Minimum Number Of Points Research Articles

Unsupervised Decision Trees for Axis Unimodal Clustering

The use of decision trees for obtaining and representing clustering solutions is advantageous, due to their interpretability property. We propose a method called Decision Trees for Axis Unimodal Clustering (DTAUC), which constructs unsupervised binary decision trees for clustering by exploiting the concept of unimodality. Unimodality is a key property indicating the grouping behavior of data around a single density mode. Our approach is based on the notion of an axis unimodal cluster: a cluster where all features are unimodal, i.e., the set of values of each feature is unimodal as decided by a unimodality test. The proposed method follows the typical top-down splitting paradigm for building axis-aligned decision trees and aims to partition the initial dataset into axis unimodal clusters by applying thresholding on multimodal features. To determine the decision rule at each node, we propose a criterion that combines unimodality and separation. The method automatically terminates when all clusters are axis unimodal. Unlike typical decision tree methods, DTAUC does not require user-defined hyperparameters, such as maximum tree depth or the minimum number of points per leaf, except for the significance level of the unimodality test. Comparative experimental results on various synthetic and real datasets indicate the effectiveness of our method.

The minimum number of points and the calculation period of accrual as elements of the mechanism for improving the qualifications of lawyers

It is indicated that the defining elements of the lawyer’s legal status are his professional rights, duties, guarantees and responsibilities. Improving the qualifications of a lawyer is one of his fundamental professional duties (paragraph 4, part 1, article 21 of the Law of Ukraine «On Advocacy and Advocacy»). This article reveals the essence of the mechanism of the lawyer’s implementation of his professional duty to improve his qualifications, primarily through the prism of the need for him to obtain the appropriate number of points during the specified calculation period of their accrual. Attention is drawn to the dilatability of the issue not only regarding the total minimum number of points that a lawyer must receive, as well as the calculation period for their accrual, but also regarding the expediency of the existence of an institute for improving the qualifications of lawyers in general. In the framework of this article, the normative consolidation of the procedure for implementing the lawyer’s obligation to improve his qualifications in the context of the calculation of the appropriate number of points during a certain calculation period in accordance with national legislation, as well as the experience of foreign countries in determining the mechanism for improving the qualifications of lawyers, was also investigated. It is concluded that foreign countries use different positions regarding the definition of the mechanism for improving the qualifications of lawyers. Thus, a number of countries adhere to the need to use a calculation period of one year, fixing at the same time a different minimum number of credit points (hours, credits) that a lawyer must receive. Countries that not only set the minimum required number of points (hours) for a lawyer in one year, but also set a longer calculation period in general (three or five years) take a slightly different position. It is concluded that the provisions of national legislation regarding the minimum number of points (10 hours) that a lawyer must obtain within one year generally correspond to the law-making practice of European countries (the average duration of training of European professional judges and practicing lawyers is approximately 14 hours/points/credits per year).

An integrated MCDM model with enhanced decision support in transport safety using machine learning optimization

Having the capacity to effectively manage multi-criteria decision-making (MCDM) issues with considerable reliability is a crucial prerequisite for any MCDM model. This study introduces an advanced MCDM model that integrates logarithmic percentage change-driven objective weighting (LOPCOW), multi-objective optimization on the basis of a ratio analysis plus the full multiplicative form (MULTIMOORA), and density-based spatial clustering of applications with noise (DBSCAN). The goal is to provide robust decision support. Specifically, the model incorporates a machine learning tool, namely, grid search, to optimize the parameters of neighborhood radius (ε) and the minimum number of points, which significantly influence the clustering quality of DBSCAN. Subsequently, the cluster centers determined by DBSCAN serve as initial points for k-means clustering to negate the impact of outliers. This approach addresses the failures of DBSCAN in nearest neighbor search and parameter selection, and it also resolves the limitations of k-means related to the uncertainty in cluster outcomes due to varying initial centroid selections. Utilizing a real case study from the European Union, comprehensive comparisons of the model results demonstrate the adaptability, reliability, and stability of the proposed model, affirming its effectiveness in providing credible policy recommendations and practical decisions. Overall, this study presents policymakers, professionals, and administrators with a reliable decision-making system for conducting real-world MCDM tasks with enhanced confidence and robustness.

Non-crossing Hamiltonian Paths and Cycles in Output-Polynomial Time

We show that, for planar point sets, the number of non-crossing Hamiltonian paths is polynomially bounded in the number of non-crossing paths, and the number of non-crossing Hamiltonian cycles (polygonalizations) is polynomially bounded in the number of surrounding cycles. As a consequence, we can list the non-crossing Hamiltonian paths or the polygonalizations, in time polynomial in the output size, by filtering the output of simple backtracking algorithms for non-crossing paths or surrounding cycles respectively. We do not assume that the points are in general position. To prove these results we relate the numbers of non-crossing structures to two easily-computed parameters of the point set: the minimum number of points whose removal results in a collinear set, and the number of points interior to the convex hull. These relations also lead to polynomial-time approximation algorithms for the numbers of structures of all four types, accurate to within a constant factor of the logarithm of these numbers.

G2-SCANN: Gaussian-kernel graph-based SLD clustering algorithm with natural neighbourhood

For most clustering methods, not only the number of clusters must be set in advance, but also various hyperparameters such as initial centroids, number of nearest neighbours, the minimum number of points, neighbourhood radius, and cutoff distance all require pre-specification. As one of the most promising unsupervised learning methods in machine intelligence, existing clustering methods cannot simultaneously handle datasets with arbitrary shapes, different densities, distinct sizes, and overlapping. Background outliers and high dimensionality make clustering problems more challenging. In this paper, we propose a novel universal clustering methodology, called G2-SCANN, which yields the best clustering performance for all 30 synthetic and real datasets without any hyperparameter tuning if the exact number of clusters is known. Firstly, the shortest path length (SPL) in complex network or graph-based geodesic distance is used to give a locally backbone-structured description of graph vertex similarity. Accordingly, SPL-weighted local degree (SLD) is defined as vertex attributes of a SPL-weighted graph expressed by G2-SPL adjacency matrix with ε-natural neighbourhood. Secondly, the process of calculating SLD for every data point in a bottom-up way directly leads to division from a complete graph constituted by all data points to a group of SLD trees. This brings the interpretability and the elimination of lone trees. Thirdly, contrastive learning of largest SLD values for finding root vertices of each divisive tree is conducted and top-down category message is then transmitted from the root vertices to all the leaf ones of a SLD tree. It eventually produces tree-like clusters. Totally, the proposed G2-SCANN method leverages both local neighbouring similarity of data points and global information about data distribution and makes it perform better than other methods.

Registers of Educational Programmes as a Tool for Developing the Industry’s Human Resources Potential

The purpose of the article is to present a toolkit for analyzing changes in the system of library training, its subsequent adjustment and transformation into an effective tool for the development of the industry. The basis of this work is the monitoring of the functioning of the system of university and additional professional education (APE) in the field of “Library and Information Activities”.To solve this task the specialists of the Russian State Library have developed and created two registers: The Register of basic educational programmes of higher education, implemented in the direction of “Library and Information Activity”, and the Register of existing educational programmes of advanced training and professional retraining for library specialists. The registers are placed in the “Library Professionals” section of the federal state information system “National Electronic Library”. A study of these registers has been carried out and their expert evaluation has been made. The result of this work may be the creation of a “map” of higher and additional professional education of Russian library professionals.The register of basic educational programmes of higher education implemented in the field of “Library and Information Activity” contains details about 73 educational programmes of higher education of institutions from 32 subjects of the Russian Federation. The register of educational programmes of professional development and professional retraining for library specialists includes information about 241 educational programmes of additional professional development (29 professional retraining programmes and 212 professional development programmes). These programmes are implemented in 34 subjects of the Russian Federation.The programmes of APE are analyzed. The author’s methodology of evaluation of professional retraining programmes is presented. The minimum number of points that a professional retraining programme received according to the results of the examination was 6, the maximum number of points was 43.33 (out of 50 possible).Conclusions on the results of the expert evaluation are given. The prepared registers are presented as one of the elements of the information and educational platform of Russian libraries.

On the automorphism groups of rank-4 primitive coherent configurations

The minimal degree of a permutation group G is the minimum number of points not fixed by non-identity elements of G. Lower bounds on the minimal degree have strong structural consequences on G. Babai conjectured that if a primitive coherent configuration with n vertices is not a Cameron scheme, then its automorphism group has minimal degree ≥cn for some constant c>0. In 2014, Babai proved the desired lower bound on the minimal degree of the automorphism groups of strongly regular graphs, thus confirming the conjecture for primitive coherent configurations of rank 3.In this paper, we extend Babai's result to primitive coherent configurations of rank 4, confirming the conjecture in this special case. The proofs combine structural and spectral methods.Recently (March 2022) Sean Eberhard published a class of counterexamples of rank 28 to Babai's conjecture and suggested to replace “Cameron schemes” in the conjecture with a more general class he calls “Cameron sandwiches”. Naturally, our result also confirms the rank 4 case of Eberhard's version of the conjecture.

The curse of dimensionality for the Lp-discrepancy with finite p

The Lp-discrepancy is a quantitative measure for the irregularity of distribution of an N-element point set in the d-dimensional unit-cube, which is closely related to the worst-case error of quasi-Monte Carlo algorithms for numerical integration. It's inverse for dimension d and error threshold ε∈(0,1) is the minimal number of points in [0,1)d such that the minimal normalized Lp-discrepancy is less or equal ε. It is well known, that the inverse of L2-discrepancy grows exponentially fast with the dimension d, i.e., we have the curse of dimensionality, whereas the inverse of L∞-discrepancy depends exactly linearly on d. The behavior of inverse of Lp-discrepancy for general p∉{2,∞} has been an open problem for many years. In this paper we show that the Lp-discrepancy suffers from the curse of dimensionality for all p in (1,2] which are of the form p=2ℓ/(2ℓ−1) with ℓ∈N.This result follows from a more general result that we show for the worst-case error of numerical integration in an anchored Sobolev space with anchor 0 of once differentiable functions in each variable whose first derivative has finite Lq-norm, where q is an even positive integer satisfying 1/p+1/q=1.

Designing wavelength sampling for Fabry–Pérot observations

Context. Fabry–Pérot interferometers (FPIs) have become very popular in solar observations because they offer a balance between cadence, spatial resolution, and spectral resolution through a careful design of the spectral sampling scheme according to the observational requirements of a given target. However, an efficient balance requires knowledge of the expected target conditions, the properties of the chosen spectral line, and the instrumental characteristics. Aims. Our aim is to find a method that allows the optimal spectral sampling of FPI observations in a given spectral region to be found. The selected line positions must maximize the information content in the observation with a minimal number of points. Methods. In this study, we propose a technique based on a sequential selection approach in which a neural network is used to predict the spectrum (or physical quantities, if the model is known) from the information at a few points. Only those points that contain relevant information and improve the model prediction are included in the sampling scheme. Results. We have quantified the performance of the new sampling schemes by showing the lower errors in the model parameter reconstructions. The method adapts the separation of the points according to the spectral resolution of the instrument, the typical broadening of the spectral shape, and the typical Doppler velocities. The experiments that use the Ca II 8542 Å line show that the resulting wavelength scheme naturally places more points in the core than in the wings (by almost a factor of 4), consistent with the sensitivity of the spectral line at each wavelength interval. As a result, observations focused on magnetic field analysis should prioritize a denser grid near the core, while those focused on thermodynamic properties would benefit from a larger coverage. The method can also be used as an accurate interpolator to improve the inference of the magnetic field when using the weak-field approximation. Conclusions. Overall, this method offers an objective approach for designing new instrumentation or observing proposals with customized configurations for specific targets. This is particularly relevant when studying highly dynamic events in the solar atmosphere with a cadence that preserves spectral coherence without sacrificing much information.

The Making of Ship Points and Lines Assisted by the C-MAP Application to Practice Students' Collaboration Skills

One of the causes of accidents in the waters is the result of neglecting the point and the line of the ship. To indicate the presence of a ship using C-MAP, one way is to select a point using the save location in the navigator tools. Then when the ship starts sailing, immediately use the save track in the navigator tools to make a line. The minimum number of points that must be made is 5 pieces. The more places stored in a route, the neater the route will be. The method used is descriptive qualitative with data collected in the form of a display. Although this application can be used offline, it demands that the user is always present and only uses this application and not in conjunction with other applications on one device. It would be more suitable if there is more than one user using this app, working in a teams or taking turns.

Sophisticated CPBIS methods applied for FBISODATA clustering algorithm using with real time image database

Data mining is a process of mining hidden information to the previously unknown data and theoretically useful unknown information from a large amount of genuine data to be stored in a database. Image mining is a part of data mining with used as a predictive measure to identify with the age of the tiger. This research work is mainly focused on, to identify with the age of the Tiger using data mining techniques. This research work incorporates with which those domains of image processing and data mining to predict the age of the tiger using different kinds of color images are used. The fuzzy iterative self-organizing data analysis (FISODATA) clustering method requires more predefined parameters tofind the maximum number of iterations, the minimum number of points in the cluster, and smallest amount of distance with the centers of the clusters. The key undertaking of the studies of diverse colors mechanism is to decide the age of the tiger; the usage of shade action pixel primarily based on image segmentation; the usage of facts that are used in the mining techniques. However, the more matrix components to be measuring the processing time, retrieval time, accuracy, and blunders fee with the aid of using producing better performance.

A Faster DBSCAN Algorithm Based on Self-Adaptive Determination of Parameters

The DBSCAN algorithm is a well-known cluster method that is density-based and has the advantage of finding clusters of different shapes, but it also has certain shortcomings, one of which is that it cannot determine the two important parameters Eps (neighborhood of a point) and Mints (minimum number of points) by itself, and the other is that it takes a long time to traverse all points when dataset is large. In this paper, we propose an improved method which is named as K-DBSCAN to improve the running efficiency based on self-adaptive determination of parameters and this method changes the way of traversing and only deals with core points. Experiments show that it outperforms DBSCAN algorithms in terms of running time efficiency.

Performance Analysis and Architecture of a Clustering Hybrid Algorithm Called FA+GA-DBSCAN Using Artificial Datasets.

Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is a widely used algorithm for exploratory clustering applications. Despite the DBSCAN algorithm being considered an unsupervised pattern recognition method, it has two parameters that must be tuned prior to the clustering process in order to reduce uncertainties, the minimum number of points in a clustering segmentation MinPts, and the radii around selected points from a specific dataset Eps. This article presents the performance of a clustering hybrid algorithm for automatically grouping datasets into a two-dimensional space using the well-known algorithm DBSCAN. Here, the function nearest neighbor and a genetic algorithm were used for the automation of parameters MinPts and Eps. Furthermore, the Factor Analysis (FA) method was defined for pre-processing through a dimensionality reduction of high-dimensional datasets with dimensions greater than two. Finally, the performance of the clustering algorithm called FA+GA-DBSCAN was evaluated using artificial datasets. In addition, the precision and Entropy of the clustering hybrid algorithm were measured, which showed there was less probability of error in clustering the most condensed datasets.

The New Eco‐Schemes: Navigating a Narrow Fairway

SummaryThis article highlights some key challenges and trade‐offs with which national policy designers have to contend in devising national eco‐schemes for agriculture. We show that policy designers operate in a narrow design space which is constrained by various political and legal requirements. One key challenge is to design a reward system that allows the uptake of eco‐schemes by farmers to be aligned with a given budget. We present four broad implementation models for eco‐schemes and discuss their merits and shortcomings in light of stipulated requirements. These are the ‘greening model’, the ‘modified greening model’, the ‘eco‐points model’ and the ‘AECS model’ in the style of the agri‐environmental and climate schemes of CAP Pillar 2. We conclude that the eco‐points model is likely to be the most suitable. By stipulating that individual farmers must reach a certain minimum number of points per hectare (eligibility threshold), but are not entitled to payments for points that exceed a certain upper limit per hectare (cut‐off), it allows demand from farmers for inclusion in a scheme to be steered such that aggregate uptake coincides with the budget; thereby reducing the risk of over‐ or under‐subscription while maintaining flexibility to cater for heterogeneity in site conditions.

A parallel algorithm for understanding design spaces and performing convex hull computations

A novel algorithm to compute the convex hull of any given hyperdimensional data set is presented. This algorithm has lower memory requirements than state of the art software, and runtimes which are typically much faster than conventional programs and algorithms which do the same. A discussion is presented which examines the large importance that convex hull computations serve in creating general surrogate models from data sets, and their importance to machine learning algorithms. In addition to the deep reaching applications in many fields, this algorithm can be used to help solve design problems, specifically those in preliminary design when surrogate models are used to perform rapid design trades. The algorithm is presented, in addition to algorithms which compute volumes and facilitate understanding of hyperdimensional spaces which cannot be easily visualized. This paper concludes with the presentation of a representative design problem containing similar dimensionality and numbers of points as a standard engineering preliminary design problem. The minimum number of points needed for the interpolation of a general surrogate model during design and analysis is then discussed, including the proposal of a new metric.

GNN-DBSCAN: A new density-based algorithm using grid and the nearest neighbor

DBSCAN (density-based spatial clustering of applications with noise) is one of the most widely used density-based clustering algorithms, which can find arbitrary shapes of clusters, determine the number of clusters, and identify noise samples automatically. However, the performance of DBSCAN is significantly limited as it is quite sensitive to the parameters of eps and MinPts. Eps represents the eps-neighborhood and MinPts stands for a minimum number of points. Additionally, a dataset with large variations in densities will probably trap the DBSCAN because its parameters are fixed. In order to overcome these limitations, we propose a new density-clustering algorithm called GNN-DBSCAN which uses an adaptive Grid to divide the dataset and defines local core samples by using the Nearest Neighbor. With the help of grid, the dataset space will be divided into a finite number of cells. After that, the nearest neighbor lying in every filled cell and adjacent filled cells are defined as the local core samples. Then, GNN-DBSCAN obtains global core samples by enhancing and screening local core samples. In this way, our algorithm can identify higher-quality core samples than DBSCAN. Lastly, give these global core samples and use dynamic radius based on k-nearest neighbors to cluster the datasets. Dynamic radius can overcome the problems of DBSCAN caused by its fixed parameter eps. Therefore, our method can perform better on dataset with large variations in densities. Experiments on synthetic and real-world datasets were conducted. The results indicate that the average Adjusted Rand Index (ARI), Normalized Mutual Information (NMI), Adjusted Mutual Information (AMI) and V-measure of our proposed algorithm outperform the existing algorithm DBSCAN, DPC, ADBSCAN, and HDBSCAN.

Amplituhedron-like geometries

We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical form of these geometries corresponds to the product of parity conjugate amplitudes at tree as well as loop level. The product of amplitudes in superspace lifts to a star product in bosonised superspace which we give a precise definition of. We give an alternative definition of amplituhedron-like geometries, analogous to the original amplituhedron definition, and also a characterisation as a sum over pairs of on-shell diagrams that we use to prove the conjecture at tree level. The union of all amplituhedron-like geometries has a very simple definition given by only physical inequalities. Although such a union does not give a positive geometry, a natural extension of the standard definition of canonical form, the globally oriented canonical form, acts on this union and gives the square of the amplitude.

Develop a dynamic DBSCAN algorithm for solving initial parameter selection problem of the DBSCAN algorithm

<p>The amount of data has been increasing exponentially in every sector such as banking securities, healthcare, education, manufacturing, consumer-trade, transportation, and energy. Most of these data are noise, different in shapes, and outliers. In such cases, it is challenging to find the desired data clusters using conventional clustering algorithms. DBSCAN is a popular clustering algorithm which is widely used for noisy, arbitrary shape, and outlier data. However, its performance highly depends on the proper selection of cluster radius <em>(Eps)</em> and the minimum number of points <em>(MinPts)</em> that are required for forming clusters for the given dataset. In the case of real-world clustering problems, it is a difficult task to select the exact value of Eps and <em>(MinPts)</em> to perform the clustering on unknown datasets. To address these, this paper proposes a dynamic DBSCAN algorithm that calculates the suitable value for <em>(Eps)</em> and <em>(MinPts)</em> dynamically by which the clustering quality of the given problem will be increased. This paper evaluates the performance of the dynamic DBSCAN algorithm over seven challenging datasets. The experimental results confirm the effectiveness of the dynamic DBSCAN algorithm over the well-known clustering algorithms.</p>

Enhancing retinal blood vessel segmentation in medical images using combined segmentation modes extracted by DBSCAN and morphological reconstruction

In this study, a new algorithm is proposed for retinal blood vessel segmentation in medical images using the density-based spatial clustering of applications with noise (DBSCAN) and the morphological reconstruction (MR). The images are thus divided into smaller equal rectangular ones, called cells through the R variable. Upon finding the best DBSCAN clustering parameters, neighborhood radius (ɛ), and number of minimum points (Z), the pattern of the retinal blood vessels appears in the cells. Noise removal operations are also performed via median, logical AND operator (&&), and MR filters, respectively. The MR is accordingly used in a loop with an incremental K counter, as a square structuring element. Finally, the given vessels are segmented by setting four parameters of R, ɛ, Z, and K. After combining different Z and K modes, the resulting images of the thin veins are joined to the thick ones, and most of the gaps in the vessel tree are corrected. Several veins, not visible to the naked eye in the original images, are also detected. The proposed method is implemented for three datasets DRIVE, STARE and the VAMPIRE. Performance measures including sensitivity (Se) and area under the curve (AUC) correspondingly show a significant increase in these datasets. Accuracy (Acc) and specificity (Sp) values are further comparable to the results by others, and a slight decrease in some cases is attributed to the new vessels found in addition to the ground truth (GT) images.

On the spectral gap and the automorphism group of distance-regular graphs

We prove that a distance-regular graph with a dominant distance is a spectral expander. The key ingredient of the proof is a new inequality on the intersection numbers. We use the spectral gap bound to study the structure of the automorphism group.The minimal degree of a permutation group G is the minimum number of points not fixed by non-identity elements of G. Lower bounds on the minimal degree have strong structural consequences on G. In 2014 Babai proved that the automorphism group of a strongly regular graph with n vertices has minimal degree ≥cn, with known exceptions. Strongly regular graphs correspond to distance-regular graphs of diameter 2. Babai conjectured that Hamming and Johnson graphs are the only primitive distance-regular graphs of diameter d≥3 whose automorphism group has sublinear minimal degree. We confirm this conjecture for non-geometric primitive distance-regular graphs of bounded diameter. We also show if the primitivity assumption is removed, then only one additional family of exceptions arises, the crown graphs. We settle the geometric case in a companion paper.