A FUZZY INTERACTIVE BI-OBJECTIVE MODEL FOR SVM TO IDENTIFY THE BEST COMPROMISE SOLUTION FOR MEASURING THE DEGREE OF INFECTION WITH CORONA VIRUS DISEASE (COVID-19)
A support vector machine (SVM) learns the decision surface from two different classes of the input points. In several applications, some of the input points are misclassified and each is not fully allocated to either of these two groups. In this paper a bi-objective quadratic programming model with fuzzy parameters is utilized and different feature quality measures are optimized simultaneously. An ฮฑ-cut is defined to transform the fuzzy model to a family of classical bi-objective quadratic programming problems. The weighting method is used to optimize each of these problems. For the proposed fuzzy bi-objective quadratic programming model, a major contribution will be added by obtaining different effective support vectors due to changes in weighting values. The experimental results, show the effectiveness of the ฮฑ-cut with the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions. The main contribution of this paper includes constructing a utility function for measuring the degree of infection with coronavirus disease (COVID-19).
A BI-OBJECTIVE MODEL FOR SVM WITH AN INTERACTIVE PROCEDURE TO IDENTIFY THE BE...ijaia
ย
A support vector machine (SVM) learns the decision surface from two different classes of the input points, there are misclassifications in some of the input points in several applications. In this paper a bi-objective quadratic programming model is utilized and different feature quality measures are optimized simultaneously using the weighting method for solving our bi-objective quadratic programming problem. An important contribution will be added for the proposed bi-objective quadratic programming model by getting different efficient support vectors due to changing the weighting values. The numerical examples, give evidence of the effectiveness of the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions.
Analytical study of feature extraction techniques in opinion miningcsandit
ย
Although opinion mining is in a nascent stage of development but still the ground is set for
dense growth of researches in the field. One of the important activities of opinion mining is to
extract opinions of people based on characteristics of the object under study. Feature extraction
in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first
part discusses various techniques and second part makes a detailed appraisal of the major
techniques used for feature extraction
ANALYTICAL STUDY OF FEATURE EXTRACTION TECHNIQUES IN OPINION MININGcsandit
ย
Although opinion mining is in a nascent stage of development but still the ground is set for dense growth of researches in the field. One of the important activities of opinion mining is to extract opinions of people based on characteristics of the object under study. Feature extraction in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first part discusses various techniques and second part makes a detailed appraisal of the major techniques used for feature extraction
IRJET- Performance Evaluation of Various Classification AlgorithmsIRJET Journal
ย
This document evaluates the performance of various classification algorithms (logistic regression, K-nearest neighbors, decision tree, random forest, support vector machine, naive Bayes) on a heart disease dataset. It provides details on each algorithm and evaluates their performance based on metrics like confusion matrix, precision, recall, F1-score and accuracy. The results show that naive Bayes had the best performance in correctly classifying samples with an accuracy of 80.21%, while SVM had the worst at 46.15%. In general, random forest and naive Bayes performed best according to the evaluation.
Machine Learning Algorithms for Image Classification of Hand Digits and Face ...IRJET Journal
ย
This document discusses machine learning algorithms for image classification using five different classification schemes. It summarizes the mathematical models behind each classification algorithm, including Nearest Class Centroid classifier, Nearest Sub-Class Centroid classifier, k-Nearest Neighbor classifier, Perceptron trained using Backpropagation, and Perceptron trained using Mean Squared Error. It also describes two datasets used in the experiments - the MNIST dataset of handwritten digits and the ORL face recognition dataset. The performance of the five classification schemes are compared on these datasets.
This document summarizes a research paper on using support vector machines (SVM) for anomaly detection, specifically for credit card fraud detection. It discusses how SVM is a supervised machine learning technique that can handle large, high-dimensional datasets. The document provides an overview of SVM, comparing it to other techniques like neural networks and clustering. It summarizes the methodology used in the research, which applied SVM to real credit card transaction data. The results showed SVM achieved high accuracy and a low false positive rate for fraud detection. In conclusion, the document states that applying this SVM method could help banks better predict fraudulent credit card transactions.
MARGINAL PERCEPTRON FOR NON-LINEAR AND MULTI CLASS CLASSIFICATION ijscai
ย
Generalization error of classifier can be reduced by larger margin of separating hyperplane. The proposed classification algorithm implements margin in classical perceptron algorithm, to reduce generalized errors by maximizing margin of separating hyperplane. Algorithm uses the same updation rule with the perceptron, to converge in a finite number of updates to solutions, possessing any desirable fraction of the margin. This solution is again optimized to get maximum possible margin. The algorithm can process linear, non-linear and multi class problems. Experimental results place the proposed classifier equivalent to the support vector machine and even better in some cases. Some preliminary experimental results are briefly discussed.
FUZZY IMAGE SEGMENTATION USING VALIDITY INDEXES CORRELATIONijcsit
ย
This paper introduces an algorithm for image segmentation using a clustering technique; the technique is
based on the fuzzy c means algorithm (FCM) that is executed iteratively with different number of clusters.
Furthermore, simultaneously five validity indexes are calculated and their information is correlated to
determine the optimal number of clusters in order to segment an image, results and simulations are shown
in the paper.
A BI-OBJECTIVE MODEL FOR SVM WITH AN INTERACTIVE PROCEDURE TO IDENTIFY THE BE...ijaia
ย
A support vector machine (SVM) learns the decision surface from two different classes of the input points, there are misclassifications in some of the input points in several applications. In this paper a bi-objective quadratic programming model is utilized and different feature quality measures are optimized simultaneously using the weighting method for solving our bi-objective quadratic programming problem. An important contribution will be added for the proposed bi-objective quadratic programming model by getting different efficient support vectors due to changing the weighting values. The numerical examples, give evidence of the effectiveness of the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions.
Analytical study of feature extraction techniques in opinion miningcsandit
ย
Although opinion mining is in a nascent stage of development but still the ground is set for
dense growth of researches in the field. One of the important activities of opinion mining is to
extract opinions of people based on characteristics of the object under study. Feature extraction
in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first
part discusses various techniques and second part makes a detailed appraisal of the major
techniques used for feature extraction
ANALYTICAL STUDY OF FEATURE EXTRACTION TECHNIQUES IN OPINION MININGcsandit
ย
Although opinion mining is in a nascent stage of development but still the ground is set for dense growth of researches in the field. One of the important activities of opinion mining is to extract opinions of people based on characteristics of the object under study. Feature extraction in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first part discusses various techniques and second part makes a detailed appraisal of the major techniques used for feature extraction
IRJET- Performance Evaluation of Various Classification AlgorithmsIRJET Journal
ย
This document evaluates the performance of various classification algorithms (logistic regression, K-nearest neighbors, decision tree, random forest, support vector machine, naive Bayes) on a heart disease dataset. It provides details on each algorithm and evaluates their performance based on metrics like confusion matrix, precision, recall, F1-score and accuracy. The results show that naive Bayes had the best performance in correctly classifying samples with an accuracy of 80.21%, while SVM had the worst at 46.15%. In general, random forest and naive Bayes performed best according to the evaluation.
Machine Learning Algorithms for Image Classification of Hand Digits and Face ...IRJET Journal
ย
This document discusses machine learning algorithms for image classification using five different classification schemes. It summarizes the mathematical models behind each classification algorithm, including Nearest Class Centroid classifier, Nearest Sub-Class Centroid classifier, k-Nearest Neighbor classifier, Perceptron trained using Backpropagation, and Perceptron trained using Mean Squared Error. It also describes two datasets used in the experiments - the MNIST dataset of handwritten digits and the ORL face recognition dataset. The performance of the five classification schemes are compared on these datasets.
This document summarizes a research paper on using support vector machines (SVM) for anomaly detection, specifically for credit card fraud detection. It discusses how SVM is a supervised machine learning technique that can handle large, high-dimensional datasets. The document provides an overview of SVM, comparing it to other techniques like neural networks and clustering. It summarizes the methodology used in the research, which applied SVM to real credit card transaction data. The results showed SVM achieved high accuracy and a low false positive rate for fraud detection. In conclusion, the document states that applying this SVM method could help banks better predict fraudulent credit card transactions.
MARGINAL PERCEPTRON FOR NON-LINEAR AND MULTI CLASS CLASSIFICATION ijscai
ย
Generalization error of classifier can be reduced by larger margin of separating hyperplane. The proposed classification algorithm implements margin in classical perceptron algorithm, to reduce generalized errors by maximizing margin of separating hyperplane. Algorithm uses the same updation rule with the perceptron, to converge in a finite number of updates to solutions, possessing any desirable fraction of the margin. This solution is again optimized to get maximum possible margin. The algorithm can process linear, non-linear and multi class problems. Experimental results place the proposed classifier equivalent to the support vector machine and even better in some cases. Some preliminary experimental results are briefly discussed.
FUZZY IMAGE SEGMENTATION USING VALIDITY INDEXES CORRELATIONijcsit
ย
This paper introduces an algorithm for image segmentation using a clustering technique; the technique is
based on the fuzzy c means algorithm (FCM) that is executed iteratively with different number of clusters.
Furthermore, simultaneously five validity indexes are calculated and their information is correlated to
determine the optimal number of clusters in order to segment an image, results and simulations are shown
in the paper.
IRJET-An Effective Strategy for Defense & Medical Pictures Security by Singul...IRJET Journal
ย
The document proposes an effective strategy for encrypting medical and defense images using singular value decomposition (SVD) and fractional Fourier transform (FrFT). It discusses generating shares of an image by applying FrFT to the SVD components, specifically the S matrix of singular values. Multiple shares are created using a sharing matrix. The strategy aims to securely transmit images over unreliable networks. Quantitative analysis shows the approach encrypts images quickly, with high sensitivity to changes and resistance to differential attacks, making it effective for encrypting sensitive images.
A comparative study of three validities computation methods for multimodel ap...IJECEIAES
ย
The multimodel approach offers a very satisfactory results in modelling, diagnose and control of complex systems. In the modelling case, this approach passes by three steps: the determination of the modelโs library, the validities computation and the establishment of the final model. In this context, this paper focuses on the elaboration of a comparative study between three recent methods of validities computation. Thus, it highlight the method that offers the best performances in term of precision. To achieve this goal, we apply, these three methods on two simulation examples in order to compare their performances.
The document provides an overview of dimensionality reduction techniques. It discusses linear dimensionality reduction methods like principal component analysis (PCA) as well as non-linear dimensionality reduction techniques. For non-linear dimensionality reduction, it describes the concept of manifolds and manifold learning. Specific manifold learning algorithms covered include Isomap, locally linear embedding (LLE), and applications of manifold learning.
Color Image Watermarking Application for ERTU CloudCSCJournals
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Color image is one of the the Egyptian Radio and Television Union (ERTU)โs content should be saved from any abuse from outside or inside the organization alike. The application of saving color image deploys the watermarking techniques based on Discrete Wavelet Transform (DWT). This application is implemented by software that suits the ERTUโs cloud besides many tests to insure the originality of the photo and if there is any changes applied on. All that provides the essential objectives of the cloud to overcome the limitation of distance as well as provide reliable and trusted services to Authorized group.
Methodological study of opinion mining and sentiment analysis techniquesijsc
ย
Decision making both on individual and organizational level is always accompanied by the search of
otherโs opinion on the same. With tremendous establishment of opinion rich resources like, reviews, forum
discussions, blogs, micro-blogs, Twitter etc provide a rich anthology of sentiments. This user generated
content can serve as a benefaction to market if the semantic orientations are deliberated. Opinion mining
and sentiment analysis are the formalization for studying and construing opinions and sentiments. The
digital ecosystem has itself paved way for use of huge volume of opinionated data recorded. This paper is
an attempt to review and evaluate the various techniques used for opinion and sentiment analysis.
1) The document discusses various methods for interpreting machine learning models, including global and local surrogate models, feature importance plots, Shapley values, partial dependence plots, and individual conditional expectation plots.
2) It explains that interpretability refers to how understandable the reasons for a model's predictions are to humans. Interpretability methods can provide global explanations of entire models or local explanations of individual predictions.
3) The document advocates that improving interpretability is important for addressing issues like bias in machine learning systems and increasing trust in applications used for high-stakes decisions like criminal justice.
Abstract This paper presents a novel approach for the gesture recognition system using software. In this paper the real time image is taken and is compared with a training set of images and displays a matched training image. In this approach we have used skin detection techniques for detecting the skin threshold regions, Principle Component Analysis (PCA) algorithm and Linear Discriminant Analysis (LDA) for data compressing and analyzing and K-Nearest Neighbor (KNN), Support Vector Machine (SVM) classification for matching the appropriate training image to the real-time image. The software used is MATLAB. The hand gestures used are taken from the American Sign Language. Keywordsโ PCA algorithm, LDA algorithm, skin detection, KNN and SVM classification
The document provides a tutorial on support vector machines (SVM). It begins with an abstract briefly introducing SVM and discussing how the tutorial was compiled from various sources. It then provides an introduction on machine learning and how SVM relates. The core concepts of SVM are explained, including statistical learning theory, maximizing margins, soft-margin classifiers, and the kernel trick. Common kernel functions for SVM are also listed. The tutorial is intended to give a brief overview of SVM for readers familiar with linear algebra, analysis, neural networks, and artificial intelligence concepts.
This document discusses using fuzzy clustering to group real estate properties. It presents a case study clustering 46 real estate listings into 3 groups based on price, area, and region attributes. The fuzzy c-means clustering algorithm in MATLAB is used to assign membership levels and cluster centroids. The results identify 3 clusters - one for mid-priced properties in good regions and average areas, one for high-priced properties in excellent regions and large areas, and one for low-priced properties in poor regions and small areas. Graphs and tables show the clustered properties and centroids.
This document summarizes research on using spectral clustering methods to impute missing pixel values in images. It first tests several spectral clustering algorithms on artificial datasets to compare their performance. It then explores feature selection and the number of clusters for image segmentation. Finally, it proposes two imputation algorithms based on pixel proximity and applies them to example images.
This document proposes a dynamic clustering algorithm using fuzzy c-means clustering. It begins with an introduction to fuzzy c-means clustering and its limitations when the chosen number of clusters is incorrect. It then proposes a dynamic clustering algorithm that starts with a fixed number of clusters but can automatically increase the number of clusters during iterations based on the data, improving purity. The algorithm is described and examples are provided to illustrate its effectiveness at forming clear clusters after iterations and determining when clustering has terminated.
IRJET- Evaluation of Classification Algorithms with Solutions to Class Imbala...IRJET Journal
ย
This document discusses evaluating various classification algorithms to address class imbalance problems using the bank marketing dataset in WEKA. It first introduces data mining and classification algorithms like decision trees, naive Bayes, neural networks, support vector machines, logistic regression and random forests. It then discusses the class imbalance problem that occurs when one class is underrepresented. To address this, it explores sampling techniques like random under-sampling of the majority class, random over-sampling of the minority class, and SMOTE. It uses these techniques on the bank marketing dataset to evaluate the algorithms based on metrics like precision, recall, F1-score, ROC and AUCPR for the minority class.
This document summarizes recent convergence results for the fuzzy c-means clustering algorithm (FCM). It discusses both numerical convergence, referring to how well the algorithm attains the minima of an objective function, and stochastic convergence, referring to how accurately the minima represent the actual cluster structure in data. For numerical convergence, the document outlines global and local convergence theorems, showing FCM converges to minima or saddle points globally and linearly to local minima. For stochastic convergence, it discusses a consistency result showing the minima accurately represent cluster structure under certain statistical assumptions.
IMPROVING SUPERVISED CLASSIFICATION OF DAILY ACTIVITIES LIVING USING NEW COST...csandit
ย
The growing population of elders in the society calls for a new approach in care giving. By
inferring what activities elderly are performing in their houses it is possible to determine their
physical and cognitive capabilities. In this paper we show the potential of important
discriminative classifiers namely the Soft-Support Vector Machines (C-SVM), Conditional
Random Fields (CRF) and k-Nearest Neighbors (k-NN) for recognizing activities from sensor
patterns in a smart home environment. We address also the class imbalance problem in activity
recognition field which has been known to hinder the learning performance of classifiers. Cost
sensitive learning is attractive under most imbalanced circumstances, but it is difficult to
determine the precise misclassification costs in practice. We introduce a new criterion for
selecting the suitable cost parameter C of the C-SVM method. Through our evaluation on four
real world imbalanced activity datasets, we demonstrate that C-SVM based on our proposed
criterion outperforms the state-of-the-art discriminative methods in activity recognition.
The document summarizes statistical pattern recognition techniques. It is divided into 9 sections that cover topics like dimensionality reduction, classifiers, classifier combination, and unsupervised classification. The goal of pattern recognition is supervised or unsupervised classification of patterns based on features. Dimensionality reduction aims to reduce the number of features to address the curse of dimensionality when samples are limited. Multiple classifiers can be combined through techniques like stacking, bagging, and boosting. Unsupervised classification uses clustering algorithms to construct decision boundaries without labeled training data.
A BI-OBJECTIVE MODEL FOR SVM WITH AN INTERACTIVE PROCEDURE TO IDENTIFY THE BE...gerogepatton
ย
A support vector machine (SVM) learns the decision surface from two different classes of the input points, there are misclassifications in some of the input points in several applications. In this paper a bi-objective quadratic programming model is utilized and different feature quality measures are optimized simultaneously using the weighting method for solving our bi-objective quadratic programming problem. An important contribution will be added for the proposed bi-objective quadratic programming model by getting different efficient support vectors due to changing the weighting values. The numerical examples, give evidence of the effectiveness of the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions.
The International Journal of Engineering and Science (The IJES)theijes
ย
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Single to multiple kernel learning with four popular svm kernels (survey)eSAT Journals
ย
Abstract Machine learning applications and pattern recognition have gained great attention recently because of the variety of applications
depend on machine learning techniques, these techniques could make many processes easier and also reduce the amount of
human interference (more automation). This paper research four of the most popular kernels used with Support Vector Machines
(SVM) for Classification purposes. This survey uses Linear, Polynomial, Gaussian and Sigmoid kernels, each in a single form and
all together as un-weighted sum of kernels as form of Multi-Kernel Learning (MKL), with eleven datasets, these data sets are
benchmark datasets with different types of features and different number of classes, so some will be used with Two-Classes
Classification (Binary Classification) and some with Multi-Class Classification. Shogun machine learning Toolbox is used with
Python programming language to perform the classification and also to handle the pre-classification operations like Feature
Scaling (Normalization).The Cross Validation technique is used to find the best performance Out of the suggested different
kernels' methods .To compare the final results two performance measuring techniques are used; classification accuracy and Area
Under Receiver Operating Characteristic (ROC). General basics of SVM and used Kernels with classification parameters are
given through the first part of the paper, then experimental details are explained in steps and after those steps, experimental
results from the steps are given with final histograms represent the differences of the outputs' accuracies and the areas under
ROC curves (AUC). Finally best methods obtained are applied on remote sensing data sets and the results are compared to a
state of art work published in the field using the same set of data.
Keywords: Machine Learning, Classification, SVM, MKL, Cross Validation and ROC
This document discusses using support vector machines (SVM) for anomaly detection, specifically for credit card fraud detection. It contains the following key points:
1. SVM is a supervised machine learning technique that can be used for anomaly detection tasks like fraud detection. It works by mapping data to a higher dimensional space to find a hyperplane that maximizes separation between classes.
2. The document evaluates SVM for credit card fraud detection using real transaction data and compares it to other techniques like neural networks and clustering. SVM achieved higher accuracy and lower false positive rates than these other methods.
3. A theoretical comparison found that SVM requires no parameter tuning, works well in high dimensions, and has lower computational cost than neural networks and
Real-Time Stock Market Analysis using Spark StreamingSigmoid
ย
This document proposes using support vector machines (SVMs) to model high-frequency limit order book dynamics and predict metrics like mid-price movement and price spread crossing. It describes representing each limit order book entry as a vector of attributes, then using multi-class SVMs to build models for each metric. Experiments on real data show the selected features are effective for short-term price forecasts. The document provides background on SVMs, describing how they find an optimal separating hyperplane to classify data points into labels.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Radial Basis Function Neural Network (RBFNN), Induction Motor, Vector control...cscpconf
ย
Although opinion mining is in a nascent stage of development but still the ground is set for dense growth of researches in the field. One of the important activities of opinion mining is to
extract opinions of people based on characteristics of the object under study. Feature extraction in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first part discusses various techniques and second part makes a detailed appraisal of the major techniques used for feature extraction.
IRJET-An Effective Strategy for Defense & Medical Pictures Security by Singul...IRJET Journal
ย
The document proposes an effective strategy for encrypting medical and defense images using singular value decomposition (SVD) and fractional Fourier transform (FrFT). It discusses generating shares of an image by applying FrFT to the SVD components, specifically the S matrix of singular values. Multiple shares are created using a sharing matrix. The strategy aims to securely transmit images over unreliable networks. Quantitative analysis shows the approach encrypts images quickly, with high sensitivity to changes and resistance to differential attacks, making it effective for encrypting sensitive images.
A comparative study of three validities computation methods for multimodel ap...IJECEIAES
ย
The multimodel approach offers a very satisfactory results in modelling, diagnose and control of complex systems. In the modelling case, this approach passes by three steps: the determination of the modelโs library, the validities computation and the establishment of the final model. In this context, this paper focuses on the elaboration of a comparative study between three recent methods of validities computation. Thus, it highlight the method that offers the best performances in term of precision. To achieve this goal, we apply, these three methods on two simulation examples in order to compare their performances.
The document provides an overview of dimensionality reduction techniques. It discusses linear dimensionality reduction methods like principal component analysis (PCA) as well as non-linear dimensionality reduction techniques. For non-linear dimensionality reduction, it describes the concept of manifolds and manifold learning. Specific manifold learning algorithms covered include Isomap, locally linear embedding (LLE), and applications of manifold learning.
Color Image Watermarking Application for ERTU CloudCSCJournals
ย
Color image is one of the the Egyptian Radio and Television Union (ERTU)โs content should be saved from any abuse from outside or inside the organization alike. The application of saving color image deploys the watermarking techniques based on Discrete Wavelet Transform (DWT). This application is implemented by software that suits the ERTUโs cloud besides many tests to insure the originality of the photo and if there is any changes applied on. All that provides the essential objectives of the cloud to overcome the limitation of distance as well as provide reliable and trusted services to Authorized group.
Methodological study of opinion mining and sentiment analysis techniquesijsc
ย
Decision making both on individual and organizational level is always accompanied by the search of
otherโs opinion on the same. With tremendous establishment of opinion rich resources like, reviews, forum
discussions, blogs, micro-blogs, Twitter etc provide a rich anthology of sentiments. This user generated
content can serve as a benefaction to market if the semantic orientations are deliberated. Opinion mining
and sentiment analysis are the formalization for studying and construing opinions and sentiments. The
digital ecosystem has itself paved way for use of huge volume of opinionated data recorded. This paper is
an attempt to review and evaluate the various techniques used for opinion and sentiment analysis.
1) The document discusses various methods for interpreting machine learning models, including global and local surrogate models, feature importance plots, Shapley values, partial dependence plots, and individual conditional expectation plots.
2) It explains that interpretability refers to how understandable the reasons for a model's predictions are to humans. Interpretability methods can provide global explanations of entire models or local explanations of individual predictions.
3) The document advocates that improving interpretability is important for addressing issues like bias in machine learning systems and increasing trust in applications used for high-stakes decisions like criminal justice.
Abstract This paper presents a novel approach for the gesture recognition system using software. In this paper the real time image is taken and is compared with a training set of images and displays a matched training image. In this approach we have used skin detection techniques for detecting the skin threshold regions, Principle Component Analysis (PCA) algorithm and Linear Discriminant Analysis (LDA) for data compressing and analyzing and K-Nearest Neighbor (KNN), Support Vector Machine (SVM) classification for matching the appropriate training image to the real-time image. The software used is MATLAB. The hand gestures used are taken from the American Sign Language. Keywordsโ PCA algorithm, LDA algorithm, skin detection, KNN and SVM classification
The document provides a tutorial on support vector machines (SVM). It begins with an abstract briefly introducing SVM and discussing how the tutorial was compiled from various sources. It then provides an introduction on machine learning and how SVM relates. The core concepts of SVM are explained, including statistical learning theory, maximizing margins, soft-margin classifiers, and the kernel trick. Common kernel functions for SVM are also listed. The tutorial is intended to give a brief overview of SVM for readers familiar with linear algebra, analysis, neural networks, and artificial intelligence concepts.
This document discusses using fuzzy clustering to group real estate properties. It presents a case study clustering 46 real estate listings into 3 groups based on price, area, and region attributes. The fuzzy c-means clustering algorithm in MATLAB is used to assign membership levels and cluster centroids. The results identify 3 clusters - one for mid-priced properties in good regions and average areas, one for high-priced properties in excellent regions and large areas, and one for low-priced properties in poor regions and small areas. Graphs and tables show the clustered properties and centroids.
This document summarizes research on using spectral clustering methods to impute missing pixel values in images. It first tests several spectral clustering algorithms on artificial datasets to compare their performance. It then explores feature selection and the number of clusters for image segmentation. Finally, it proposes two imputation algorithms based on pixel proximity and applies them to example images.
This document proposes a dynamic clustering algorithm using fuzzy c-means clustering. It begins with an introduction to fuzzy c-means clustering and its limitations when the chosen number of clusters is incorrect. It then proposes a dynamic clustering algorithm that starts with a fixed number of clusters but can automatically increase the number of clusters during iterations based on the data, improving purity. The algorithm is described and examples are provided to illustrate its effectiveness at forming clear clusters after iterations and determining when clustering has terminated.
IRJET- Evaluation of Classification Algorithms with Solutions to Class Imbala...IRJET Journal
ย
This document discusses evaluating various classification algorithms to address class imbalance problems using the bank marketing dataset in WEKA. It first introduces data mining and classification algorithms like decision trees, naive Bayes, neural networks, support vector machines, logistic regression and random forests. It then discusses the class imbalance problem that occurs when one class is underrepresented. To address this, it explores sampling techniques like random under-sampling of the majority class, random over-sampling of the minority class, and SMOTE. It uses these techniques on the bank marketing dataset to evaluate the algorithms based on metrics like precision, recall, F1-score, ROC and AUCPR for the minority class.
This document summarizes recent convergence results for the fuzzy c-means clustering algorithm (FCM). It discusses both numerical convergence, referring to how well the algorithm attains the minima of an objective function, and stochastic convergence, referring to how accurately the minima represent the actual cluster structure in data. For numerical convergence, the document outlines global and local convergence theorems, showing FCM converges to minima or saddle points globally and linearly to local minima. For stochastic convergence, it discusses a consistency result showing the minima accurately represent cluster structure under certain statistical assumptions.
IMPROVING SUPERVISED CLASSIFICATION OF DAILY ACTIVITIES LIVING USING NEW COST...csandit
ย
The growing population of elders in the society calls for a new approach in care giving. By
inferring what activities elderly are performing in their houses it is possible to determine their
physical and cognitive capabilities. In this paper we show the potential of important
discriminative classifiers namely the Soft-Support Vector Machines (C-SVM), Conditional
Random Fields (CRF) and k-Nearest Neighbors (k-NN) for recognizing activities from sensor
patterns in a smart home environment. We address also the class imbalance problem in activity
recognition field which has been known to hinder the learning performance of classifiers. Cost
sensitive learning is attractive under most imbalanced circumstances, but it is difficult to
determine the precise misclassification costs in practice. We introduce a new criterion for
selecting the suitable cost parameter C of the C-SVM method. Through our evaluation on four
real world imbalanced activity datasets, we demonstrate that C-SVM based on our proposed
criterion outperforms the state-of-the-art discriminative methods in activity recognition.
The document summarizes statistical pattern recognition techniques. It is divided into 9 sections that cover topics like dimensionality reduction, classifiers, classifier combination, and unsupervised classification. The goal of pattern recognition is supervised or unsupervised classification of patterns based on features. Dimensionality reduction aims to reduce the number of features to address the curse of dimensionality when samples are limited. Multiple classifiers can be combined through techniques like stacking, bagging, and boosting. Unsupervised classification uses clustering algorithms to construct decision boundaries without labeled training data.
Similar to A FUZZY INTERACTIVE BI-OBJECTIVE MODEL FOR SVM TO IDENTIFY THE BEST COMPROMISE SOLUTION FOR MEASURING THE DEGREE OF INFECTION WITH CORONA VIRUS DISEASE (COVID-19)
A BI-OBJECTIVE MODEL FOR SVM WITH AN INTERACTIVE PROCEDURE TO IDENTIFY THE BE...gerogepatton
ย
A support vector machine (SVM) learns the decision surface from two different classes of the input points, there are misclassifications in some of the input points in several applications. In this paper a bi-objective quadratic programming model is utilized and different feature quality measures are optimized simultaneously using the weighting method for solving our bi-objective quadratic programming problem. An important contribution will be added for the proposed bi-objective quadratic programming model by getting different efficient support vectors due to changing the weighting values. The numerical examples, give evidence of the effectiveness of the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions.
The International Journal of Engineering and Science (The IJES)theijes
ย
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Single to multiple kernel learning with four popular svm kernels (survey)eSAT Journals
ย
Abstract Machine learning applications and pattern recognition have gained great attention recently because of the variety of applications
depend on machine learning techniques, these techniques could make many processes easier and also reduce the amount of
human interference (more automation). This paper research four of the most popular kernels used with Support Vector Machines
(SVM) for Classification purposes. This survey uses Linear, Polynomial, Gaussian and Sigmoid kernels, each in a single form and
all together as un-weighted sum of kernels as form of Multi-Kernel Learning (MKL), with eleven datasets, these data sets are
benchmark datasets with different types of features and different number of classes, so some will be used with Two-Classes
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Python programming language to perform the classification and also to handle the pre-classification operations like Feature
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A FUZZY INTERACTIVE BI-OBJECTIVE MODEL FOR SVM TO IDENTIFY THE BEST COMPROMISE SOLUTION FOR MEASURING THE DEGREE OF INFECTION WITH CORONA VIRUS DISEASE (COVID-19)
1. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
DOI : 10.5121/ijfls.2021.11102 13
A FUZZY INTERACTIVE BI-OBJECTIVE MODEL FOR
SVM TO IDENTIFY THE BEST COMPROMISE
SOLUTION FOR MEASURING THE DEGREE OF
INFECTION WITH CORONA VIRUS
DISEASE (COVID-19)
Mohammed Zakaria Moustafa1
, Hassan Mahmoud Elragal2
,
Mohammed Rizk Mohammed2
, Hatem Awad Khater3
and Hager Ali Yahia2
1
Department of Electrical Engineering (Power and Machines Section)
ALEXANDRIA University, Alexandria, Egypt
2
Department of Communication and Electronics Engineering,
ALEXANDRIA University, Alexandria, Egypt
3
Department of Mechatronics, Faculty of Engineering,
Horus University, Egypt
ABSTRACT
A support vector machine (SVM) learns the decision surface from two different classes of the input points.
In several applications, some of the input points are misclassified and each is not fully allocated to either
of these two groups. In this paper a bi-objective quadratic programming model with fuzzy parameters is
utilized and different feature quality measures are optimized simultaneously. An ฮฑ-cut is defined to
transform the fuzzy model to a family of classical bi-objective quadratic programming problems. The
weighting method is used to optimize each of these problems. For the proposed fuzzy bi-objective quadratic
programming model, a major contribution will be added by obtaining different effective support vectors
due to changes in weighting values. The experimental results, show the effectiveness of the ฮฑ-cut with the
weighting parameters on reducing the misclassification between two classes of the input points. An
interactive procedure will be added to identify the best compromise solution from the generated efficient
solutions. The main contribution of this paper includes constructing a utility function for measuring the
degree of infection with coronavirus disease (COVID-19).
KEYWORDS
Support vector machine (SVMs); Classification; Multi-objective problems; Weighting method; fuzzy
mathematics; Quadratic programming; Interactive approach; COVID-19.
1. INTRODUCTION
Nowadays, the coronavirus spread between people all over the world, every day the number of
infected people is increased. These diseases can infect both humans and animals. So, the
detection of coronavirus (COVID-19) is now a critical task for the medical practitioner. In this
paper, the support vector machine is suggested for detection of coronavirus infected patient using
different features (X-ray images, Fever, Cough and Shortness of breath), and help the decision
makers to determine the number of patients who must be isolated according to the degree of
infection.
2. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
14
Support Vector Machines (SVMs) are a classification technique developed by Vapnik at the end
of โ60s [1]. The theory of support vector machines (SVMs) is a new classification technique and
has drawn much attention on this topic in recent years [6]. Since then the technique has been
deeply improved, being applied in many different contexts.
In many applications, SVM has been shown to provide higher performance than traditional
learning machines [6]. SVMs are known as maximum margin classifiers, since they find the
optimal hyperplane between two classes as shown in figure1, defined by a number of support
vectors [4].
Figure 1. Maximization of the margin between two classes
The well-known generalization feature of the technique is mainly due to the introduction of a
penalty factor, named C that allows us to prevent the effects of outliers by permitting a certain
amount of misclassification errors.
In this paper, the idea is to apply the fuzzy multi-objective programming technique for
developing the set of all efficient solutions for the classification problem with minimum errors.
An ฮฑ-cut is taken to transform the fuzzy multi-objective problem model to a classical one (ฮฑ
problem). The weighting method is used to solve the ฮฑ problem proposed to generate the set of
efficient solutions for the proposed model. The remainder of this paper is organized as follows. A
brief review for the SVM is described in section 2. The proposed fuzzy bi-objective model for the
Support Vector Machine will be derived in section 3. NEXT, section 4 presents three numerical
examples corresponding to three different ฮฑ-cut. Section 5 provides our general conclusions.
2. SUPPORT VECTOR MACHINES
SVM is an efficient classifier to classify two different sets of observations into their relevant class
as shown in figure 2 where there are more than straight line separates between the two sets. SVM
mechanism is based upon finding the best hyperplane that separates the data of two different
classes of the category. The best hyperplane is the one that maximizes the margin, i.e., the
distance from the nearest training points [2].
3. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
15
Support vector machine has been utilized in many applications such as biometrics,
chemoinformatics, and agriculture. SVM has penalty parameters, and kernel parameters that have
a great influence on the performance of SVM [3]. We review the basis of the theory of SVM in
classification problems [7].
Let a set S of labelled training points
(๐ฆ1,๐ฅ1)โฆ (๐ฆ๐,๐ฅ๐). (1)
Where,xi โ โN
belongs to either of two classes and is given a labelyi = {โ1,1} for i = 1, โฆ , l.
Figure 2. Data classification using support vector machine
In some cases, to get the suitable hyperplane in an input space, mapping the input space into a
higher dimension feature space and searching the optimal hyperplane in this feature space.
Let z = ๐(๐ฅ) denote the corresponding feature space vector with mapping ๐ from โ๐
to a feature
space แตถ. We wish to find the hyperplane
๐ค. ๐ง + ๐ = 0 (2)
defined by the pair (w, b) according to the function
๐(๐ฅ๐) = ๐ ๐๐๐(๐ค. ๐ง๐ + ๐) = {
1, ๐๐๐ฆ๐ = 1
โ1, ๐๐๐ฆ๐ = โ1
(3)
where w โ แตถ and b โ โ. For more precisely the equation will be
{
(๐ค. ๐ง๐ + ๐) โฅ 1, ๐๐๐ฆ๐ = 1
(๐ค. ๐ง๐ + ๐) โค โ1, ๐๐๐ฆ๐ = โ1,
๐ = 1, โฆ , ๐ (4)
For the linearly separable set S, we can find a unique optimal hyperplane for which the margin
between the projections of the training points of two different classes is maximized.
For the data that are not linearly separable figure 3, the previous analysis can be generalized by
introducing some nonnegative variables ฮพ๐
โฅ 0 then,
๐ฆ๐(๐ค. ๐ง๐ + ๐) โฅ 1 โ ฮพ๐
, ๐ = 1, โฆ , ๐. (5)
4. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
16
The term โ ฮพ๐
๐
๐=1 can be thought of as some measure of the amount of misclassifications.
The optimal hyperplane problem is then regarded as the solution to the problem
๐๐๐๐๐๐๐ง๐
1
2
๐ค. ๐ค + ๐ถ โ ฮพ๐
๐
๐=1
๐ ๐ข๐๐๐๐๐ก๐ก๐๐ฆ๐(๐ค. ๐ง๐ + ๐) โฅ 1 โ ฮพ๐
, (6)
๐ = 1, โฆ , ๐
ฮพ๐
โฅ 0, ๐ = 1, โฆ , ๐
where, ๐ถ is a constant. The parameter ๐ถ can be regarded as a regularization parameter [5]. SVM
algorithms use a set of mathematical functions that are defined as the kernel.
The function of kernel is to take data as input and transform it into the required form. Different
SVM algorithms use different types of kernel functions. For example, linear, nonlinear,
polynomial, radial basis function (RBF), and sigmoid.
Basically, the training part consists in finding the best separating plane (with maximal margin)
based on specific vector called support vector. If the decision is not feasible in the initial
description space, you can increase space dimension thanks to kernel functions and may be find a
hyperplane that will be your decision separator.
Figure 3. Linearly separable and nonlinearly separable
3. FORMULATION OF THE FUZZY BI-OBJECTIVE QUADRATIC
PROGRAMMING MODEL OF SVM
In this section, we make a detail description about the idea and formulation of the fuzzy bi
objective programming model for the SVM. SVM is a powerful tool for solving classification
problems, but due to the nonlinearity separable in some of the input data, there is an error in
measuring the amount of misclassification. In the same time, in many real-world applications,
each of the input points does not exactly belong to one of the two classes [11].
From this point of view, we reformulate the classical model of the SVM to the following bi-
objective programming model with fuzzy parameters.
5. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
17
3.1. The Fuzzy Bi-Objective Support Vector Machine (FSVM):
Now, we add another objective function with fuzzy parameters แฟฆ๐,๐ = 1,2, โฆ , ๐ for the previous
model in section 2 to be in the form [14]
Min โฅ ๐ค โฅ2
,
Min โ แฟฆ๐ ฮพ๐
๐
๐=1
Subject to (7)
๐ฆ๐(๐ค. ๐ฅ๐ + ๐) โฅ 1 + ฮพ๐
, ๐ = 1,2, โฆ , ๐
ฮพ๐
โฅ 0 , ๐ = 1,2, โฆ , ๐
By taken an ฮฑ-cut for the membership functions corresponding to the fuzzy parameters แฟฆ๐, ๐ =
1,2, โฆ , ๐, we get the following ฮฑ-problem:
Min โฅ ๐ค โฅ2
,
Min โ ฮฑ๐ฮพ๐
๐
๐=1
Subject to (8)
๐ฆ๐(๐ค. ๐ฅ๐ + ๐) โฅ 1 + ฮพ๐
, ๐ = 1,2, โฆ , ๐
ฮพ๐
โฅ 0 , ๐ = 1,2, โฆ , ๐
ฯ โค ฮฑ๐ โค 1 , ๐ = 1,2, โฆ , ๐
With sufficient small ฯ > 0.
Where the parameter ฮพ๐
is a measure of the error in the SVM and the term ฮฑ๐ฮพ๐
is a measure of
the error with different degrees ฮฑ๐. The (ฮฑ-problem) is solved by the weighting method to get the
set of all efficient solutions.
This problem is a bi-objective quadratic programming problem. The first objective is to
maximize the gap between the two hyperplanes which used to classify the input points. The
second objective is to minimize the error (with different degrees ฮฑ๐ , ๐ = 1,2, โฆ , ๐) in measuring
the amount of misclassification in case of nonlinearity separable input points [11].
Problem 8 can be solved by the weighting method to get the set of all efficient solutions for the
classification problem.
The right choice of weightage for each of these objectives is critical to the quality of the classifier
learned, especially in case of the class imbalanced data sets. Therefore, costly parameter tuning
has to be undertaken to find a set of suitable relative weights [10].
3.2. The Weighting Method
In this method each objective ๐๐(๐), ๐ = 1,2, โฆ , ๐, is multiplied by a scalar weigh๐ค๐ โฅ
0 ๐๐๐ โ ๐ค๐ = 1.
๐
๐=1 Then, the k weighted objectives are summed to form a weighted-sums
objective function [8][12].
๐ด๐ ๐ ๐ข๐๐ ๐ as {
๐ค โ ๐ ๐
: ๐ค๐ โฅ 0,
๐ = 1,2, โฆ , ๐
๐๐๐ โ ๐ค๐ = 1
๐
๐=1
}(9)
be the set of nonnegative weights. Then the weighting problem is defined as:
6. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
18
๐(๐): ๐๐๐ โ ๐ค๐๐๐
๐
๐=1
Subject to ๐ = {
๐ โ ๐ ๐
: ๐๐(๐) โค 0,
๐ = 1,2, โฆ , ๐
}. (10)
Then, in this paper the weighting method takes the form
Inf z =๐ค1 โฅ ๐ค โฅ2
+ ๐ค2 โ ฮฑ๐ฮพ๐
๐
๐=1
Subject to
๐ฆ๐(๐ค. ๐ฅ๐ + ๐) โฅ 1 + ฮพ๐
, ๐ = 1,2, โฆ , ๐
ฮพ๐
โฅ 0 , ๐ = 1,2, โฆ , ๐ (11)
๐ค1 > 0, ๐ค2 โฅ 0
๐ค1 + ๐ค2 = 1
ฯ โค ฮฑ๐ โค 1 , ๐ = 1,2, โฆ , ๐
With sufficient small ฯ > 0
Here we use โInf โinstead of โMinโ since the set of constraints is unbounded, where ๐ค1 โ 0.
Also, we avoid the redundant solutions by adding the constraint ๐ค1 + ๐ค2 = 1.
3.3. An Interactive Procedure to Identify the Best Compromise Solution
For the version of our bi-objective (SVM) model which applies to determine the best compromise
solution, we need the following hypothesis (after the interaction with the decision maker) [13]:
The best compromise solution from the set of the generated efficient solutions is that efficient one
corresponding to
min
ฮฑ
๐+
โค min
ฮฑ
๐โ
Where, ๐โ
is the number of support vectors of the negative class,
๐+
is the number of support vectors of the positive class.
We must notice that this hypothesis can be reversed according to the preference of the decision
maker (see Yaochu Jin,2006) [9].
Considering the utility function u(xi) is the distance between xi, i=1,2,3,โฆ,nand the best
compromise hyperplane, then we can construct the membership degree of each xi belonging to its
+ve or -ve class as follow:
degree of ๐ฅ๐
+
= ๐(๐ฅ๐
+) =
๐ข(๐ฅ๐
+)
๐๐๐ฅ๐=1
๐ ๐ข(๐ฅ๐
+)
โ [0 1]
Similarly, degree of ๐ฅ๐
โ
= ๐(๐ฅ๐
โ) =
๐ข(๐ฅ๐
โ)
๐๐๐ฅ๐=1
๐ ๐ข(๐ฅ๐
โ)
โ [0 1], l + m = n (11)
For our problem of corona virus disease, the decision maker can take a threshold level ๐+
(๐๐ ๐โ
)
to isolate ones with ๐(๐ฅ๐
+) โฅ ๐+
, or to be in the safe side, he can decide to isolate ones with
๐(๐ฅ๐
โ) โค ๐โ
, that is according to his preferences.
The following figure shows how to predict the number of the infected people by using SVM.
7. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
19
Figure 4. detection No. of infected people by SVM
4. NUMERICAL EXAMPLES
By using python program, we can solve the previous problem and show the effect of different
values of the weighting parameters. The data set that is used in these examples consist of 51
points and each point has two features, table 1 shows part of this data.
Table 1. Description of part of datasets used in our study.
X1 X2 Y
1.9643 4.5957 1
2.2753 3.8589 1
2.9781 4.5651 1
2.932 3.5519 1
3.5772 2.856 1
0.9044 3.0198 0
0.76615 2.5899 0
0.086405 4.1045 0
Figure 5. ๐ค2 =
1
2
, ๐ค1 =
1
2
, ฮฑ=
1
4
, number of support vectors = 20
8. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
20
Figure 6. ๐ค2 =
1
2
, ๐ค1 =
1
2
, ฮฑ=
1
2
, number of support vectors = 16
Figure 7. ๐ค2 =
1
2
, ๐ค1 =
1
2
, ฮฑ=1, number of support vectors = 12
So, the previous results, by using different degrees (ฮฑ) at the same weights (๐ค1 & ๐ค2), show how
these parameters (ฮฑ, ๐ค1, ๐ค2) effect on the performance of SVM. When the value of ฮฑ is increased
the number of support vectors is reduced.
There are good reasons to prefer SVMs with few support vectors (SVs). In the hard-margin case,
the number of SVs (#SV) is an upper bound on the expected number of errors made by the leave-
one-out procedure [9].
So, we can control the performance of SVM according to our requirements by adjusting the
values of the parameters (ฮฑ, ๐ค1, ๐ค2).
According to our hypothesis that presented in section 3.3, the best compromise solution is that
corresponding to ฮฑ=1.
9. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
21
Table 2. Description of membership degree of some points used in our study
If the decision maker put ๐+
= 0.3, then he will isolate ones that are corresponding
to(๐ฅ1
+
, ๐ฅ3
+
, ๐ฅ4
+
, ๐ฅ6
+
, ๐ฅ7
+
, ๐ฅ8
+
,๐ฅ9
+
, ๐ฅ10
+
, ๐ฅ11
+
, ๐ฅ13
+
, ๐ฅ14
+
, ๐ฅ16
+
, ๐ฅ17
+
, ๐ฅ18
+
, ๐ฅ19
+
, ๐ฅ50
+
, ๐ฅ51
+
), it will be 15 patients of
51. But if he wants to be in the safe side, he will put ๐โ
=0.1, then he will isolate ones that are
correspondingto the positive side
(๐ฅ1
+
, ๐ฅ2
+
, ๐ฅ3
+
, ๐ฅ4
+
, ๐ฅ5
+
,๐ฅ6
+
, ๐ฅ7
+
, ๐ฅ8
+
, ๐ฅ9
+
, ๐ฅ10
+
, ๐ฅ11
+
, ๐ฅ12
+
, ๐ฅ13
+
, ๐ฅ14
+
, ๐ฅ15
+
, ๐ฅ16
+
, ๐ฅ17
+
, ๐ฅ18
+
, ๐ฅ19
+
, ๐ฅ20
+
, ๐ฅ50
+
, ๐ฅ51
+
), it
will be 22 patients of 51.
We think that is a simple decision rule for any decision make in case of infection diseases like the
coronavirus disease(COVID-19).
5. CONCLUSIONS
This paper introduced the fuzzy multi-objective programming technique for developing the set of
all efficient solutions for the classification problem with minimum errors. The weighting method
is used to solve our fuzzy model after defuzzification by using the ฮฑ โ cut technique. The
experimental evaluation was carried out using 51 datasets, each one has two features. The
๐ฅ๐
+
๐(๐ฅ๐
+
)
๐ฅ1
+ 0.55
๐ฅ2
+
0.275
๐ฅ3
+
0.875
๐ฅ4
+
0.325
๐ฅ5
+ 0.175
๐ฅ6
+
0.525
๐ฅ7
+
0.425
๐ฅ8
+
1
๐ฅ9
+ 0.55
๐ฅ10
+
0.775
๐ฅ11
+
0.675
๐ฅ12
+
0.125
๐ฅ13
+ 0.25
๐ฅ14
+
0.55
๐ฅ15
+
0.2
๐ฅ16
+
0.8
๐ฅ17
+ 0.75
๐ฅ18
+
0.625
๐ฅ19
+
0.475
๐ฅ20
+
0.25
๐ฅ50
โ 0.925
๐ฅ51
โ
0.375
๐ฅ๐
โ
๐(๐ฅ๐
โ
)
๐ฅ21
โ
0.25
๐ฅ22
โ
0.175
๐ฅ23
โ
0.425
๐ฅ24
โ
0.35
๐ฅ25
โ
0.175
๐ฅ26
โ 0.175
๐ฅ27
โ 0.3
๐ฅ28
โ 0.625
๐ฅ29
โ 0.425
๐ฅ30
โ
0.8
๐ฅ๐31
โ
0.625
๐ฅ32
โ
0.925
๐ฅ33
โ
0.375
๐ฅ34
โ
0.375
๐ฅ35
โ
0.6
๐ฅ36
โ
0.7
๐ฅ37
โ
0.975
๐ฅ38
โ
0.8
๐ฅ39
โ
0.6
๐ฅ40
โ
0.725
๐ฅ41
โ
0.4
๐ฅ42
โ
0.45
๐ฅ43
โ
0.25
๐ฅ44
โ
0.625
๐ฅ45
โ
0.325
๐ฅ46
โ 0.525
๐ฅ47
โ
1
๐ฅ48
โ 0.15
๐ฅ49
โ
0.65
10. International Journal of Fuzzy Logic Systems (IJFLS) Vol.11, No.1, January 2021
22
experimental results show the effect of the parameters (ฮฑ, ๐ค1, ๐ค2) on the misclassification
between two sets. An interactive hypothesis is added to identify the best compromise hyperplane
from the generated efficient set.
Finally, a utility function is constructed to select the best compromised hyperplane from the
generated set of the efficient solutions and it is used to measure the degree of infection with
coronavirus disease (COVID-19) to help the decision maker to detect the number of patients who
must be isolated.
Our future work is to apply our model for large scale.
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