Neighbor Density Estimation Research Articles

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.

Optimized Gabor Filter Banks and Autoencoder Models for Enhanced Knitted Fabric Defect Detection

There is a high need for an automated system to detect fabric defects, as the current manual methods used in the garment industries in Nepal are unreliable and costly. Previous research has focused on specific fabric defects rather than overall fabric defects efficiently. This research employs two autoencoder models to identify different defects across different types of knitted fabrics, utilizing two datasets: the SFDG dataset and a custom dataset prepared from Butwal’s garment industries. The models benefit from a carefully designed Gabor filter bank to examine fabric compositions. This filter bank is fine-tuned by modifying parameters, wavelength, and orientation to detect varieties of defects in knitted fabrics. These models get feature representations from the Gabor filter bank’s outputs and help the system adapt to different types of defect patterns, making defect detection more reliable and accurate. The nearest neighbor density estimator finds possible defects and marks on the fabric images. The model's effectiveness and strength are shown by validating it on different types of knitted fabrics, including plain and patterned fabrics, using evaluation metrices like cTPR and ROC AUC. The first model achieves a cTPR of 0.879 and an AUC score of 0.947, while the second model achieves a cTPR of 0.899 and an AUC score of 0.958.

Multivariate functional data clustering using adaptive density peak detection.

Clustering for multivariate functional data is a challenging problem since the data are represented by a set of curves and functions belonging to an infinite-dimensional space. In this article, we propose a novel clustering method for multivariate functional data usingan adaptive density peak detection technique. It is a quick cluster center identification algorithm based on the two measures of each functional data observation: the functional density estimate and the distance to the closest observation with a higher functional density. We suggest two types of functional density estimators for multivariate functional data. The first one is a functional -nearest neighbor density estimator based on (a) an L2 distance between raw functional curves, or (b) a semimetric of multivariate functional principal components. The second one is a -nearest neighbor density estimator based on multivariate functional principal scores. Our clustering method is computationally fast since it does not need an iterative process. The flexibility and advantages of the method are examined by comparing it with other existing clustering methods in simulation studies. A user-friendly R package FADPclust is developed for public use. Finally, our method is applied to a real case study in lung cancer research.

Relative density clouds: Visualizing and exploring multivariate patterns of group differences.

This paper introduces relative density clouds, a simple but powerful method to visualize the relative density of two groups in multivariate space. Relative density clouds employ k-nearest neighbor density estimates to provide information about group differences throughout the entire distribution of the variables. The method can also be used to decompose overall group differences into the specific contributions of differences in location, scale, and covariation. Existing relative distribution methods offer a flexible toolkit for the analysis of univariate differences; relative density clouds bring some of the same advantages to fruition in the context of multivariate research. They can assist in the exploration of complex patterns of group differences, and help break them down into simpler, more interpretable effects. An easy-to-use R function is provided to make this visualization method widely accessible to researchers.

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.

The consistency and convergence rate for the nearest neighbor density estimator based on -mixing random samples

In this work, we mainly investigate the consistency and strong convergence rate for the nearest neighbor density estimator based on -mixing random samples. The weak consistency, complete consistency, the rates of complete consistency and strong consistency for the nearest neighbor estimator of density function based on -mixing random samples are established. The results obtained in the article extend some corresponding ones for independent samples.

Cytometry TOF identifies alveolar macrophage subtypes in acute respiratory distress syndrome.

Studies in human peripheral blood monocyte-derived macrophages in vitro have shown clear evidence that multiple macrophage polarization states exist. The extent to which different alveolar macrophage (AM) polarization states exist in homeostasis or in the setting of severe injury such as acute respiratory distress syndrome (ARDS) is largely unknown. We applied single-cell cytometry TOF (CyTOF) to simultaneously measure 36 cell-surface markers on CD45+ cells present in bronchoalveolar lavage from healthy volunteers, as well as mechanically ventilated subjects with and without ARDS. Visualization of the high-dimensional data with the t-distributed stochastic neighbor embedding algorithm demonstrated wide diversity of cell-surface marker profiles among CD33+CD71+CD163+ AMs. We then used a κ-nearest neighbor density estimation algorithm to statistically identify distinct alveolar myeloid subtypes, and we discerned 3 AM subtypes defined by CD169 and PD-L1 surface expression. The percentage of AMs that were classified into one of the 3 AM subtypes was significantly different between healthy and mechanically ventilated subjects. In an independent cohort of subjects with ARDS, PD-L1 gene expression and PD-L1/PD-1 pathway-associated gene sets were significantly decreased in AMs from patients who experienced prolonged mechanical ventilation or death. Unsupervised CyTOF analysis of alveolar leukocytes from human subjects has potential to identify expected and potentially novel myeloid populations that may be linked with clinical outcomes.

Neural Network and Nearest Neighbor Algorithms for Enhancing Sampling of Molecular Dynamics.

The free energy calculations of complex chemical and biological systems with molecular dynamics (MD) are inefficient due to multiple local minima separated by high-energy barriers. The minima can be escaped using an enhanced sampling method such as metadynamics, which apply bias (i.e., importance sampling) along a set of collective variables (CV), but the maximum number of CVs (or dimensions) is severely limited. We propose a high-dimensional bias potential method (NN2B) based on two machine learning algorithms: the nearest neighbor density estimator (NNDE) and the artificial neural network (ANN) for the bias potential approximation. The bias potential is constructed iteratively from short biased MD simulations accounting for correlation among CVs. Our method is capable of achieving ergodic sampling and calculating free energy of polypeptides with up to 8-dimensional bias potential.

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.

Airfoil shape optimization using improved Multiobjective Territorial Particle Swarm algorithm with the objective of improving stall characteristics

In this paper, a new robust optimization technique with the ability of solving multi-objective constrained design optimization problems in aerodynamics is presented. This new technique is Multi-objective Territorial Particle Swarm Optimization (MOTPSO) algorithm in which diversity is actively preserved by avoiding overcrowded clusters of particles and encouraging broader exploration. Adaptively varying "territories" are formed around promising individuals to prevent many of the lesser individuals from premature clustering and encouraged them to explore new neighborhoods based on a hybrid self-social metric. Also, a new social interaction scheme is introduced which guided particles towards the weighted average of their "elite" neighbors' best found positions instead of their own personal bests which in turn helps the particles to exploit the candidate local optima more effectively. The MOTPSO algorithm takes into account multiple objective functions using a Pareto-Based approach. The non-dominated solutions found by swarm are stored in an external archive and nearest neighbor density estimator method is used to select a leader for the individual particles in the swarm. Efficiency and robustness of the proposed algorithm is demonstrated using multiple traditional and newly-composed optimization benchmark functions and aerodynamic design problems. In final airfoil designs obtained from the Multi Objective Territorial Particle Swarm Optimization algorithm, separation point is delayed to make the airfoil less susceptible to stall in critical operating conditions and it also reveal an evident improvement over the test case airfoil across all objective functions presented.

THE TWO-DIMENSIONAL PROJECTED SPATIAL DISTRIBUTION OF GLOBULAR CLUSTERS. I. METHOD AND APPLICATION TO NGC 4261

We present a new method for the determination of the two-dimensional (2D) projected spatial distribution of globular clusters (GCs) in external galaxies. This method is based on the K-Nearest Neighbor density estimator of Dressler (1980), complemented by MonteCarlo simulations to establish the statistical significance of the results. We apply this method to NGC4261, a "test galaxy" where significant 2D anisotropy in the GC distribution has been reported. We confirm that the 2D distribution of GC is not azimuthally isotropic. Moreover, we demonstrate that the 2D distribution departures from the average GC radial distribution results in highly significant spiral-like or broken shell features. Overall, the same perturbations are found in "red" and "blue" GCs, but with some differences. In particular, we observe a central feature, roughly aligned with the minor axis of NGC4261, composed of red and most luminous GCs. Blue and fainter GCs are more frequent at large radial distances and follow the spiral-like features of the overall density structure. These results suggest a complex merging history for NGC4261.

The Rate of Strong Consistency of the Nearest Neighbor Density Estimator for Negatively Dependent Random Variables

Let {Xn:n≥1} be a sequence of negatively dependent random variables. Based on (X1,…,Xn), in this paper we investigate the rate of pointwise consistency and strong consistency of the nonparametric density estimator proposed by Yu. We extend the correspondent results under the negatively dependent samples.

The consistency and asymptotic normality of nearest neighbor density estimator under α-mixing condition

We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases.

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.

Higher order estimation at Lebesgue points

The symmetric derivative of a probability measure at a Lebesgue point can often be specified by an exact relation involving a regularity index. Knowledge of this index is of practical interest, for example to specify the local behavior of the measure under study and to evaluate bandwidths or number of neighbors to take into account in smoothing techniques. This index also determines local rates of convergence of estimators of particular points of curves and surfaces, like minima and maxima. In this paper, we consider the estimation of the d-dimensional regularity index. We introduce an estimator and derive the basic asymptotic results. Our estimator is inspired by an estimator proposed in Drees and Kaufmann (1998, Stochastic Processes and their Applications, 75, 149–172) in the context of extreme value statistics. Then, we show how (estimates of) the regularity index can be used to solve practical problems in nearest neighbor density estimation, such as removing bias or selecting the number of neighbors. Results of simulations are presented.

Consistency of a nearest neighbor density estimator for dependent variables

In this article, pointwise consistency and uniform complete consistency of an alternative nonparametric density estimator are proved for φ-mixing and α-mixing processes.

Uniform convergence rates for a nearest neighbor density estimator under dependence assumptions

In this paper the rates of strong uniform convergence over any compact set for an alternative nearest neighbor density estimator are obtained when the observations satisfy a ø-mixing or an a-mixing condition. In the ø-mixing case we obtain a quite better convergence rate than for a-mixing processes and we do not require a geometric condition on the mixing coefficients. For independent or m-dependent observations, as a special case of ømixing, the result gives us the optimal rate of strong uniform convergence for density estimators.

Improving k-nearest neighbor density and error estimates

The subject of this paper is the estimation of the probability density function and probability of Bayes error using the k-nearest neighbor method. Modified formulas for density estimator are proposed, based on the analysis of the bias and the variance expressions. The modified density estimators are then used for Bayes error estimation. Performances of the newly proposed procedures are examined by executing controlled experiments on Gaussian data. The procedures exhibit slightly improved error estimates in the cases important for practical purposes.

An asymptotic optimality of the discriminant procedure based on a nearest neighbor density estimator

An asymptotic optimality of the discriminant procedure based on a nearest neighbor density estimator