized Cross-Validation is the optimal parameter. We apply the optimal smoothing parameter for local polynomial regression modelling using data on the regional domestic product growth rate of the business field in North Sumatra Province. The simulation results show a polynomial of degree two is better than degree one. Investigation of the effects of the Covid-19 pandemic shows that the predicted growth rate is far from the expected growth.

Optical See-Through displays (OST Displays) require the appearance of the virtual content to closely resemble that of the real world. However, current OST displays typically show color distortion due to hardware limitations. To overcome this problem, we propose a chromaticity based local linear regression model for color distortion estimation of OST displays. From our initial experiments, it was observed that local samples with similar chromaticity can be modeled more linearly rather than simple nearest neighbors in a color space. We argue that the accuracy of local linear regression can be further improved by placing emphasis on similarity of chromaticity. Experimental results showed that the proposed chromaticity based color correction achieves higher accuracy compared to the nearest neighbor method, for any training set size or neighborhood size as well as global regression. It confirms that chromaticity based nearest neighbors can be modeled more linearly together than simple nearest neighbors in a color space.

This paper describes an approach to multivariate regression that aims at improving the computational efficiency and comprehensibility of local regression techniques. Local regression modeling is known for its ability to accurately approximate quite diverse regression surfaces with high accuracy. However, these methods are also known for being computationally demanding and for not providing any comprehensible model of the data. These two characteristics can be regarded as major drawbacks in the context of a typical data mining scenario. The method we describe tackles these problems by integrating local regression within a partition-based induction method.

Local linear regression models, a kind of nonparametric structures that locally perform a linear estimation of the target function, are analyzed in the context of empirical risk minimization (ERM) for function learning. The analysis is carried out with emphasis on geometric properties of the available data. In particular, the discrepancy of the observation points used both to build the local regression models and compute the empirical risk is considered. This allows to treat indifferently the case in which the samples come from a random external source and the one in which the input space can be freely explored. Both consistency of the ERM procedure and approximating capabilities of the estimator are analyzed, proving conditions to ensure convergence. Since the theoretical analysis shows that the estimation improves as the discrepancy of the observation points becomes smaller, low-discrepancy sequences, a family of sampling methods commonly employed for efficient numerical integration, are also analyzed. Simulation results involving two different examples of function learning are provided.

Introduction: Macroeconomic problems such as inflation and exchange rates are often highlighted as benchmarks for achieving economic progress. The stability of both must be monitored by the government in order to control the inflation rate and exchange rate. This instability is a phenomenon of fluctuation, namely the phenomenon of the rise and fall of the exchange rate of a currency based on demand and supply. Given the large impact of exchange rate fluctuations on the economy, the prediction of the wage exchange rate against the US dollar is considered necessary because it is useful to anticipate and minimize bad possibilities that arise. Method: Methods that can be used to analyze fluctuating currency exchange rate data are nonparametric regression, Nadaraya-Watson estimator, Gaussian kernel function, and Local Polynomial Regression. Results and Discussion: The results of a nonparametric regression comparison between the Nadaraya-Watson estimator, Gaussian kernel function, and local polynomial regression were obtained by MAPE of 2.508% and 0.179%, respectively. This shows that the best model uses the local polynomial regression method and predicted USD exchange rate data against IDR using the best model, namely Local polynomial Regression where the MAPE value is less than 10%, which means the prediction rate is very good. Conclusion: The nonparametric regression method of the Nadaraya-Watrson estimator, Gaussian kernel function, and local polynomial regression shows that the best model uses the local polynomial regression method.

Background/objectivesREALITY is an international observational retrospective registry of LHON patients evaluating the visual course and outcome in Leber hereditary optic neuropathy (LHON).Subjects/methodsDemographics and visual function data were collected from medical charts of LHON patients with visual loss. The study was conducted in 11 study centres in the United States of America and Europe. The collection period extended from the presymptomatic stage to at least more than one year after onset of vision loss (chronic stage). A Locally Weighted Scatterplot Smoothing (LOWESS) local regression model was used to analyse the evolution of best-corrected visual acuity (BCVA) over time.Results44 LHON patients were included; 27 (61%) carried the m.11778G>A ND4 mutation, 8 (18%) carried the m.3460G>A ND1 mutation, and 9 (20%) carried the m.14484T>C ND6 mutation. Fourteen (32%) patients were under 18 years old at onset of vision loss and 5 (11%) were below the age of 12. The average duration of follow-up was 32.5 months after onset of symptoms. At the last observed measure, mean BCVA was 1.46 LogMAR in ND4 patients, 1.52 LogMAR in ND1 patients, and 0.97 LogMAR in ND6 patients. The worst visual outcomes were reported in ND4 patients aged at least 15 years old at onset, with a mean BCVA of 1.55 LogMAR and no tendency for spontaneous recovery. The LOESS modelling curve depicted a severe and permanent deterioration of BCVA.ConclusionsAmongst LHON patients with the three primary mtDNA mutations, adult patients with the m.11778G>A ND4 mutation had the worst visual outcomes, consistent with prior reports.

Let $\rho(x, y)$ be a positive definite symmetric kernel defined over the unit square such that $\rho(x, y) = K(x, y) - \sum^k_{i=1} \psi_i(x)\psi_i (y), 0 \leqq x, y \leqq 1$, where $K(x, y)$ is a bounded symmetric positive definite kernel defined over the unit square, and $\psi_i(x) \in L_2(0, 1)$. Methods of finding Fredholm determinant $D(\lambda)$ of $\rho(x, y)$ in terms of the eigenvalues and the eigenfunctions of $K(x, y)$ are given. A kernel of the type of $\rho(x, y)$ arises as the covariance function of a Gaussian process in the limiting distribution of the modified Cramer-Smirnov test statistic in the $k$-parameter case which may be described as follows: Let $X_1, \cdots, X_n$ be $n$ independent observations (random variables) from a population with a continuous distribution function $G(x)$. Suppose for every $\theta = (\theta_1, \cdots, \theta_k) \in \mathbf{I,I}$ being an open interval in the $k$-dimensional Euclidean space $R^k, F(x, \theta)$ is a continuous distribution function. Let $\hat{\theta}_n$ be an estimate of $\theta$ obtained from the sample. A test of the hypothesis $H: G(x) = F(x, \theta)$ for some unspecified $\theta \in \mathbf{I}$ based on the statistic $C_n^2 = n \int^{+\infty}_{-\infty} \lbrack F_n(x) - F(x, \hat{\theta}_n) \rbrack^2 dF(x, \hat{\theta}_n),$ is considered and the characteristic function of the asymptotic distribution of $C_n^2$ is shown to be the Fredholm determinant of a kernel of the type of $\rho(x, y)$ with $K(x, y) = \min (x, y) - xy$ whose eigenvalues and eigenfunctions are known. Results are also used to obtain the limiting distribution of $l$-sample analogue of $C_n^2$.

Aerial surveying with unmanned aerial vehicles (UAVs) has been popularly employed in river management and flood monitoring. One of the major processes in UAV aerial surveying for river applications is to demarcate the cross-section of a river. From the photo images of aerial surveying, a point cloud dataset can be abstracted with the structure from motion (SfM) technique. To accurately demarcate the cross-section from the cloud points, an appropriate delineation technique is required to reproduce the characteristics of natural and manmade channels, including abrupt changes, bumps, and lined shapes, even though the basic shape of natural and manmade channels is a trapezoidal shape. Therefore, a nonparametric-based estimation technique, called the K-nearest neighbor local linear regression (KLR) model, was tested in the current study to demarcate the cross-section of a river with a point cloud dataset from aerial surveying. The proposed technique was tested with a simulated dataset based on trapezoidal channels and compared with the traditional polynomial regression model and another nonparametric technique, locally weighted scatterplot smoothing (LOWESS). Furthermore, the KLR model was applied to a real case study in the Migok-cheon stream, South Korea. The results indicate that the proposed KLR model can be a suitable alternative for demarcating the cross-section of a river with point cloud data from UAV aerial surveying by reproducing the critical characteristics of natural and manmade channels, including abrupt changes and small bumps, as well as the overall trapezoidal shape.

PurposeAn accurate prediction of the deformation of retaining structures is critical for ensuring the stability and safety of braced deep excavations, while the high nonlinear and complex nature of the deformation makes the prediction challenging. This paper proposes an explainable boosted combining global and local feature multivariate regression (EB-GLFMR) model with high accuracy, robustness and interpretability to predict the deformation of retaining structures during braced deep excavations.Design/methodology/approachDuring the model development, the time series of deformation data is decomposed using a locally weighted scatterplot smoothing technique into trend and residual terms. The trend terms are analyzed through multiple adaptive spline regressions. The residual terms are reconstructed in phase space to extract both global and local features, which are then fed into a gradient-boosting model for prediction.FindingsThe proposed model outperforms other established approaches in terms of accuracy and robustness, as demonstrated through analyzing two cases of braced deep excavations.Research limitations/implicationsThe model is designed for the prediction of the deformation of deep excavations with stepped, chaotic and fluctuating features. Further research needs to be conducted to expand the model applicability to other time series deformation data.Practical implicationsThe model provides an efficient, robust and transparent approach to predict deformation during braced deep excavations. It serves as an effective decision support tool for engineers to ensure the stability and safety of deep excavations.Originality/valueThe model captures the global and local features of time series deformation of retaining structures and provides explicit expressions and feature importance for deformation trends and residuals, making it an efficient and transparent approach for deformation prediction.

The aim of signal image super resolution is to generate a high-resolution image from a given low-resolution (LR) input. Learning regression for low-high resolution patch pairs show promise in image super resolution. Gaussian process regression (GPR) is a typically probability model, has strong compatibility, but it is time consuming for building large numbers of samples modeling. In this paper, we extend a GPR based method and propose a nearest neighbor local Gaussian process regression (NNLGPR) that learns the function relationship from the low-resolution patch to the corresponding high frequency patch efficiently. At first, we search the nearest neighbor patches in the sample set for each input low resolution patch. Secondly, we establish local Gaussian process regression model from the searched nearest neighbor low-resolution patches to their corresponding high frequency patches for each low resolution patch. And then, the initial high resolution patch is restored by combining the up-scaled low-resolution patch with the high frequency patch. Finally, the non-local similarity and IBP are utilized to improve the quality of reconstruction image. Experimental results show that our approach acquires better results in the peak signal to noise ratio and the visual effects against several state of the arts methods.