Optimal Number Of Groups Research Articles

Systematization of sunflower genotypes based on seed phenotypic characteristics using neural networks

In recent years, various datasets related to the phenotyping of sunflower genotypes have become increasingly accessible. However, one of the key challenges remains the efficient and accurate prediction of phenotypes based on genotypes in the context of climate change. Analyzing phenotypes at different levels of organization and detecting connections between phenotypes and genotypes require the integration and processing of large, diverse, and often noisy datasets. Machine learning offers a broad arsenal of methods and approaches for identifying predictive patterns in such data. Therefore, the research aimed to develop a methodology for the systematization of sunflower genotypes based on seed phenotypic characteristics using the data vector quantization method and neural networks. The study revealed the phenotypic characteristics of sunflower seeds from various genotypes selected by the Institute of Oilseed Crops of NAAS, grown in the southern Steppe of Ukraine, including seed length, width, thickness, seed mass, kernel mass, and seed coat cracking force. For this purpose, appropriate laboratory equipment was developed, including two modules for determining the morphological and rheological properties of seeds. The developed methodology for the systematization of sunflower genotypes based on seed phenotypic characteristics includes the following steps: measuring the characteristics of sunflower seeds from various samples (parental components); studying the mutual correlation of characteristics; conducting hierarchical cluster analysis of the data using the Ward's method; determining the optimal number of groups; performing k-means clustering using the vector quantization method; determining the correspondence of ranges of characteristics to the group; training a neural network to group the data by samples and created groups; verifying the adequacy of the neural network on test data. The developed methodology was tested, and the MLP 30-15-3 neural network for grouping data by samples and created groups of sunflower seeds was developed in the Statistica software package. The network's training efficiency was 99.4%, and such of testing and validation was 95.6% and 96.7%, respectively.

A matheuristic applied to clustering rural properties and allocating plants for biogas generation

Establishing partnerships among agro-industrial properties and selecting ideal locations for biogas plants are crucial challenges in large-scale biogas production and can influence both operational efficiency and waste management. In this context, this research proposes a new matheuristic that addresses the problems of defining a group of properties and an optimal number of groups and identifies the best allocation to the biogas plant. The group properties were defined by hierarchical and K-means cluster algorithms. The best location for the biogas plant was determined by the proposed multiobjective mathematical model. The best cluster number was decided by two strategies: (1) one that selected the closest non-dominated solutions to the ideal solution (M1) and (2) one that favored the most environmentally friendly solution (M2). The matheuristic was tested using three real databases, which yielded strategic clusters with an average daily biogas production of 544.93 m³/day (M1 and M2) for DataBase 1, 1635,156.00 m³/day (M1) and 403,497.50 m³/day (M2) for DataBase 2, and 318,662.50 m³/day (M1) and 20,479.58 m³/day (M2) for DataBase 3. This research provides an opportunity to add value to agro-industrial properties by achieving energy security and developing new business networks.

Research on the Short-Term Prediction of Offshore Wind Power Based on Unit Classification

The traditional power prediction methods cannot fully take into account the differences and similarities between units. In the face of the complex and changeable sea climate, the strong coupling effect of atmospheric circulation, ocean current movement, and wave fluctuation, the characteristics of wind processes under different incoming currents and different weather are very different, and the spatio-temporal correlation law of offshore wind processes is highly complex, which leads to traditional power prediction not being able to accurately predict the short-term power of offshore wind farms. Therefore, aiming at the characteristics and complexity of offshore wind power, this paper proposes an innovative short-term power prediction method for offshore wind farms based on a Gaussian mixture model (GMM). This method considers the correlation between units according to the characteristics of the measured data of units, and it divides units with high correlation into a category. The Bayesian information criterion (BIC) and contour coefficient method (SC) were used to obtain the optimal number of groups. The average intra-group correlation coefficient (AICC) was used to evaluate the reliability of measurements for the same quantized feature to select the representative units for each classification. Practical examples show that the short-term power prediction accuracy of the model after unit classification is 2.12% and 1.1% higher than that without group processing, and the mean square error and average absolute error of the short-term power prediction accuracy are reduced, respectively, which provides a basis for the optimization of prediction accuracy and economic operation of offshore wind farms.

Model Based Clustering for Regency/City Grouping Based on Community Welfare Indicators in North Sumatra

This thesis aims to apply model-based clustering in grouping regencies/cities in North Sumatra based on Community Welfare Indicators to determine the number of groups (clusters) formed based on community welfare indicators in regencies/cities in North Sumatra and to understand the level of community welfare from this grouping in planning and managing community welfare in regencies/cities in North Sumatra, with the hope of achieving equal welfare in every region. The research method used is Model-Based Clustering, which uses 5 research data variables: HDI, Poor Population, Unemployment Rate, GDP, and Health. In this millennial era, the assessment of community welfare requires more attention. Rapid social, technological, and environmental changes have created new dynamics that can affect community welfare. The evaluation of community welfare is not only limited to economic parameters but also considers health, unemployment, and other factors. By using Model-Based Clustering, it is possible to determine the optimal number of groups (clusters) from various and possibly correlated variables, and the results are easier to understand, making the analysis and understanding of the results easier. Readers can learn about the level of community welfare, and the community and government can evaluate their welfare for future improvements. The research results show that among the groups of regencies/cities formed, five cities consistently show lower Gross Regional Domestic Product (GDP) and Human Development Index (HDI) than other cities. Therefore, a sustainable approach is needed to improve these cities' economic conditions and social welfare.

Miara stabilności w wyborze liczby grup w taksonomii zagregowanej z zastosowaniem analizy spektralnej i metody propagacji podobieństwa

Since the 1990s, the aggregate approach and the stability of grouping methods have been concepts frequently discussed in the field of taxonomy. So far, they have been considered separately, but recently, there has been a postulate in the literature to combine these two concepts in the form of the PAC (proportion of ambiguously clustered pairs) stability measure, which can be used in the aggregate approach to taxonomy and which is intended to serve as a criterion for selecting an optimal number of groups. The aim of the research presented in this article is to compare the results of the selection of the optimal number of groups in aggregate taxonomy on the example of the attainment of three Sustainable Development Goals (SDGs) by EU countries. The PAC measure and selected classic indices, namely the Caliński-Harabasz, the Dunn and the Davies-Bouldin indices were applied for this purpose. The affinity propagation method and spectral clustering served as base methods in the aggregate approach. The study used Eurostat data for 2019. The obtained results demonstrate that both the choice of the criterion for determining the number of groups and the choice of the base method in aggregate taxonomy have an influence on the final decision on how to determine the number of groups. Regardless of whether the affinity propagation method or spectral taxonomy with classic indices was used, or whether these methods were used as base ones in the aggregate approach and the number of groups was selected using the PAC measure, the differences between the indicated numbers of groups were very large.

New method to identify optimal discontinuity set number of rock tunnel excavation face orientation based on Fisher mixed evaluation

Discontinuity is critical for strength, deformability, and permeability of rock mass. Set information is one of the essential discontinuity characteristics and is usually accessed by orientation grouping. Traditional methods of identifying optimal discontinuity set numbers are usually achieved by clustering validity indexes, which mainly relies on the aggregation and dispersion of clusters and leads to the inaccuracy and instability of evaluation. This paper proposes a new method of Fisher mixed evaluation (FME) to identify optimal group numbers of rock mass discontinuity orientation. In FME, orientation distribution is regarded as the superposition of Fisher mixed distributions. Optimal grouping results are identified by considering the fitting accuracy of Fisher mixed distributions, the probability monopoly and central location significance of independent Fisher centers. A Halley-Expectation-Maximization (EM) algorithm is derived to achieve an automatic fitting of Fisher mixed distribution. Three real rock discontinuity models combined with three orientation clustering algorithms are adopted for discontinuity grouping. Four clustering validity indexes are used to automatically identify optimal group numbers for comparison. The results show that FME is more accurate and robust than the other clustering validity indexes in optimal discontinuity group number identification for different rock models and orientation clustering algorithms.

Molecular characteristics of eight lignites based on the big data obtained from Orbitrap mass spectrometry

Eight lignites from different regions were selected for thermal dissolution (TD) sequentially using cyclohexane, methanol and ethanol. The TD extracts of the eight coal samples were characterized using atmospheric pressure chemical ionization source (APCI)-Orbitrap mass spectrometry (MS). Chemometric methods were employed to deeply explore the molecular structural and composition information of the organic compounds detected by Orbitrap MS. The longest distance method in systematic clustering of chemometrics was employed to ascertain the optimal number of groups, which was found to be 7 by clustering 24 soluble portions (SPs) using Euclidean distance. Taking one group as an example, the similarities and differences of SPs within the group were derived based on the compositional class of O1N1, N1, O2N1 and O2, and heteroatom distribution patterns of the SPs were proposed and compared. The integration of high-resolution MS data and chemometric methods not only exposes the existence of heteroatomic compounds in lignite but also furnishes evidence for the origin and evolution of lignite, as well as a methodology for the high-value utilization of lignites from different sources.

On the ideal number of groups for isometric gradient propagation

Recently, various normalization layers have been proposed to stabilize the training of deep neural networks. Among them, group normalization is a generalization of layer normalization and instance normalization by allowing a degree of freedom in the number of groups it uses. However, to determine the optimal number of groups, trial-and-error-based hyperparameter tuning is required, and such experiments are time-consuming. In this study, we discuss a reasonable method for setting the number of groups. First, we find that the number of groups influences the gradient behavior of the group normalization layer. Based on this observation, we derive the ideal number of groups, which calibrates the gradient scale to facilitate gradient descent optimization. This paper is the first to propose an optimal number of groups that is theoretically grounded, architecture-aware, and can provide a proper value in a layer-wise manner for all layers. The proposed method exhibited improved performance over existing methods in numerous neural network architectures, tasks, and datasets.

Spatial clustering based gene selection for gene expression analysis in microarray data classification

A typical application of categorization in data mining is to uncover interesting distributions and significant patterns in the information that underlies it using density-based spatial clustering for workloads with noise. In these conditions, it is anticipated that the classification of the microarray gene expression database will have the necessary clustering property that may be utilized to emphasize the effects of the alterations. The proposed method typically guarantees that the subsequent identification of gene clusters’ best global arrangement of genes. It provides an iterative method for figuring out the precise number of clusters needed for each data collection. The technique is based on practices frequently used in statistical tests. The key idea is to coordinate gene redistribution optimization across clusters with the search for the optimal number of groups. An experiment that finds the most effective number of genes over time was used to evaluate the effectiveness of the suggested strategy. It used this stringent statistical test to show that our technique accurately clusters more than 95% of the genes. Finally, since the basic principles of gene development and gene cluster assignment have been well characterized by earlier studies and the technique was verified using real gene expression information.

ANALYSIS OF CUSTOMER PROFILE CHARASTERISTIC WITH CREDIT QUALITY USING THE CLUSTERING METHOD FOR RISK MITIGATION AND SMALL MEDIUM ENTERPRISE CREDIT PORTOFOLIO EXPANSION PLANNING

in managing the Small Medium Enterprise credit portfolio. The strategy taken by a bank must be adapted to the general characteristics of the target debtors for business expansion and risk mitigation so that business expansion and risk mitigation efforts can be carried out effectively for certain groups. Based on these problems, the purpose of this research is to identify groups of debtors with similar characteristics based on debtor profile data and their credit quality, and to understand the differences in credit risk and opportunities for business expansion among these groups. The data used is the profile of the distribution of debtors from Bank ABC of 5088 debtors. The analysis technique used is K-Means and KMedoids with the evaluation criteria used are silhouette score, davies-bouldin index and computation time. Completion of the optimal number of groups is done by analyzing the WSS graph using the elbow method. Analysis of business expansion and risk reduction is carried out separately where business expansion analysis is carried out for debtors with a collectibility value of 1 and risk reduction analysis is carried out for debtors who have a collectibility value of 2 – 5. The results show that there are 5 groups in the business expansion analysis and 3 groups in risk mitigation analysis. The high value of the silhouette index and davies-bouldin index makes the grouping results have a strong structure. The KMedoids method is used in this analysis because it has better evaluation criteria than K-Means. Priority is also determined for each group formed so that it can be determined which group has the greatest opportunity to become target expansion and which group has the greatest risk that needs to be mitigated. In general, business sectors such as agriculture and plantations are experiencing a decline in economic activity in 2022, so it needs attention from the bank so that it does not disrupt the credit portfolio. To complement the results of this study, an analysis of external and internal business health needs to be carried out in more depth so that the big picture of credit problems at Bank ABC can be identified.

Dominant Partitioning of Rock Masses Discontinuities Based on Information Entropy Selective Heterogeneous Ensemble

In order to make up for the shortcomings of traditional discontinuity occurrence clustering algorithms, such as narrow application scope, difficulty in effectively identifying noise points, and susceptibility to initial conditions and hyperparameters. In this work, the dominant partitioning of rock masses discontinuities based on information entropy selective heterogeneous ensemble (DRIE) model is proposed. Firstly, the base cluster set is generated by four base-clustering algorithms. Secondly, the comprehensive quality evaluation index is obtained by evaluating the quality and difference of the base cluster, and the information entropy weighting matrix is integrated. Finally, the number of integrated base clusters and the optimal number of groups are determined, and the noise points are eliminated. In addition, this work lists four base-clustering algorithm models, establishes nine comparison models, and applies all models to the dominant partitioning of an adit discontinuity of Songta Hydropower Station in Tibet, China. The results show that the DRIE model and the above 13 models are evaluated by combining the silhouette index and the ability to identify and eliminate noise. Compared with other models, the DRIE model has wide applicability and objective grouping results. It provides a new idea for the study of the dominant occurrence grouping of discontinuity.

A New Separation Index and Classification Techniques Based on Shannon Entropy

The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well.

IMPLEMENTATION OF THE FUZZY GUSTAFSON-KESSEL METHOD ON GROUPING DISTRICTS/CITIES IN KALIMANTAN ISLAND BASED ON POVERTY ISSUES FACTORS

Cluster analysis is an analysis that is useful in summarizing data by grouping objects based on certain similarity characteristics. One of the group analysis is Fuzzy Gustafson-Kessel (FGK) which is the development of the Fuzzy C-Means (FCM) method. The FGK method has a good way in adjusting the form of cluster membership function correctly for a data. This study aims to determine the results of the optimal number of groups based on the Partition Coefficient (PC) and Classification Entropy (CE) validity indexes and to find out the results of grouping 56 districts/cities on the island of Kalimantan based on poverty issue factors in 2021. The optimal number of groups using the FGK method based on the validity indexes of PC and CE are two groups. The first group and the second group each consist of 28 districts/cities in Kalimantan Island.

Correction of the Values of the Classification Feature of Objects on the Example of the Diagnosis of Multiple Myeloma

The clinical features of changes in multiple myeloma indicators of different types associated with the gender of patients (objects) are considered. The methods of data mining examine the truth of the statement about the presence of many patients for whom gender is not significant in making a diagnosis. It is proposed to use the preprocessing of heterogeneous data to unify the description of objects in the binary space. The conditions for selecting and removing noise features from the set are determined. In order to reduce the dimensionality of the space, latent features are calculated by groups of binary generalized estimates of objects. A criterion is proposed for dividing patients into the optimal number of groups, taking into account their gender authenticity. From these groups, a new classification of objects is formed, differentiated by gender. The formation process is illustrated through the visualization of object descriptions, recognition accuracy and selection of informative feature sets according to the new classification. The selection procedure is implemented according to the rules of a hierarchical agglomerative algorithm. The property of invariance to the measurement scales of quantitative traits is an important argument for using the obtained results on data samples from the general population.

PREVENTION STRATEGY OF MAIN NON-COMMUNICABLE DISEASES USING ARTIFICIAL NEURAL NETWORKS

ABSTRACT: The aim of this work was to build four models for the prediction of Noncommunicable Diseases (NCD) to support early diagnosis by applying deep Artificial Neural Networks (ANN) and clustering; through comparative analysis, the best paradigm was chosen. Following the methodology for data science, the objectives, project requirements and the quality of the data were analyzed, cleaning and normalization was carried out, the identification of the optimal number of groups by means of the silhouette method. Each model was trained with 70% of records and validated with the remaining 30% using the confusion matrix and F1. The comparative analysis showed the best performance of the multilayer perceptron with deep learning (over a network with clustering radial basis functions), its accuracy, precision, sensitivity, specificity and F1 were 99%, 97%, 100%, 97% and 98% respectively for lung cancer, 99%, 98%, 100%, 100% and 98% for breast cancer, Alzheimer with 98.6%, 100%, 96%, 100% and 97%, and depression with 91% , 87%, 93%, 88% and 88%, these models constitute an automated solution to strengthen medical diagnosis, they are considered a strategic support in the prevention of NCD, will contribute to improving the prognosis and quality of life of vulnerable people. Keywords: Prediction, artificial neural networks, data science, physical disorders, mental disorders

Cacaueiros cultivados em sistema agroflorestais da Bahia revelam ampla variabilidade genética em caracteres morfoagronômicos

ABSTRACT Cacao fruits are agronomically important and show wide variability for several morphological descriptors. The present study aimed to characterize the genetic distance of 51 genotypes of Theobroma cacao L. in the cocoa-producing region of Southern Bahia (Brazil) based on morpho-agronomic descriptors. The inference of genetic similarity was performed from the phenotypic data derived simultaneously from qualitative and quantitative variables, using the Ward-MLM procedure (Modified Location Model) with the SAS® software. The distance matrix was obtained using the Gower logarithmic function. For this, 28 descriptors were evaluated, five qualitative and 23 quantitative. Furthermore, using the likelihood function procedure, the optimal number of groups was five indicating wide variability. Of 23 quantitative descriptors evaluated by fruits and leaves, 95% showed significant differences. The exception was seed width. Groups 1 and 5 were the most distant, while groups 2, 3, and 4 were closest to each other. The greatest difference between increments was 35.32 for the fifth group. The analysis of the first two canonical axes revealed that both represented 81.88% of the variation, with CAN1 and CAN2 responsible for 53.66% and 28.22% of the variation. The most promising genotypes for breeding programs belong to group 5 due to their superior performance for almost all characteristics analyzed.

GrCol-PPFL: User-Based Group Collaborative Federated Learning Privacy Protection Framework

With the increasing number of smart devices and the development of machine learning technology, the value of users’ personal data is becoming more and more important. Based on the premise of protecting users’ personal privacy data, federated learning (FL) uses data stored on edge devices to realize training tasks by contributing training model parameters without revealing the original data. However, since FL can still leak the user's original data by exchanging gradient information. The existing privacy protection strategy will increase the uplink time due to encryption measures. It is a huge challenge in terms of communication. When there are a large number of devices, the privacy protection cost of the system is higher. Based on these issues, we propose a privacy-preserving scheme of user-based group collaborative federated learning (GrCol-PPFL). Our scheme primarily divides participants into several groups and each group communicates in a chained transmission mechanism. All groups work in parallel at the same time. The server distributes a random parameter with the same dimension as the model parameter for each participant as a mask for the model parameter. We use the public datasets of modified national institute of standards and technology database (MNIST) to test the model accuracy. The experimental results show that GrCol-PPFL not only ensures the accuracy of the model, but also ensures the security of the user’s original data when users collude with each other. Finally, through numerical experiments, we show that by changing the number of groups, we can find the optimal number of groups that reduces the uplink consumption time.

Method for inferring the number of clusters based on a range of attribute values with subsequent automatic data labeling

Machine learning is a suitable pattern recognition technique for detecting correlations between data. In the case of unsupervised learning, the groups formed from these correlations must receive a label, which consists of describing them in terms of their most relevant attributes and their respective ranges of values so that they are understood automatically. In this research work, this process is called labeling. However, a challenge for researchers is to establish the optimal number of groups submitted to grouping, which influences the performance of this process. Therefore, this research aims to provide an inference approach to the number of clusters used in the clustering based on the range of attribute values, followed by automatic data labeling to maximize the understanding of the groups obtained. This methodology was applied to four databases, and the results show that it contributes to the interpretation of groups since it generates more accurate labels with a hit rate above 93%.

Amputated Life Testing for Weibull-Fréchet Percentiles: Single, Double and Multiple Group Sampling Inspection Plans with Applications

When a life test is terminated at a predetermined time to decide whether to accept or refuse the submitted batches, the types of group sampling inspection plans (single, two, and multiple-stages) are introduced. The tables in this study give the optimal number of groups for various confidence levels, examination limits, and values of the ratio of the determined experiment time to the fixed percentile life. At various quality levels, the operating characteristic functions and accompanying producer's risk are derived for various types of group sampling inspection plans. At the determined producer's risk, the optimal ratios of real percentile life to a fixed percentile life are obtained. Three case studies are provided to illustrate the processes described here. Comparisons of single-stage and iterative group sampling plans are introduced. The first, second, and third sample minimums must be used to guarantee that the product's stipulated mean and median lifetimes are reached at a certain degree of customer trust. The suggested sample plans' operational characteristic values and the producer's risk are given. In order to show how the suggested approaches based on the mean life span and median life span of the product may function in reality, certain real-world examples are examined.

Polygenic risk score association with cognitive decline in Parkinson’s Disease

AbstractBackgroundCognitive impairment is a common and debilitating symptom in Parkinson’s disease (PD) with high variability in individual trajectory of decline. We sought to explore heterogeneity in the trajectory of individual cognitive change in a cohort of early stage PD patients and test association to cumulative genetic risk identified in large scale Genome Wide Association Studies (GWAS).MethodUsing longitudinal measures of the Montreal Cognitive Assessment (MoCA) we employed latent class mixed modelling (LCMM) to identify and investigate unknown populations in the Parkinson’s Progression Markers Inititative (PPMI) de‐novo PD cohort. Tranformed MoCA scores were modelled as a quadratic function of years from baseline, controlling for age, gender and motor symptom severity. Optimal group number was identified and determined using standardly advised model fit metrics. Polygenic risk scores (PRS) for five GWAS were calculated using PRSice‐2 applied to genotyping array data. Association of PRS with cognitive groups was tested using linear models and ANOVA tests.ResultLCMM showed optimal fit statistics for three classes (lowest BIC, high entropy) and these groups were retained for further analysis The largest identified class (n = 240) on average, presented at baseline with higher MoCA scores and remained stable over time. The second class (n = 132) presented with lower MoCA scores and showed a slow declining trajectory whilst the smallest class (n = 13) presented with lower MoCA scores but declined at a rapid rate. Educational attainment and Alzheimer’s disease (AD) GWAS derived PRS were significantly associated with cognitive class and explained the highest amount of phenotypic variance. For PD case‐control status, only the PD PRS was significantly associated with Parkinson’s status and explained a similar level of phenotypic variation.ConclusionLatent class analysis may provide utility in subsetting longitudinal cognitive outcome groups for use in groupwise comparisons. Using this method we show evidence for association of educational attainment and AD cumulative genetic risk and worse cognitive outcomes in early PD.