K-nearest Neighbor Density Estimation Research Articles

Slope Collapse Prediction Using Bayesian Framework with K-Nearest Neighbor Density Estimation: Case Study in Taiwan

AbstractSlope failures across mountain roads can damage man-made structures, interrupt traffic, and give rise to fatal accidents. Disastrous consequences of these hazards necessitate the approach for predicting their occurrences. In practice, slope collapse prediction can be formulated as a classification problem with two class labels: collapse and noncollapse. This study aims at proposing a novel approach for slope collapse assessment. The newly established method integrates the Bayesian framework and the K-nearest neighbor density estimation technique. The Bayesian framework is employed to achieve probabilistic slope stability estimations. Meanwhile, the K-nearest neighbor technique is a nonparametric approach to approximate the conditional probability density functions. In addition, a database that contains 211 slope evaluation samples has been collected in the Taiwan Provincial Highway Nos. 18 and 21 is used to construct and verify the slope assessment model. Experimental results point out that the pr...

A novel groutability estimation model for ground improvement projects in sandy silt soil based on Bayesian framework

In construction engineering, permeation grouting with microfine cement is a widely utilized approach for soil improvement. Hence, estimating groutability is a very important task that should be carried out in the planning phase of any grouting project. This research aims at establishing a novel method for groutability prediction with the utilization of microfine cement in sandy silt soil. The newly proposed approach integrates the Bayesian framework and the K-nearest neighbor (K-NN) density estimation technique. The Bayesian framework is used to achieve probabilistic groutability estimations. Meanwhile, the K-NN method is employed to approximate the conditional probability density functions. Moreover, to establish the new approach, 240 in-situ grouting cases have been recorded during the progress of Mass Rapid Transit and highway projects in Taiwan. Experimental results point out that the proposed method can deliver superior prediction accuracy. Hence, the new groutability estimation approach is a promising alternative to help construction engineers in grouting process assessment.

A statistical model of cluster stability

In the current paper we present a method for assessing cluster stability. This method, combined with a clustering algorithm, yields an estimate of the data partition, namely, the number of clusters. We adopt the cluster stability standpoint where clusters are imagined as islands of “high” density in a sea of “low” density. Explicitly, a cluster is associated with its high density core. Our approach offers to evaluate the goodness of a cluster by the similarity amongst the entire cluster and its core. We propose to measure this resemblance by two-sample tests or by probability distances between appropriate probability distributions. The distances are calculated on clustered samples drawn from the source population according to two different distributions. The first law is the underlying set distribution. The second law is constructed so that it represents the clusters’ cores. Here, a variant of the k-nearest neighbor density estimation is applied, so that items belonging to cores have a much higher chance to be selected. As the sample distribution is unknown a distribution-free two-sample test is required to examine the mentioned correspondence. For constructing such a test, we use distance functions built on negative definite kernels. In practice, outliers in the samples and limitations of the clustering algorithm heavily contribute to the noise level. As a result of this shortcoming the distance values have to be determined for many pairs of samples and therefore an empirical distance's distribution is obtained. The distribution is dependent on the examined number of clusters. To prevent this property for biasing the results we normalize the distances. It is conjectured that the true number of clusters yields the most concentrated normalized distribution. To measure the concentration we use the sample mean and the sample 25th percentile. The paper exhibits the good performance of the proposed method on synthetic and real-world data.

Multivariate data-driven k-NN function estimation

In Bhattacharya and Mack ( Ann. Statist. 15 (1987), 976–994), it was shown (among other things) that adapting for the optimal choice of k in univariate k-nearest neighbor density and regression estimation is feasible using weak convergence techniques. We now show that the same holds true for the multivariate case. Our results parallel Krieger and Pickands ( Ann. Statist. 9 (1981), 1066–1078) and Mack and Müller ( J. Multivariate Anal. 23 (1987), 169–182) for adaptive multivariate kernel density, respectively, regression, estimation.

A nearest neighbor hazard tare estimator for randomly censored data

A nearest-neighbor type estimator of the hazard rate of lifetimes that are randomly right-censored is studied. This estimator is formulated through combining the ideas of the k-nearest neighbor density estimation and of the hazard rate estimation by ratio-form estimators for randomly right-censored data. Under standard conditions mean square consistency, strong consistency and asymptotic normality are established altogether. Comparisons with results in the literature are also remarked.

Comparison of decision rules for automatic EEG classification

Discusses eight classification rules, four based on parametric Gaussian assumptions and four based on nonparametric k-nearest neighbor density estimation, which were tested on human EEG samples representing seven forms of mental activity. With a set of primary EEG features, the k-NN rules, as a class, were significantly more effective than the parametric classifiers; best results were obtained with an optimized version of the generalized k-NN rule. With a reduced set of secondary features, the two types performed approximately equally, but below the best k-NN performances in the original space.