Nearest-neighbor Estimators Research Articles

Small area estimators in a simulation test

The Finnish National Forest Inventory produces municipality level results either with an indirect model-based K nearest neighbor estimator or a direct design-based post-stratification estimator. Design-based approach is unbiased, but not always feasible due to low number of field plots. The K nearest neighbor estimator is lacking an analytical estimator for the variance. A composite estimator combining the indirect and direct estimates could be an attractive solution. In this article, estimators for small-area estimation are analyzed in a simulation experiment with varying size small areas and quality auxiliary data. The potential of estimators is assessed based on the true standard errors and RMSEs in the simulation experiment. Direct estimators and composite estimators work reasonably well with varying quality models, but the performance of indirect estimators is dependent on the quality of the model used. The performance of different estimators also depends on the size of the small areas. Linear models in which the weight of plots outside the target domain is smaller than those within the target domain, performed better than an unweighted model, suggesting that localizing the models for the small areas is beneficial. EBLUP approach also performed well, both in connection of a KNN model and a linear model.

DPC clustering algorithm based on K-nearest neighbors and kernel density estimation

Clustering by fast search and find of density peaks (DPC) is a density-based clustering algorithm. This algorithm does not require iteration and too many parameter settings, but it cannot identify cluster centers with small cluster density because the local structure of the data is not considered when calculating the local density. To address the above problems, a DPC clustering algorithm (KKDPC) based on K-reciprocal Neighbors (KN) and Kernel Density Estimation (KDE) is proposed. First, the number of reciprocal neighbors and local kernel density of data points are obtained by nearest neighbor and kernel density estimation methods ; second, the number of K reciprocal neighbors is added to the local kernel density to obtain a new local density; finally, the relative distance is obtained according to the local density of the data points, and the cluster center is selected and the non-center point is allocated by constructing a decision graph. Experiments are conducted using artificial and real data sets, and compared with seven clustering algorithms: DPC, DBSCAN, K-means, FCM, DPC-KNN, DPC-NN, and DPC-FWSN. The performance of the KKDPC clustering algorithm is verified by calculating the adjusted mutual information (AMI), adjusted Rand index (ARI), and normalized mutual information (NMI). The experimental results show that this method can more accurately identify the cluster center and effectively improve the clustering accuracy.

A Comparison Between Local Linear Regression and K- Nearest Neighbor Methods in Estimating the Nonparametric Regression Model with Simulation and Application

In this paper, the nonparametric regression model was estimated using two common estimation methods (Local Linear Regression Estimator (LLRE) and K-Nearest Neighbor Estimator (KNNE). The simulation process was conducted using the statistical programming language, R, for these methods, and they were compared using the Average Root Mean Squares Error (ARMSE) criterion, with three sample sizes (50, 100, 150), three levels of error variance (0.3, 0.7, 1) and two non-linear models. The results for the first model showed the superiority of the nearest neighbor estimator (KNNE) method in most cases, and for the second model the local linear regression estimator (LLRE) was superior at all sample sizes and for all levels of variance. On the applied side, the effect of hemoglobin (Hb) on the packed cell volume (PCV) of 150 patients with chronic kidney disease was studied. The estimation process was made using the two methods, and the comparison between them was made using the root mean square error (RMSE) criterion. It was shown through the results of the applied side that the preference was for the nearest neighbor estimator (KNNE) method.

On Consistency of the Nearest Neighbor Estimator of the Density Function for m-AANA Samples

In this paper, by establishing a Bernstein inequality for m-asymptotically almost negatively associated random variables, some results on consistency for the nearest neighbor estimator of the density function are further established. The results generalize some existing ones in the literature. Some numerical simulations are also provided to support the results.

Robust Max Entrywise Error Bounds for Tensor Estimation From Sparse Observations via Similarity-Based Collaborative Filtering

Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from sparse observations and argue that it achieves sample complexity that nearly matches the conjectured computationally efficient lower bound on the sample complexity for the setting of low-rank tensors. Our algorithm uses the matrix obtained from the flattened tensor to compute similarity, and estimates the tensor entries using a nearest neighbor estimator. We prove that the algorithm recovers a finite rank tensor with maximum entry-wise error (MEE) and mean-squared-error (MSE) decaying to $0$ as long as each entry is observed independently with probability $p = \Omega(n^{-3/2 + \kappa})$ for any arbitrarily small $\kappa > 0$. More generally, we establish robustness of the estimator, showing that when arbitrary noise bounded by $\varepsilon \geq 0$ is added to each observation, the estimation error with respect to MEE and MSE degrades by $\text{poly}(\varepsilon)$. Consequently, even if the tensor may not have finite rank but can be approximated within $\varepsilon \geq 0$ by a finite rank tensor, then the estimation error converges to $\text{poly}(\varepsilon)$. Our analysis sheds insight into the conjectured sample complexity lower bound, showing that it matches the connectivity threshold of the graph used by our algorithm for estimating similarity between coordinates.

Implications for surveillance for breast cancer patients based on the internally and externally validated BRENDA-metastatic recurrence score

PurposeAlthough the incidence of distant relapse is decreasing, 20–30% of patients with early breast cancer die of metastasis. The aim of this study is to characterize patients with metastasis-free survival(MFS) less than 5 years, to analyze the most probable site of metastases according to the internally and externally validated BRENDA-score. The BRENDA-score is a combination of the biological subtype and clinical staging.Method3832 patients with primary diagnosis of breast cancer and either distant metastatic recurrence within 5 years or MFS ≥ 5 years were assigned to this study. Patients were classified for metastatic recurrence according to the BRENDA-score. 1765 patients were in a validation set. Statistical methods were Kaplan–Meier curves, Cox regression analysis, Exhausted CHAID, likelihood-ratio tests and the Nearest Neighbor Estimation method.ResultsThere was a significant(p < 0.001) difference between the Kaplan–Meier MFS-functions of M0-patients stratified by BRENDA-score. The BRENDA score outperforms intrinsic subtypes and the Nottingham prognostic score. It fits the original data and the validation set equally well (p = 0.179).There was a significant(p < 0.001) difference between mean BRENDA-Index for patients with MFS < 5y(21.0 ± 9.0) and patients with MFS ≥ 5y(mean BRENDA-Index 11.7 ± 8.2). 55.6% of the very high risk patients(BRENDA-Index ≥ 27) had metastases within 5 years. The most likely primary metastatic site was bone(30%) followed by liver(19%) and lung(18%). The discriminatory ability(areas under the time dependent ROC curve) of the BRENDA score is good to acceptable for the first 5 years. In the very low/low risk (intermediate, high/very high) risk group 50% of all metastases were diagnosed within 26 months. Guideline adherence had a highly significant influence on outcome independent of the risk group.ConclusionThe evaluation showed that the BRENDA-Score is a robust predictive tool for breast cancer recurrence and site of metastases in the first five years after diagnosis. It outperforms intrinsic subtypes and the Nottingham prognostic score. The BRENDA-score could be a tool for a risk orientated and targeted follow up.

Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures.

Heart Rate Variability (HRV) and Blood Pressure Variability (BPV) are widely employed tools for characterizing the complex behavior of cardiovascular dynamics. Usually, HRV and BPV analyses are carried out through short-term (ST) measurements, which exploit ~five-minute-long recordings. Recent research efforts are focused on reducing the time series length, assessing whether and to what extent Ultra-Short-Term (UST) analysis is capable of extracting information about cardiovascular variability from very short recordings. In this work, we compare ST and UST measures computed on electrocardiographic R-R intervals and systolic arterial pressure time series obtained at rest and during both postural and mental stress. Standard time-domain indices are computed, together with entropy-based measures able to assess the regularity and complexity of cardiovascular dynamics, on time series lasting down to 60 samples, employing either a faster linear parametric estimator or a more reliable but time-consuming model-free method based on nearest neighbor estimates. Our results are evidence that shorter time series down to 120 samples still exhibit an acceptable agreement with the ST reference and can also be exploited to discriminate between stress and rest. Moreover, despite neglecting nonlinearities inherent to short-term cardiovascular dynamics, the faster linear estimator is still capable of detecting differences among the conditions, thus resulting in its suitability to be implemented on wearable devices.

Semi Parametric Logistic Regression Model with the Outputs Representing Trapezoidal Intuitionistic Fuzzy Number

In this paper, the fuzzy logic and the trapezoidal fuzzy intuitionistic number were presented, as well as some properties of the trapezoidal fuzzy intuitionistic number and semi- parametric logistic regression model when using the trapezoidal fuzzy intuitionistic number. The output variable represents the dependent variable sometimes cannot be determined in only two cases (response, non-response)or (success, failure) and more than two responses, especially in medical studies; therefore so, use a semi parametric logistic regression model with the output variable (dependent variable) representing a trapezoidal fuzzy intuitionistic number.&#x0D; the model was estimated on simulation data when sample sizes 25,50 and 100, as the parametric part was estimated by two methods of estimation, are fuzzy ordinary least squares estimators FOLSE method and suggested fuzzy weighted least squares estimators SFWLSE , while the non-parametric part is estimated by Nadaraya Watson estimation and Nearest Neighbor estimator. The results were the fuzzy ordinary least squares estimators method was better than the suggested fuzzy weighted least squares estimators while, in the non-parametric portion, the Nadaraya Watson estimators had better than Nearest Neighbor estimators to estimate the model

Time-Dependent Receiver Operating Characteristic Analysis and Applications in the Field of Medicine

When there is a time-dependency between the biomarker and the event of interest (death, disease, relapse etc.), classical receiver operating characteristic (ROC) analysis may not be able to estimate the true performance of the biomarker. For such cases, time-dependent ROC, an extended version of the standard ROC, is developed. In this study, the aim is to demonstrate applications of this modified ROC method on medical datasets and find out if it should be preferred over classical ROC for time-dependent situations. Comparison between classical ROC and Kaplan-Meier (KM) estimator, which is one of the two time-dependent ROC estimators, has been made using datasets in this study. Nearest Neighbor Estimator (NNE), the alternative of KM estimator, is also applied on all datasets. Then the findings of these two approaches are compared. It is concluded that time-dependent ROC method is superior to the standard ROC analysis. In general, the closer to the event time, the higher performance is observed. Especially, biomarkers measured at last 12 or 6 months before the event are determined to be better at classification than the earlier measurements. Though in all applications KM and NNE yielded very similar results, the latter is considered to be more appropriate to evaluate the performance of a biomarker when a time dependent data is also censored. Results of this study show that time-dependent ROC analysis performs more accurately when there is a time dependency between the biomarker and the event of interest; therefore, it is recommended.

Consistency of nearest neighbor estimator of density function for m-END samples

In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on m-extended negatively dependent samples. The weak consistency, strong consistency, uniformly strong consistency and the convergence rate are established under some mild conditions. The results obtained in this paper extend and improve some existing ones in the literature.

Limit behaviors of the estimator of non parametric regression model based on extended negatively dependent errors

In this article, we study the complete consistency for the estimator of non parametric regression model based on extended negatively dependent errors, and obtain the convergence rates of the complete consistency by using the inequalities for extended negatively dependent random variables. As an application, the complete consistency and convergence rate for the nearest neighbor estimator are obtained. Finally, some simulations are illustrated.

Nearest neighbor estimates of Kaniadakis entropy

Abstract The aim of this paper is to develop new nonparametric estimators of entropy based on the kth nearest neighbor distances that are considered between n sample points, k ≤ (n − 1) being a positive integer, fixed. The Method consists in using the new estimators which were useful in order to evaluate the entropies for random vectors. As results, using the Kaniadakis entropy measure, the asymptotic unbiasedness and consistency of the estimators are proven.

Recovering Missing Data via Top-k Repeated Patterns for Fuzzy-Based Abnormal Node Detection in Sensor Networks

The stream data acquired by heterogeneous Internet of Things (IoT) sensors are seldom perfect. Most of the collected data streams include either missing or abnormal values caused by various factors such as failure, malfunction, or integrity attacks. Such unreliable data affect the real-time monitoring and compromise the quality of data analysis. By simply analyzing the sensor data via anomaly detection, applications may still be unreliable over the incomplete sensor data streams. Therefore, a reliable method for recovering the missing data and detecting the abnormal ones is indispensable in the IoT environment. This paper presents FuzHD++, a new method to recover missing sensor data and detect abnormal nodes jointly rather than independently. Both elements, data recovery and abnormal node detection, rely on the observed temporal and spatial correlation of sensor data to effectively achieve reliable recovery estimation and detection performance. In the data recovery process, the system adopts a matrix profile to extract the top-<i>k</i> repeated patterns from different sensor nodes. Furthermore, it utilizes the <i>k</i>-nearest neighbor estimator to recover the missing data based on the extracted pattern information of multiple neighbor nodes. During the abnormal node detection process, the system adopts a refined fuzzy rule-based detection method. The refined fuzzy rule-based inference system integrates the expert rules and the rules obtained from sensor data analysis to treat the ambiguity in the decision-making process. We validated the performance of FuzHD++ by comparing it with existing methods using two real-world datasets. Our results showed that the proposed missing sensor data recovery method achieves more than 20% improved root mean square error results than most existing methods. Furthermore, FuzHD++ achieved an average accuracy of 92% for analyzing the sensor readings and detecting the abnormal ones. According to the results, the proposed mechanisms based on the observed temporal and spatial correlation analysis improve the robustness of IoT against data loss and integrity attacks.

Denoising modulo samples: k-NN regression and tightness of SDP relaxation

Abstract Many modern applications involve the acquisition of noisy modulo samples of a function $f$, with the goal being to recover estimates of the original samples of $f$. For a Lipschitz function $f:[0,1]^d \to {{\mathbb{R}}}$, suppose we are given the samples $y_i = (f(x_i) + \eta _i)\bmod 1; \quad i=1,\dots ,n$, where $\eta _i$ denotes noise. Assuming $\eta _i$ are zero-mean i.i.d Gaussian’s, and $x_i$’s form a uniform grid, we derive a two-stage algorithm that recovers estimates of the samples $f(x_i)$ with a uniform error rate $O\big(\big(\frac{\log n}{n}\big)^{\frac{1}{d+2}}\big)$ holding with high probability. The first stage involves embedding the points on the unit complex circle, and obtaining denoised estimates of $f(x_i)\bmod 1$ via a $k$NN (nearest neighbor) estimator. The second stage involves a sequential unwrapping procedure which unwraps the denoised mod $1$ estimates from the first stage. The estimates of the samples $f(x_i)$ can be subsequently utilized to construct an estimate of the function $f$, with the aforementioned uniform error rate. Recently, Cucuringu and Tyagi proposed an alternative way of denoising modulo $1$ data, which works with their representation on the unit complex circle. They formulated a smoothness regularized least squares problem on the product manifold of unit circles, where the smoothness is measured with respect to the Laplacian of a proximity graph $G$ involving the $x_i$’s. This is a nonconvex quadratically constrained quadratic program (QCQP) hence they proposed solving its semidefinite program (SDP) based relaxation. We derive sufficient conditions under which the SDP is a tight relaxation of the QCQP. Hence under these conditions, the global solution of QCQP can be obtained in polynomial time.

Impact of small-scale irrigation on household food security: evidence from Ethiopia

BackgroundAdamitulu Jido Komoblcha is one of the districts located in lowland areas of the Oromia region with irrigation potentials of 14,000 hectares out of which only 2568 hectares are under small-scale irrigation practices. Though there are a lot of households using irrigation in the study area, the impact that it has brought on the food security of the household is not yet well studied in the area. Several related studies reviewed lack appropriate impact evaluation methods in studying the impact of small-scale irrigation on food security that may result in overestimation or underestimation of the impact. To this end, the main motivation behind this study was to examine whether small-scale irrigation in the study area is creating positive change on household food security or not using the propensity score matching approach.MethodologyBoth primary and secondary data were collected and used in the study. The primary data were collected from randomly selected 94 irrigation users and 100 non-user households from February to March 2018. Secondary data were collected from a review of different works of literature. Both descriptive statistics and econometric models were applied to analyze the data using Stata software version 13. The study applied the propensity score matching (PSM) model to analyze the impact of small-scale irrigation on food security. In analyzing the impact of small scale irrigation on food security, we have used calorie intake, crop harvest and consumption both from own production and bought from the sale of the crop harvest produced through irrigation as an indicator of food security.ResultThe study has found that participation in irrigation is positively determined by age, education, land size, access to extension service, and participation in off or non-farm activities. In contrast to this, participation in irrigation is negatively determined by distance from farm plot to water source and distance from the main market. The results of the nearest neighbor and caliper matching estimators show that participation in small-scale irrigation increased the daily calorie intake of the small-scale irrigation users by 643.76 kcal over non-user households. Similarly, it increased their daily calorie intake to 596.43 kcal and 591.74 kcal, respectively, with radius and kernel matching estimators. The result further indicted that irrigation had positive impact on crop production, consumption and revenue generation which all together indicated improvement in food security. The sensitivity analysis test shows that impact results estimated by this study were insensitive to unobserved selection bias which shows it is a real impact of the irrigation.ConclusionIt was concluded that irrigation has a positive and significant impact on household food security. Concerned bodies that working on small-scale irrigation development therefore should continue investment in irrigation activities for poverty reduction strategies and scale-up irrigation interventions to the other areas where there is potentially irrigable land.

Multidimensional spatial clustering and visualization of 3D topographic relief data

Point cloud contains a large collection of point data as surface returns to describe the multidimensional aspect of the topographic features. Data points within these point clouds at the atomic level convey little or no information about the structural, physical, and spatial information about objects of interest within the scene in its raw form. Analyzing the surface described as a set of the point is complex and challenging. This paper describes the framework and methods for analyzing topographical reliefs and terrain regions to extract surface features using spatial clustering and aggregation of point cloud data. The method also describes the effectiveness of Kd- tree and nearest neighbor estimates in segmenting and visualizing the surface topographical terrain and relief region. The morphological correspondence between the points within clusters and the corresponding surface is demonstrated. It is also defined as clusters and spatially varying aspects of the object structures for further studies. The result obtained with the experiments shows significant improvement in classifying and clustering small and large surface structures of topographic reliefs over other known methods. It establishes the relevance of using spatial clustering and the use of surface normals for clustering object structures of varying sizes on the earth's surface.

The effects of windstorm in African medium-sized cities: An analysis of the degree of damage using KDE hotspots and EF-scale matrix

Violent windstorms are becoming more prevalent in African inland towns and cities. Yet, very few studies have reported on their increasing occurrences in sub-Saharan Africa's low-density and medium-sized cities and towns. This study uses Enhanced Fujita's F-scale matrix to estimate the intensity and rank the damage severity of a windstorm on June 16, 2018 that ruined more than 30 lives and thousand buildings and other essential structures within the 2-h of its destructive span in Bauchi city in northern Nigeria. A pictorial ranking of some typical damage was carried out to supplement the results of the F-scale decision matrix. In total, 1,236 buildings and structures were identified with varying levels of damage. Two techniques - Average Nearest Neighbor and Kernel Density Estimation (KDE) were implemented using Geographic information system (GIS) in mapping out the spatial patterns and damage hotspots. The results of the F-scale matrix reveal that the dominant wind speed with the most significant damage to buildings and structures is 67 ± 20 ms – 1 with the traditional parts of the city being the worst hit by the disaster. The art and science of visual ranking and hotspots mapping can support policymakers, first respondents, and other stakeholders to co-design strategies and co-produce effective solutions for the increasing climate extreme events and their related disaster risk.

Complete consistency and convergence rate of the nearest neighbor estimator of the density function based on WOD samples

Complete consistency and convergence rate of the nearest neighbor estimator of the density function based on WOD samples

Deciphering High-Order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational Entropy.

We employ the kth nearest-neighbor estimator of configurational entropy in order to decode within a parameter-free numerical approach the complex high-order structural correlations in fluxional molecules going much beyond the usual linear, bivariate correlations. This generic entropy-based scheme for determining many-body correlations is applied to the complex configurational ensemble of protonated acetylene, a prototype for fluxional molecules featuring large-amplitude motion. After revealing the importance of high-order correlations beyond the simple two-coordinate picture for this molecule, we analyze in detail the evolution of the relevant correlations with temperature as well as the impact of nuclear quantum effects down to the ultralow temperature regime of 1 K. We find that quantum delocalization and zero-point vibrations significantly reduce all correlations in protonated acetylene in the deep quantum regime. Even at low temperatures up to about 100 K, most correlations are essentially absent in the quantum case and only gain importance at higher temperatures. In the high temperature regime, beyond roughly 800 K, the increasing thermal fluctuations are found to exert a destructive effect on the presence of correlations. At intermediate temperatures of approximately 100-800 K, a quantum-to-classical cross-over regime is found where classical mechanics starts to correctly describe trends in the correlations whereas it even qualitatively fails below 100 K. Finally, a classical description of the nuclei provides correlations that are in quantitative agreement with the quantum ones only at temperatures exceeding 1000 K. This data-intensive analysis has been made possible due to recent developments of machine learning techniques based on high-dimensional neural network potential energy surfaces in full dimensionality that allow us to exhaustively sample both the classical and quantum ensemble of protonated acetylene at essentially converged coupled cluster accuracy from 1 to more than 1000 K. The presented non-parametric analysis of correlations beyond usual linear two-coordinate terms is transferable to other system classes. The technique is also expected to complement and guide the analysis of experimental measurements, in particular multidimensional vibrational spectroscopy, by revealing the complex coupling between various degrees of freedom.

On Complete Consistency for the Estimator of Nonparametric Regression Model Based on Asymptotically Almost Negatively Associated Errors

In this paper, we mainly study the consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated (AANA, in short) errors. Firstly, the Bernstein type inequality for AANA random variables is established. By using the Bernstein type inequality and moment inequalities, we investigate the complete consistency and convergence rate for the estimator of nonparametric regression model based on AANA errors. As applications, the complete consistency and convergence rate for the nearest neighbor estimator are obtained.