Optimal Number of Classes in Fuzzy Partitions

2021 ◽  
pp. 129-141
Author(s):  
Fabian Castiblanco ◽  
Camilo Franco ◽  
J. Tinguaro Rodriguez ◽  
Javier Montero
Keyword(s):  
Optimal Number ◽  
Fuzzy Partitions ◽  
Number Of Classes

Allocation of teachers among public schools and minimization of cost: The case of public education in Sri Lanka

2020 ◽  
pp. 205789112093599
Author(s):  
Tikiri Nimal Herath
Keyword(s):  
Public Schools ◽  
Optimal Number ◽  
Primary Data ◽  
Sri Lankan ◽  
Transfer Policy ◽  
The North ◽  
Logical Method ◽  
North Central Province ◽  
Number Of Classes ◽  
Minimize Costs

Overall, in Sri Lankan public schools, the student–teacher ratio is very low. The number of teachers is considerably greater than the number of classes; sometimes the former is double or more than double the latter. In a school in which all the teachers are individually deployed in each class, many teachers have to remain idle. Thus, every day a certain number of teachers remain idle. This situation points to two issues. Firstly, in Sri Lankan public schools, resources are underutilized and hence costs are not minimized. Secondly, since there is an excess of teachers in schools, a formal and logical method is required to determine the optimal number of teachers. This article tries to develop a formula to determine the required number of teachers for a school, and thereby to find ways to minimize costs when employing teachers. Primary data on classes, teachers and subjects offered with respect to 40 public schools in the North Central Province were collected. When empirical data on the number of teachers in sampled schools were compared with calculated teacher requirements in terms of the developed formula, it was found that school authorities are underutilizing teachers. The article concludes that (a) based on the developed formula to determine the required number of teachers, many public schools have an excess of teachers and hence current transfer policy for school teachers is not logical, (b) teacher requirement can be decided according to the developed formula and (c) by adopting one teacher-two subjects-one school and one teacher-one subject-more schools models, government authorities can minimize costs further.

scholarly journals Integrating latent classes in the Bayesian shared parameter joint model of longitudinal and survival outcomes

2020 ◽  
Vol 29 (11) ◽  
pp. 3294-3307
Author(s):  
Eleni-Rosalina Andrinopoulou ◽  
Kazem Nasserinejad ◽  
Rhonda Szczesniak ◽  
Dimitris Rizopoulos
Keyword(s):  
Cystic Fibrosis ◽  
Lung Function ◽  
Latent Class ◽  
Joint Model ◽  
Forced Expiratory Volume ◽  
Optimal Number ◽  
Latent Classes ◽  
Joint Models ◽  
Number Of Classes ◽  
Strength Of Association

Cystic fibrosis is a chronic lung disease requiring frequent lung-function monitoring to track acute respiratory events (pulmonary exacerbations). The association between lung-function trajectory and time-to-first exacerbation can be characterized using joint longitudinal-survival modeling. Joint models specified through the shared parameter framework quantify the strength of association between such outcomes but do not incorporate latent sub-populations reflective of heterogeneous disease progression. Conversely, latent class joint models explicitly postulate the existence of sub-populations but do not directly quantify the strength of association. Furthermore, choosing the optimal number of classes using established metrics like deviance information criterion is computationally intensive in complex models. To overcome these limitations, we integrate latent classes in the shared parameter joint model through a fully Bayesian approach. To choose the optimal number of classes, we construct a mixture model assuming more latent classes than present in the data, thereby asymptotically “emptying” superfluous latent classes, provided the Dirichlet prior on class proportions is sufficiently uninformative. Model properties are evaluated in simulation studies. Application to data from the US Cystic Fibrosis Registry supports the existence of three sub-populations corresponding to lung-function trajectories with high initial forced expiratory volume in 1 s ( FEV1), rapid FEV1 decline, and low but steady FEV1 progression. The association between FEV1 and hazard of exacerbation was negative in each class, but magnitude varied.

Digital soil mapping of a coastal acid sulfate soil landscape

Soil Research ◽  
2014 ◽  
Vol 52 (4) ◽  
pp. 327 ◽  
Author(s):  
Jingyi Huang ◽  
Terence Nhan ◽  
Vanessa N. L. Wong ◽  
Scott G. Johnston ◽  
R. Murray Lark ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Traditional Approach ◽  
Management Strategies ◽  
Error Variance ◽  
Optimal Number ◽  
Soil Mapping ◽  
Digital Soil Mapping ◽  
Acid Sulfate ◽  
Soil Landscape ◽  
Number Of Classes

Coastal floodplains are commonly underlain by sulfidic sediments and coastal acid sulfate soils (CASS). Oxidation of sulfidic sediments leads to increases in acidity and mobilisation of trace metals, resulting in an increase in the concentrations of conducting ions in sediment and pore water. The distribution of these sediments on floodplains is highly heterogeneous. Accurately identifying the distribution of CASS is essential for developing targeted management strategies. One approach is the use of digital soil mapping (DSM) using ancillary information. Proximal sensing instruments such as an EM38 can provide data on the spatial distribution of soil salinity, which is associated with CASS, and can be complemented by digital elevation models (DEM). We used EM38 measurements of the apparent soil electrical conductivity (ECa) in the horizontal and vertical modes in combination with a high resolution DEM to delineate the spatial distribution of CASS. We used a fuzzy k-means algorithm to cluster the data. The fuzziness exponent, number of classes (k) and distance metric (i.e. Euclidean, Mahalanobis and diagonal) were varied to determine a set of parameters to identify CASS. The mean-squared prediction error variance of the class mean of various soil properties (e.g. EC1:5 and pH) was used to identify which of these metrics was suitable for further analysis (i.e. Mahalanobis) and also determine the optimal number of classes (i.e. k = 4). The final map is consistent with previously defined soil–landscape units generated using traditional soil profile description, classification and mapping. The DSM approach is amenable for evaluation on a larger scale and in order to refine CASS boundaries previously mapped using the traditional approach or to identify CASS areas that remain unmapped.

Affinity Propagation for the Context Quantization

2013 ◽  
Vol 791-793 ◽  
pp. 1533-1536 ◽  
Author(s):  
Min Chen ◽  
Jian Hua Chen ◽  
Mo Hai Guo
Keyword(s):  
Probability Distributions ◽  
Conditional Entropy ◽  
Optimal Number ◽  
Affinity Propagation ◽  
Code Length ◽  
Propagation Algorithm ◽  
Affinity Propagation Algorithm ◽  
Number Of Classes ◽  
The Given ◽  
Adaptive Code

In this paper, the context quantization for I-ary sources based on the affinity propagation algorithm is presented. In purpose of finding the optimal number of classes, the increment of the adaptive code length is suggested to be the similarity measure between two conditional probability distributions, by which the similarity matrix is constructed as the input of the affinity propagation algorithm. After the given number of iterations, the optimal quantizer with the optimal number of classes is achieved and the adaptive code length is minimized at the same time. The simulations indicate that the proposed algorithm produces results that are better than the results obtained by the minimum conditional entropy context quantization implemented by K-means with lower computational complexity.

scholarly journals Illiteracy Classification Using K Means-Naïve Bayes Algorithm

2018 ◽  
Vol 2 (3) ◽  
pp. 153 ◽  
Author(s):  
Muhammad Firman Aji Saputra ◽  
Triyanna Widiyaningtyas ◽  
Aji Prasetya Wibawa
Keyword(s):  
Error Rate ◽  
Naive Bayes ◽  
Research Result ◽  
Naïve Bayes ◽  
Optimal Number ◽  
Testing Method ◽  
The World ◽  
Bayes Algorithm ◽  
Number Of Classes

Illiteracy is an inability to recognize characters, both in order to read and write. It is a significant problem for countries all around the world including Indonesia. In Indonesia, illiteracy rate is generally set as an indicator to see whether or not education in Indonesia is successful. If this problem is not going to be overcome, it will affect people’s prosperity. One system that has been used to overcome this problem is prioritizing the treatment from areas with the highest illiteracy rate and followed by areas with lower illiteracy rate. The method is going to be a way easier to be applied if it is supported by classification process. Since the classification process needs a class, and there has not been any fine classification of illiteracy rate, there is needed a clustering process before classification process. This research is aimed to get optimal number of classes through clustering process and know the result of illiteracy classification process. The clustering process is conducted by using k means algorithm, and for the classification process is conducted by using Naïve Bayes algorithm. The testing method used to assess the success of classification process is 10-fold method. Based on the research result, it can be concluded that the optimal illiteracy classes are three classes with the classification accuracy value of 96.4912% and error rate value of 3.5088%. Whereas the classification with two classes get the accuracy value of 93.8596% and error rate value of 6.1404%. And for the classification with five classes get the accuracy value of 90.3509% and error rate value of 9.6491%.

A Shape Annealing Approach to Optimal Truss Design With Dynamic Grouping of Members

1995 ◽  
Author(s):  
Kristina Shea ◽  
Jonathan Cagan ◽  
Steven J. Fenves
Keyword(s):  
Optimal Number ◽  
Cross Sectional Area ◽  
Topology Design ◽  
Sectional Area ◽  
Cross Sectional ◽  
Truss Topology Design ◽  
Optimal Truss Design ◽  
Optimal Grouping ◽  
The Cost ◽  
Number Of Classes

Abstract A shape annealing approach to truss topology design considering the tradeoff between the mass of a structure and multiple members of the same size, called a class of members, is presented. The problem of optimal grouping involves finding a structural design with an optimal number of classes and the optimal sizes of those classes; cross-sectional area is considered as the measure of size in this paper. Multiple members of a uniform cross-sectional area is advantageous when considering the cost of purchasing and fabricating materials to build a structure. The shape annealing method (Reddy and Cagan 1994) is used as an approach to solve this problem by incorporating a method for dynamic grouping of members into classes and adding a constraint for the number of allowable classes. This method is demonstrated on arch and truss problems. As well, results from an imposed symmetry constraint for the truss problem will be shown.

Long-term financial sustainability: An evaluation methodology with threats considerations

2020 ◽  
pp. 47-69
Author(s):  
Lidiya Guryanova ◽  
Olena Bolotova ◽  
Vitalii Gvozdytskyi ◽  
Sergienko Olena
Keyword(s):  
Management Strategies ◽  
Optimal Number ◽  
Evaluation Methodology ◽  
Security Level ◽  
Preventive Strategy ◽  
Optimal Dimension ◽  
Long Term Stability ◽  
Proactive Management ◽  
Number Of Classes

It is shown that one of the directions for increasing the efficiency of managing corporate systems (CS) under the influence of a large number of destabilizing fa-tors ("shocks", threats) is the development of a set of models of estimation and analysis of the long-term stability of CS in proactive contour of management, which allow timely diagnosing a decrease in the company's security level and adopting effective preventive management decisions. A review of existing approa-ches to the formation of such a set of models showed a number of limitations, the result of which is a low forecasting accuracy. The proposed approach, unlike the existing ones, allows to: 1) determine the optimal dimension of the information space of diagnostic factors; 2) find the optimal number of classes of situations for which differentiated management strategies can be developed; 3) determine the period of pre-emption, which does not require updating the models of retrospective diagnostics. This makes it possible to identify the class of not only current, but also forecast situations for a given horizon of proactive management and to choose an adequate preventive strategy.

scholarly journals Artificial Neural Network-Statistical Approach for PET Volume Analysis and Classification

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Mhd Saeed Sharif ◽  
Maysam Abbod ◽  
Abbes Amira ◽  
Habib Zaidi
Keyword(s):  
Neural Network ◽  
Intelligent System ◽  
Optimal Number ◽  
Response To Therapy ◽  
Automated System ◽  
Accurate Analysis ◽  
Data Set ◽  
Volume Analysis ◽  
Artificial Neural ◽  
Number Of Classes

The increasing number of imaging studies and the prevailing application of positron emission tomography (PET) in clinical oncology have led to a real need for efficient PET volume handling and the development of new volume analysis approaches to aid the clinicians in the clinical diagnosis, planning of treatment, and assessment of response to therapy. A novel automated system for oncological PET volume analysis is proposed in this work. The proposed intelligent system deploys two types of artificial neural networks (ANNs) for classifying PET volumes. The first methodology is a competitive neural network (CNN), whereas the second one is based on learning vector quantisation neural network (LVQNN). Furthermore, Bayesian information criterion (BIC) is used in this system to assess the optimal number of classes for each PET data set and assist the ANN blocks to achieve accurate analysis by providing the best number of classes. The system evaluation was carried out using experimental phantom studies (NEMA IEC image quality body phantom), simulated PET studies using the Zubal phantom, and clinical studies representative of nonsmall cell lung cancer and pharyngolaryngeal squamous cell carcinoma. The proposed analysis methodology of clinical oncological PET data has shown promising results and can successfully classify and quantify malignant lesions.

scholarly journals Sustainable Growth of Social Tourism: A Growth Mixture Modeling Approach Using Heterogeneous Travel Frequency Trajectories

2021 ◽  
Vol 18 (10) ◽  
pp. 5241
Author(s):  
Jaeseok Lee ◽  
Jooa Baek
Keyword(s):  
Latent Variable ◽  
Growth Mixture Modeling ◽  
Mixture Modeling ◽  
Optimal Number ◽  
Sustainable Growth ◽  
Growth Mixture ◽  
Latent Variable Analysis ◽  
Curve Modeling ◽  
Tourism And Hospitality ◽  
Number Of Classes

As travel activity has gained attention as one of the essential ways of understanding the sustainable growth of social tourism, a growing number of research projects have been conducted to elucidate the relationship between residents’ travel quantity (frequency) and quality (experience) in both macro and micro perspectives. Yet, very little research has highlighted that travel opportunities are not equally available to residents, especially a longitudinal perspective. The current study classified domestic travelers into four distinct classes using four years of longitudinal data from 5054 Korean residents. Latent growth curve modeling (LGCM) and growth mixture modeling (GMM) were employed to find out (1) the optimal number of classes, (2) the longitudinal travel frequency trajectory of each class, and (3) the distinctive demographic and travel characteristics of the four classes. This study provides some practical implications for policymakers when optimizing available resources for sustainable travel opportunities to relevant target sub-populations. Furthermore, detailed step-by-step analytic tutorials are also introduced for the extended application of longitudinal latent variable analysis in the tourism and hospitality fields, providing additional insights for relevant stakeholders.

Use of Region-Oriented Segmentation in Coin Recognition

2005 ◽  
Vol 277-279 ◽  
pp. 312-317
Author(s):  
Ming Ma ◽  
Kulwinder Singh ◽  
Dong Won Park ◽  
Juno Chang
Keyword(s):  
Clustering Algorithm ◽  
Cluster Algorithm ◽  
Optimal Number ◽  
Robust Method ◽  
Speed Up ◽  
Number Of Classes

Region-oriented segmentation is a simple relatively robust method for coin recognition. In this paper we present the use of Region-oriented segmentation for Coin Recognition. We use an improved K-Means Clustering Algorithm, which has the advantage to speed up the automatic determining of the optimal number of classes, to group all the gray-levels into several clusters. With the help of this cluster algorithm a label image of original coin image is obtained. In turn, the features such as area, perimeter, compactness and polar distance are extracted from the label image. The coins presented in the image could be recognized by matching the classifiers stored in the database. Several common segmentation approaches are also presented here in comparing to the region-oriented segmentation.

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