Natural Neighbor Research Articles

A neighborhood-based robust clustering algorithm using Apollonius function kernel

Density Peak Clustering (DPC) is a useful algorithm for grouping data points based on their closeness and density. It is widely used in various areas of computer science. It can detect the peak density in each period of the clustering steps and assign the rest of the data to the next steps. Peak density clustering analysis is able to discover clusters of arbitrary shapes, but usually, when the data set is large, it is computationally expensive and difficult to apply to high-dimensional data. When the distance between clusters is significantly different, it is unable to distinguish adjacent clusters with different densities. To deal with such issues, a new clustering algorithm based on neighborhoods and the Apollonius kernel is proposed. The proposed algorithm can be implemented with four steps. 1) Estimation of natural neighbor, 2) Identification of core points, 3) Merging the cores of a cluster and separating the cores of different clusters, 4) Using the Apollonius kernel between the core points and the farthest points to assign the remaining points to the clusters and find the noise points. The local density estimation process based on the natural neighborhood of high-density points and their integration, as well as border point classification, allows the proposed method to reveal the local cluster structure. As a result, the adjoining clusters with distinctive densities are recognized, and the computation is substantially reduced. The proposed method is validated on some synthetic data sets and the UCI data set experimentally and has a high 10% accuracy.

A hybrid sampling method for highly imbalanced and overlapped data classification with complex distribution

Class imbalance and overlap coupling is the primary cause of performance degradation for classifiers. Unfortunately, it always occurs. In this paper, we propose a hybrid sampling method derived from optimized generative adversarial network and natural neighbor search (HD-GNNS) for this scenario. The new approach considers both the global distribution and local distribution of the minority class to improve the data distribution fundamentally. First, natural neighbor search with Fisher’s discriminant ratio is conducted to screen overlapped sample subset and remove noise samples. It effectively overcomes the parameter sensitivity by adaptively determining the search radius. Then, an encoder with squeeze and excite block is introduced into generative adversarial network, and the structure of generative adversarial network is optimized with cross-layer and low-rank matrix. It better captures the distribution characteristics of minority samples in overlapped subset for oversampling. Afterwards, the local density of majority samples in overlapped subset is calculated by the aforementioned natural neighbor search method, and Thornton’s Separation Index is used to implement under-sampling adaptively. We evaluate the proposed approach on 1 artificial dataset, 14 UCI datasets and 8 real-word datasets. The experimental results show that the proposed HD-GNNS exhibits more impressive performance compared to other benchmark methods.

A Shared Natural Neighbors Based-Hierarchical Clustering Algorithm for Discovering Arbitrary-Shaped Clusters

A Shared Natural Neighbors Based-Hierarchical Clustering Algorithm for Discovering Arbitrary-Shaped Clusters

A smoothed natural neighbour Galerkin method for flexoelectric solids

A smoothed natural neighbour Galerkin method for flexoelectric solids

Visean terrigenous sediments of the South Tatar Arch (Volga-Urals oil and gas bearing province) – multifacial filling of the karst surface of the Tournaisian isolated carbonate platform

The paper presents new thickness and sandiness maps of the Visean terrigenous strata (Radayevkian and Bobrikian regional stages, Lower Carboniferous) of the South Tatar Arch, constructed using the “Natural Neighbour” spatial interpolation method in ArcGIS Pro software based on the analysis of geophysical survey data for more than 30,000 boreholes. The interpretation of the maps in combination with the results of sedimentological, ichnotextural and petrophysical core studies, supplemented by the analysis of archival and published materials, provided an opportunity to update the approach to modelling the sedimentation of the terrigenous Lower Carboniferous of the South Tatar Arch. The proposed sedimentation models of terrigenous and coal-bearing sediments take into account the chronostratigraphic data, the karstification of isolated carbonate platforms, the sediment accumulation rates and the ichnotextural characteristics of the sediments. It is concluded that the accumulation and preservation of terrigenous and peat (coal-bearing) sediments differ in duration (0.1 million years vs. 1.5–2 million years) and are consequently associated with transgressive and regressive phases. The accumulation of terrigenous sediments includes: (a) transgressive eustatic episodes – short-term incursions of a marine basin onto the eroded surface of an isolated carbonate platform, during which silty and sandy, well-sorted bioturbated sediments were accumulated, often with a variety of ichnofossils of marine benthic organisms; (b) the regressive eustatic phase resulted in the predominant erosion of sediments on the arch; whereas sediments in the incisions were largely preserved. The accumulation of peat (coal-bearing) deposits includes (a) the regressive eustatic phase, during which the vast area of the eastern Volga-Urals region was covered with flourishing vegetation and stable swamp environments were forming in the incisions of the Tournaisian surface; (b) the transgressive phase – the peat was overlaid and buried by transgressive marine silt-sand sediments; then it was compacted and transformed into coal. The alternation of coal-bearing and transgressive intervals indicates the cyclicity of these processes. The proposed sedimentation models extend the concepts of previous studies and are consistent with the developed maps of thickness and sandiness of the Lower Carboniferous terrigenous sediments, explaining the complex, covering and mosaic distribution of sand bodies over the area, as well as the filling of incisions with sediments of different lithological types.

Comparative Study of Geospatial Techniques for Interpolating Groundwater Quality Data in Agricultural Areas of Punjab, Pakistan

Groundwater Arsenic (As) data are often sparse and location-specific, making them insufficient to represent the heterogeneity in groundwater quality status at unsampled locations. Interpolation techniques have been used to map groundwater As data at unsampled locations. However, the results obtained from these techniques are affected by various inherent and external factors, which lead to uncertainties in the interpolated data. This study was designed to determine the best technique to interpolate groundwater As data. We selected ten interpolation techniques to predict the As concentration in the groundwater resources of Punjab, Pakistan. Two external factors, the spatial extent of the study area and data density, were considered to assess their impact on the performance of interpolation techniques. Our results show that the Inverse Distance Weighting (IDW) and Spline interpolation techniques demonstrate the highest accuracy with the lowest RMSE (13.5 ppb and 16.7 ppb) and MAE (87.8 ppb and 89.5 ppb), respectively, while the Natural Neighbor technique shows the lowest accuracy with the highest RMSE (2508.7 ppb) and MAE (712.1 ppb) to interpolate groundwater As data. When the study area’s extent was modified, IDW showed the best performance, with errors within ±1.5 ppb for 95% of the wells across the study area. While data density has a positive correlation with interpolation accuracy among all techniques, the IDW remained the best method for interpolation. It is therefore concluded that IDW should be used to interpolate groundwater quality data when observed data are sparse and randomly distributed. The utilization of IDW can be useful for As monitoring and management in groundwater resources.

C-VoNNI: a precise fingerprint construction for indoor positioning systems using natural neighbor methods with clustering-based Voronoi diagrams

C-VoNNI: a precise fingerprint construction for indoor positioning systems using natural neighbor methods with clustering-based Voronoi diagrams

Utilization of Curvelet Transform in Reconstructing Cellular Images for Undersampled Optical-resolution Photoacoustic Microscopy.

We address the problem of limited temporal resolution in optical-resolution microscopy (OR-PAM) for cellular imaging by undersampling and reconstruction. A curvelet transform method in a compressed sensing framework (CS-CVT) was devised to specifically reconstruct the boundary and separability of cells object in an image. The performance of CS-CVT approach was justified by comparisons with the natural neighbor interpolation (NNI) followed by smoothing filters on various imaging objects. In addition, a full-raster scanned image was provided as reference. In terms of structure, CS-CVT produces cellular images with smoother boundary but less aberration. We found the strength of CS-CVT in recovering high frequency that is important in representing sharp edges which often missing in typical smoothing filter. In a noisy environment, CS-CVT was less affected by the noise compared to NNI with smoothing filter. Furthermore, CS-CVT could attenuate noise beyond the full raster scanned image. By considering the finest structure in the cellular image, CS-CVT was performing well with minimum range of undersampling around 5% to 15%. In practice, this undersampling were easily translates into 8- to 4-fold faster OR-PAM imaging. In summary, our approach improves temporal resolution of OR-PAM without significant trade-off in image quality.

WRND: A weighted oversampling framework with relative neighborhood density for imbalanced noisy classification

Imbalanced data and label noise are ubiquitous challenges in data mining and machine learning that severely impair classification performance. The synthetic minority oversampling technique (SMOTE) and its variants have been proposed, but they are easily constrained by hyperparameter optimization such as k-nearest neighbors, their performance deteriorates owing to noise, they rarely consider data distribution information, and they cause high complexity. Furthermore, SMOTE-based methods perform random linear interpolation between each minority class sample and its randomly selected k-nearest neighbors, regardless of sample differences and distribution information. To address the above problems, an adaptive, robust, and general weighted oversampling framework based on relative neighborhood density (WRND) is proposed. It can combine with most SMOTE-based sampling algorithms easily and improve performance. First, it adaptively distinguishes and filters noisy and outlier samples by introducing the natural neighbor, which inherently avoids the extra noise and overlapping samples introduced by the synthesis of noisy samples. The relative neighborhood density of each sample can then be obtained, which reflects the intra-class and inter-class distribution information within the natural neighborhood. To alleviate the blindness of SMOTE-based methods, the number and locations of synthetic samples are informedly assigned based on distribution information and reasonable generalization of natural neighborhoods of original samples. Extensive experiments on 23 benchmark datasets and six classic classifiers with eight pairs of representative sampling algorithms and two state-of-the-art frameworks, significantly demonstrate the effectiveness of the WRND framework. Code and framework are available at https://github.com/dream-lm/WRND_framework.

Elastoplastic Analysis of Frame Structures Using Radial Point Interpolation Meshless Methods

The need to design structures and structural elements that are more efficient in terms of performance is a key aspect of engineering. For a given material to be used at its maximum capacity, considering non-linear characteristics is mandatory. The non-linear regime is a subject of extreme interest for this reason and is an area with intense research activity. In this work, advanced discretization techniques (i.e., meshless methods) are applied in the elastoplastic analysis of 2D and 3D structural elements. The literature shows that meshless methods are capable of producing more accurate and smoother strain and stress fields, which are the variable fields required in the non-linear models describing elastoplasticity. Thus, in this study, the Radial Point Interpolation Method (RPIM) and the Natural Neighbor Radial Point Interpolation Method (NNRPIM) are combined with a non-linear iterative algorithm, fully developed by the authors, with the objective of analyzing for the first time the elastoplastic behavior of a two-bay asymmetric frame and bowstring bridge considering 2D and 3D analysis. The accuracy and robustness of the RPIM and the NNRPIM are shown in the end, comparing the obtained results with FEM solutions and the available literature.

A robust interpolation-based method for forensic soil provenancing: A Bayesian likelihood ratio approach

Soil is a complex and spatially variable material that has a demonstrated potential as a useful evidence class in forensic casework and intelligence operations. Here, the capability to spatially constrain police search areas and prioritise resources by triaging areas as low and high interest is advantageous. Conducted between 2017 and 2021, a forensically relevant topsoil survey (0–5 cm depth; 1 sample per 1 km2) was carried out over Canberra, Australia, aiming to document the distribution of chemical elements in an urban/suburban environment, and of acting as a testbed for investigating various aspects of forensic soil provenancing. Geochemical data from X-Ray Fluorescence (XRF; for total major oxides) and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS; for trace elements) following a total digestion (HF + HNO3) of the fused XRF beads were obtained from the survey’s 685 topsoil samples (plus 138 additional quality control samples and six “Blind” simulated evidentiary samples). Using those “Blind” samples, we document a likelihood ratio approach where for each grid cell the analytical similarity between the grid cell and evidentiary sample is attributed from a measure of overlap between the two Cauchy distributions, including appropriate uncertainties. Unlike existing methods that base inclusion/exclusion on an arbitrary threshold (e.g., ± three standard deviations), our approach is free from strict binary or Boolean thresholds, providing an unconstrained gradual transition dictated by the analytical similarity. Using this provenancing model, we present and evaluate a new method for upscaling from a fine (25 m x 25 m) interpolated grid to a more appropriate coarser (500 m x 500 m) grid. In addition, an objective method using Random Match Probabilities for ranking individual variables to be used for provenancing prior to receiving evidentiary material was demonstrated. Our results show this collective procedure generates more consistent and robust provenance maps when applied to two different interpolation algorithms (e.g., inverse distance weighting, and natural neighbour), with different grid placements (e.g., grid shifts to the north or east) and by different theoretical users (e.g., different computer systems, or forensic geoscientists).

A novel outlier detecting algorithm based on the outlier turning points

Outlier detection is one of the hot research in data mining, and has been applied to various fields such as network anomaly detection, image abnormal analysis, etc. In recent years, many outlier detecting algorithms have been proposed. However, these outlier detecting algorithms are hard to effectively detect global outliers, local outliers and outlier clusters at the same time. In this paper, we propose a novel outlier detecting algorithm based on the following ideas: (1) the density distribution should not be changed dramatically on local area; (2) the ratio of the number of k nearest neighbors and the number of reverse k nearest neighbors should not be very big. Based on above ideas, the proposed algorithm aims to find outlier turning points, then regards all outlier turning points and its sparse neighbors as outliers. Futhermore, the proposed algorithm use natural neighbors to obtain the neighborhood parameter k adaptively. The formal analysis and extensive experiments demonstrate that this technique can detect global outliers, local outliers and outlier clusters without neighborhood parameter k.

Allometric scaling of retrogressive thaw slumps

Abstract. In the warming Arctic, retrogressive thaw slumping (RTS) has emerged as the primary thermokarst modifier of ice-rich permafrost slopes, raising urgency to investigate the distribution and intensification of disturbances and the cascade of effects. Tracking RTS is challenging due to the constraints of remote sensing products and a narrow understanding of complex, thaw-driven landforms; however, high-resolution elevation models provide new insights into geomorphic change. Structural traits, such as RTS depth of thaw or volume, can be obtained through allometric scaling. To address fundamental knowledge gaps related to area–volume scaling of RTS, a suitable surface interpolation technique was first needed to model pre-disturbance topography upon which volume estimates could be based. Among eight methods with 32 parameterizations, natural neighbour surface interpolation achieved the best precision in reconstructing pre-disturbed slope topography (90th percentile root mean square difference ±1.0 m). An inverse association between RTS volume and relative volumetric error was observed, with uncertainties < 10 % for large slumps and < 20 % for small to medium slumps. Second, a multisource slump inventory (MSI) for two study areas in the Beaufort Delta (Canada) region was developed to characterize the diverse range of disturbance morphologies and activity levels, which provided consistent characterization of thaw-slump-affected slopes between regions and through time. The MSI delineation of high-resolution hillshade digital elevation models (DEMs) for three time periods (airborne stereo-imagery, lidar, ArcticDEM) revealed temporal and spatial trends in these chronic mass-wasting features. For example, in the Tuktoyaktuk Coastlands, a +38 % increase in active RTS counts and +69 % increase in total active surface area were observed between 2004 and 2016. However, the total disturbance area of RTS-affected terrain did not change considerably (+3.5 %) because the vast majority of active thaw slumping processes occurred in association with past disturbances. Interpretation of thaw-driven change is thus dependent on how active RTS is defined to support disturbance inventories. Our results highlight that active RTS is tightly linked to past disturbances, underscoring the importance of inventorying inactive scar areas. Third, the pre-disturbance topographies, MSI digitizations, and DEMs were integrated to explore allometric scaling relationships between RTS area and eroded volume. The power-law model indicated non-linearity in the rates of RTS expansion and intensification across scales (adj-R2 of 0.85, n= 1522) but also revealed that elongated, shoreline RTS reflects outliers poorly represented by the modelling. These results indicate that variation in the allometric scaling of RTS populations is based on morphometry, terrain position, and complexity of the disturbance area, as well as the method and ontology by which slumps are inventoried. This study highlights the importance of linking field-based knowledge to feature identification and the utility of high-resolution DEMs in quantifying rates of RTS erosion beyond tracking changes in the planimetric area.

Assessment of Different Spatial Interpolation Techniques for Generating Synthetic Soil Boring Data

Subsurface soil conditions usually involve special site variability that cannot be ignored for design and analysis. Therefore, the effect of site variability on associated soil properties should be assessed using gathered field data, such as soil boring data collected from discrete locations. In this study, six spatial interpolation techniques, the ordinary kriging (OK), simple kriging (SK), universal kriging (UK), inverse distance weight (IDW), spline, and natural neighbor (NaN) were evaluated to assess the best prediction strategy for considering site variability. The efficacy of these methods was tested at four soil boring sites. Boring profiles were generated using the different techniques at specified locations for each site, and the created data were compared with the measured soil boring profiles. For each location, the best-fit line of measured versus predicted undrained shear strength (Su) or standard penetration test (SPT) number, mean bias factor (λ), coefficient of effectiveness (COE), root mean square error (RMSE), and coefficient of variation (COV), were calculated and used to assess the various interpolation methods. The findings of this study demonstrated the ability of these spatial interpolations to produce precise soil boring data. The slope of best-fit line of measured/generated Su and SPT ranged from 0.89 to 0.99. The best-performing interpolation methods (in order) are: IDW, OK/UK, and SK methods. The results show that the COVs between the measured and synthetic soil boring data at the selected points are significantly lower than the COVs between the measured soil boring profiles for the entire site.

GNaN: A natural neighbor search algorithm based on universal gravitation

The natural neighbor (NaN) method and its search algorithm (NaN-Searching) are widely used in many fields, including pattern recognition and image processing. NaN-Searching fundamentally overcomes the problem of the conventional nearest neighbor algorithm in selecting parameters for datasets with arbitrary shapes and achieves good results. However, this algorithm uses the conventional distance metric as the neighbor judgment criterion, which cannot accurately reflect the overall structure of the dataset in the process of neighbor search. Inspired by Newton’s law of universal gravitation, we propose a NaN search algorithm based on universal gravitation (GNaN-Searching). Our algorithm calculates gravitation using the structural features of data points in the dataset, it utilizes the gravitation between data as the neighbor judgment criterion, and inherits the no-parameter and dynamic neighborhood characteristics of the NaN search algorithm. Experimental results show that the natural neighborhood graph obtained by our method has a high performance in the representation of manifold data. We also applied the new method to clustering and outlier detection and achieved satisfactory results.

An oversampling method based on differential evolution and natural neighbors

The classification problem of imbalanced data is a research focus in machine learning. An effective method for solving the class-imbalance problem is to generate synthetic samples for minority class data. Popular methods for synthesize samples include SMOTE, variants of SMOTE, and oversampling methods applying metaheuristic algorithms. Recently, an oversampling method DEBOHID based on differential evolutionary algorithm has been proposed. It uses nearest neighbors of the minority class to synthesize samples for balancing the data set. However, samples synthesized by nearest neighbors are easily interfered by noisy samples. Therefore, we proposed an oversampling method based on natural neighbors, called NaN-DEBOHID. In NaN-DEBOHID, minority samples are divided into dense samples and outliers according to the number of natural neighbors. Samples of different types are processed by different methods. The main advantages of NaN-DEBOHID are concluded as follows: (a) it finds samples that better represent the minority class distribution by applying natural neighbors; (b) it creates synthetic samples that showed better consistency with the surrounding samples by the DEBOHID method; (c) it removes noise samples of the minority class to enhance the classification performance. For experiments, Support Vector Machine (SVM) and k-Nearest Neighbor (kNN) are used as classifiers. The results indicated that NaN-DEBOHID performed competitively in terms of Accuracy, F-measure and AUC.

NonPC: Non-parametric clustering algorithm with adaptive noise detecting

Graph-based clustering performs efficiently for identifying clusters in local and nonlinear data Patterns. The existing methods face the problem of parameter selection, such as the setting of k of the k-nearest neighbor graph and the threshold in noise detection. In this paper, a non-parametric clustering algorithm (NonPC) is proposed to tackle those inherent limitations and improve clustering performance. The weighted natural neighbor graph (wNaNG) is developed to represent the given data without any prior knowledge. What is more, the proposed NonPC method adaptively detects noise data in an unsupervised way based on some attributes extracted from wNaNG. The algorithm works without preliminary parameter settings while automatically identifying clusters with unbalanced densities, arbitrary shapes, and noises. To assess the advantages of the NonPC algorithm, extensive experiments have been conducted compared with some classic and recent clustering methods. The results demonstrate that the proposed NonPC algorithm significantly outperforms the state-of-the-art and well-known algorithms in Adjusted Rand index, Normalized Mutual Information, and Fowlkes-Mallows index aspects.

Searching natural neighbors in an accelerated way

Natural neighbor (NaN) is an adaptive neighbor concept for automatically determining k value for k-nearest neighbors, which has been proved effective in clustering analysis, classification, and outlier detection. However, the existing algorithms for searching NaN employ the global search strategy, which increases unnecessary consumption of time on non-critical points. To solve this problem, we propose a novel accelerated algorithm by utilizing a local search strategy, called ASNN. ASNN is based on the fact that if remote points have reverse nearest neighbors, others are likely to have reverse nearest neighbors. Firstly, it extracts the remote points by defining remote radius. Secondly, only the neighbors of remote points are searched, so that ASNN can quickly obtain the natural neighbor eigenvalue (NaNE). Compared to existing algorithms for searching NaNs, ASNN drastically reduces the number of query points and time consumption. The efficiency and effectiveness of ASNN are proved on synthetic and real datasets.

Land and Seabed Surface Modelling in the Coastal Zone Using UAV/USV-Based Data Integration.

The coastal zone is an area that includes the sea coast and adjacent parts of the land and sea, where the mutual interaction of these environments is clearly marked. Hence, the modelling of the land and seabed parts of the coastal zone is crucial and necessary in order to determine the dynamic changes taking place in this area. The accurate determination of the terrain in the coastal zone is now possible thanks to the use of Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vehicles (USVs). The aim of this article is to present land and seabed surface modelling in the coastal zone using UAV/USV-based data integration. Bathymetric and photogrammetric measurements were carried out on the waterbody adjacent to a public beach in Gdynia (Poland) in 2022 using the DJI Phantom 4 Real Time Kinematic (RTK) UAV and the AutoDron USV. As a result of geospatial data integration, topo-bathymetric models in the coastal zone were developed using the following terrain-modelling methods: Inverse Distance to a Power (IDP), kriging, Modified Shepard's Method (MSM) and Natural Neighbour Interpolation (NNI). Then, the accuracies of the selected models obtained using the different interpolation methods, taking into account the division into land and seabed parts, were analysed. Research has shown that the most accurate method for modelling both the land and seabed surfaces of the coastal zone is the kriging (linear model) method. The differences between the interpolated and measurement values of the R95 measurement are 0.032 m for the land part and 0.034 m for the seabed part. It should also be noted that the data interpolated by the kriging (linear model) method showed a very good fit to the measurement data recorded by the UAVs and USVs.

Enhancing Indoor Air Quality Estimation: A Spatially Aware Interpolation Scheme

The comprehensive and accurate assessment of the indoor air quality (IAQ) in large spaces, such as offices or multipurpose facilities, is essential for IAQ management. It is widely recognized that various IAQ factors affect the well-being, health, and productivity of indoor occupants. In indoor environments, it is important to assess the IAQ in places where it is difficult to install sensors due to space constraints. Spatial interpolation is a technique that uses sample values of known points to predict the values of other unknown points. Unlike in outdoor environments, spatial interpolation is difficult in large indoor spaces due to various constraints, such as being separated into rooms by walls or having facilities such as air conditioners or heaters installed. Therefore, it is necessary to identify independent or related regions in indoor spaces and to utilize them for spatial interpolation. In this paper, we propose a spatial interpolation technique that groups points with similar characteristics in indoor spaces and utilizes the characteristics of these groups for spatial interpolation. We integrated the IAQ data collected from multiple locations within an office space and subsequently conducted a comparative experiment to assess the accuracy of our proposed method in comparison to commonly used approaches, such as inverse distance weighting (IDW), kriging, natural neighbor interpolation, and the radial basis function (RBF). Additionally, we performed experiments using the publicly available Intel Lab dataset. The experimental results demonstrate that our proposed scheme outperformed the existing methods. The experimental results show that the proposed method was able to obtain better predictions by reflecting the characteristics of regions with similar characteristics within the indoor space.