Classification in data mining is receiving immense interest in recent times. As the knowledge is based on
historical data, classifications of data are essential for discovering the knowledge. To decrease the
classification complexity, the quantitative attributes of data need splitting. But the splitting using the
classical logic is less accurate. This can be overcome by the use of fuzzy logic. This paper illustrates how to
build up the classification rules using the fuzzy logic. The fuzzy classifier is built on by using the prism
decision tree algorithm. This classifier produces more realistic results than the classical one. The
effectiveness of this method is justified over a sample dataset.
Extensive Analysis on Generation and Consensus Mechanisms of Clustering Ensem...IJECEIAES
Data analysis plays a prominent role in interpreting various phenomena. Data mining is the process to hypothesize useful knowledge from the extensive data. Based upon the classical statistical prototypes the data can be exploited beyond the storage and management of the data. Cluster analysis a primary investigation with little or no prior knowledge, consists of research and development across a wide variety of communities. Cluster ensembles are melange of individual solutions obtained from different clusterings to produce final quality clustering which is required in wider applications. The method arises in the perspective of increasing robustness, scalability and accuracy. This paper gives a brief overview of the generation methods and consensus functions included in cluster ensemble. The survey is to analyze the various techniques and cluster ensemble methods.
Cancer data partitioning with data structure and difficulty independent clust...IRJET Journal
This document discusses cancer data partitioning using clustering techniques. It begins with an introduction to clustering concepts and different clustering methods like k-means, hierarchical agglomerative clustering, and partitioning methods. It then reviews literature on clustering algorithms and ensemble methods applied to problems like speaker diarization and tumor clustering from gene expression data. The document analyzes issues with existing clustering methodology and proposes a new dynamic ensemble membership selection scheme to support data structure and complexity independent clustering for cancer data partitioning. The method combines partition around medoids clustering with an incremental semi-supervised cluster ensemble framework to improve healthcare data partitioning accuracy.
ENHANCED BREAST CANCER RECOGNITION BASED ON ROTATION FOREST FEATURE SELECTIO...cscpconf
Optimization problems are dominantly being solved using Computational Intelligence. One of
the issues that can be addressed in this context is problems related to attribute subset selection
evaluation. This paper presents a computational intelligence technique for solving the
optimization problem using a proposed model called Modified Genetic Search Algorithms
(MGSA) that avoids local bad search space with merit and scaled fitness variables, detecting
and deleting bad candidate chromosomes, thereby reducing the number of individual
chromosomes from search space and subsequent iterations in next generations. This paper aims
to show that Rotation forest ensembles are useful in the feature selection method. The base
classifier is multinomial logistic regression method integrated with Haar wavelets as projection
filter and reproducing the ranks of each features with 10 fold cross validation method. It also
discusses the main findings and concludes with promising result of the proposed model. It
explores the combination of MGSA for optimization with Naïve Bayes classification. The result
obtained using proposed model MGSA is validated mathematically using Principal Component
Analysis. The goal is to improve the accuracy and quality of diagnosis of Breast cancer disease
with robust machine learning algorithms. As compared to other works in literature survey,
experimental results achieved in this paper show better results with statistical inferenc
Analysis On Classification Techniques In Mammographic Mass Data SetIJERA Editor
Data mining, the extraction of hidden information from large databases, is to predict future trends and behaviors, allowing businesses to make proactive, knowledge-driven decisions. Data-Mining classification techniques deals with determining to which group each data instances are associated with. It can deal with a wide variety of data so that large amount of data can be involved in processing. This paper deals with analysis on various data mining classification techniques such as Decision Tree Induction, Naïve Bayes , k-Nearest Neighbour (KNN) classifiers in mammographic mass dataset.
EXTRACTING USEFUL RULES THROUGH IMPROVED DECISION TREE INDUCTION USING INFORM...ijistjournal
Classification is widely used technique in the data mining domain, where scalability and efficiency are the immediate problems in classification algorithms for large databases. We suggest improvements to the existing C4.5 decision tree algorithm. In this paper attribute oriented induction (AOI) and relevance analysis are incorporated with concept hierarchy’s knowledge and HeightBalancePriority algorithm for construction of decision tree along with Multi level mining. The assignment of priorities to attributes is done by evaluating information entropy, at different levels of abstraction for building decision tree using HeightBalancePriority algorithm. Modified DMQL queries are used to understand and explore the shortcomings of the decision trees generated by C4.5 classifier for education dataset and the results are compared with the proposed approach.
This document summarizes several major data classification techniques, including decision tree induction, Bayesian classification, rule-based classification, classification by back propagation, support vector machines, lazy learners, genetic algorithms, rough set approach, and fuzzy set approach. It provides an overview of each technique, describing their basic concepts and key algorithms. The goal is to help readers understand different data classification methodologies and which may be suitable for various domain-specific problems.
EXTRACTING USEFUL RULES THROUGH IMPROVED DECISION TREE INDUCTION USING INFORM...ijistjournal
Classification is widely used technique in the data mining domain, where scalability and efficiency are the immediate problems in classification algorithms for large databases. We suggest improvements to the existing C4.5 decision tree algorithm. In this paper attribute oriented induction (AOI) and relevance analysis are incorporated with concept hierarchy’s knowledge and HeightBalancePriority algorithm for construction of decision tree along with Multi level mining. The assignment of priorities to attributes is done by evaluating information entropy, at different levels of abstraction for building decision tree using HeightBalancePriority algorithm. Modified DMQL queries are used to understand and explore the shortcomings of the decision trees generated by C4.5 classifier for education dataset and the results are compared with the proposed approach.
This document discusses using fuzzy set theory and decision trees to predict student performance. It proposes using fuzzy sets to represent numeric student data like test scores and attendance to allow for imprecise values. A decision tree is generated on this fuzzy data set to classify students as passing or failing. The fuzzy decision tree achieves an accuracy of 81.5% compared to 76% for a non-fuzzy decision tree, indicating fuzzy sets improve predictive performance. Location, attendance, and prior academic performance were identified as important factors impacting student results.
Extensive Analysis on Generation and Consensus Mechanisms of Clustering Ensem...IJECEIAES
Data analysis plays a prominent role in interpreting various phenomena. Data mining is the process to hypothesize useful knowledge from the extensive data. Based upon the classical statistical prototypes the data can be exploited beyond the storage and management of the data. Cluster analysis a primary investigation with little or no prior knowledge, consists of research and development across a wide variety of communities. Cluster ensembles are melange of individual solutions obtained from different clusterings to produce final quality clustering which is required in wider applications. The method arises in the perspective of increasing robustness, scalability and accuracy. This paper gives a brief overview of the generation methods and consensus functions included in cluster ensemble. The survey is to analyze the various techniques and cluster ensemble methods.
Cancer data partitioning with data structure and difficulty independent clust...IRJET Journal
This document discusses cancer data partitioning using clustering techniques. It begins with an introduction to clustering concepts and different clustering methods like k-means, hierarchical agglomerative clustering, and partitioning methods. It then reviews literature on clustering algorithms and ensemble methods applied to problems like speaker diarization and tumor clustering from gene expression data. The document analyzes issues with existing clustering methodology and proposes a new dynamic ensemble membership selection scheme to support data structure and complexity independent clustering for cancer data partitioning. The method combines partition around medoids clustering with an incremental semi-supervised cluster ensemble framework to improve healthcare data partitioning accuracy.
ENHANCED BREAST CANCER RECOGNITION BASED ON ROTATION FOREST FEATURE SELECTIO...cscpconf
Optimization problems are dominantly being solved using Computational Intelligence. One of
the issues that can be addressed in this context is problems related to attribute subset selection
evaluation. This paper presents a computational intelligence technique for solving the
optimization problem using a proposed model called Modified Genetic Search Algorithms
(MGSA) that avoids local bad search space with merit and scaled fitness variables, detecting
and deleting bad candidate chromosomes, thereby reducing the number of individual
chromosomes from search space and subsequent iterations in next generations. This paper aims
to show that Rotation forest ensembles are useful in the feature selection method. The base
classifier is multinomial logistic regression method integrated with Haar wavelets as projection
filter and reproducing the ranks of each features with 10 fold cross validation method. It also
discusses the main findings and concludes with promising result of the proposed model. It
explores the combination of MGSA for optimization with Naïve Bayes classification. The result
obtained using proposed model MGSA is validated mathematically using Principal Component
Analysis. The goal is to improve the accuracy and quality of diagnosis of Breast cancer disease
with robust machine learning algorithms. As compared to other works in literature survey,
experimental results achieved in this paper show better results with statistical inferenc
Analysis On Classification Techniques In Mammographic Mass Data SetIJERA Editor
Data mining, the extraction of hidden information from large databases, is to predict future trends and behaviors, allowing businesses to make proactive, knowledge-driven decisions. Data-Mining classification techniques deals with determining to which group each data instances are associated with. It can deal with a wide variety of data so that large amount of data can be involved in processing. This paper deals with analysis on various data mining classification techniques such as Decision Tree Induction, Naïve Bayes , k-Nearest Neighbour (KNN) classifiers in mammographic mass dataset.
EXTRACTING USEFUL RULES THROUGH IMPROVED DECISION TREE INDUCTION USING INFORM...ijistjournal
Classification is widely used technique in the data mining domain, where scalability and efficiency are the immediate problems in classification algorithms for large databases. We suggest improvements to the existing C4.5 decision tree algorithm. In this paper attribute oriented induction (AOI) and relevance analysis are incorporated with concept hierarchy’s knowledge and HeightBalancePriority algorithm for construction of decision tree along with Multi level mining. The assignment of priorities to attributes is done by evaluating information entropy, at different levels of abstraction for building decision tree using HeightBalancePriority algorithm. Modified DMQL queries are used to understand and explore the shortcomings of the decision trees generated by C4.5 classifier for education dataset and the results are compared with the proposed approach.
This document summarizes several major data classification techniques, including decision tree induction, Bayesian classification, rule-based classification, classification by back propagation, support vector machines, lazy learners, genetic algorithms, rough set approach, and fuzzy set approach. It provides an overview of each technique, describing their basic concepts and key algorithms. The goal is to help readers understand different data classification methodologies and which may be suitable for various domain-specific problems.
EXTRACTING USEFUL RULES THROUGH IMPROVED DECISION TREE INDUCTION USING INFORM...ijistjournal
Classification is widely used technique in the data mining domain, where scalability and efficiency are the immediate problems in classification algorithms for large databases. We suggest improvements to the existing C4.5 decision tree algorithm. In this paper attribute oriented induction (AOI) and relevance analysis are incorporated with concept hierarchy’s knowledge and HeightBalancePriority algorithm for construction of decision tree along with Multi level mining. The assignment of priorities to attributes is done by evaluating information entropy, at different levels of abstraction for building decision tree using HeightBalancePriority algorithm. Modified DMQL queries are used to understand and explore the shortcomings of the decision trees generated by C4.5 classifier for education dataset and the results are compared with the proposed approach.
This document discusses using fuzzy set theory and decision trees to predict student performance. It proposes using fuzzy sets to represent numeric student data like test scores and attendance to allow for imprecise values. A decision tree is generated on this fuzzy data set to classify students as passing or failing. The fuzzy decision tree achieves an accuracy of 81.5% compared to 76% for a non-fuzzy decision tree, indicating fuzzy sets improve predictive performance. Location, attendance, and prior academic performance were identified as important factors impacting student results.
Multilevel techniques for the clustering problemcsandit
Data Mining is concerned with the discovery of interesting patterns and knowledge in data
repositories. Cluster Analysis which belongs to the core methods of data mining is the process
of discovering homogeneous groups called clusters. Given a data-set and some measure of
similarity between data objects, the goal in most clustering algorithms is maximizing both the
homogeneity within each cluster and the heterogeneity between different clusters. In this work,
two multilevel algorithms for the clustering problem are introduced. The multilevel
paradigm suggests looking at the clustering problem as a hierarchical optimization process
going through different levels evolving from a coarse grain to fine grain strategy. The clustering
problem is solved by first reducing the problem level by level to a coarser problem where an
initial clustering is computed. The clustering of the coarser problem is mapped back level-bylevel
to obtain a better clustering of the original problem by refining the intermediate different
clustering obtained at various levels. A benchmark using a number of data sets collected from a
variety of domains is used to compare the effectiveness of the hierarchical approach against its
single-level counterpart.
TWO PARTY HIERARICHAL CLUSTERING OVER HORIZONTALLY PARTITIONED DATA SETIJDKP
This document summarizes a research paper that proposes a two-party hierarchical clustering approach for horizontally partitioned data to enable privacy-preserving data mining. The key points are:
1) The paper presents an approach for applying hierarchical clustering across two parties that hold horizontally partitioned data, with the goal of preserving privacy.
2) Each party independently computes k-cluster centers on their own data and encrypts the distance matrices before sharing. Hierarchical clustering is then applied to merge the clusters.
3) An algorithm is provided for identifying the closest cluster for each data point based on the merged distance matrices.
4) The approach is analyzed and compared to other clustering techniques, demonstrating it has lower computational complexity
This document provides an overview of data mining techniques discussed in Chapter 3, including parametric and nonparametric models, statistical perspectives on point estimation and error measurement, Bayes' theorem, decision trees, neural networks, genetic algorithms, and similarity measures. Nonparametric techniques like neural networks, decision trees, and genetic algorithms are particularly suitable for data mining applications involving large, dynamically changing datasets.
IRJET- Optimal Number of Cluster Identification using Robust K-Means for ...IRJET Journal
This document discusses using a modified k-means algorithm to identify the optimal number of clusters in categorical sequence data. The traditional k-means algorithm requires the number of clusters to be predefined, which can impact performance. The proposed Robust K-means for Sequences algorithm aims to predict the optimal number of clusters by removing noise clusters. It evaluates cluster validation to assess clustering quality for categorical sequence data, where defining similarity is challenging. The algorithm combines a partition-based clustering method and a cluster validity index within a model selection process to determine the best number of clusters for categorical sequence sets.
A Survey on Constellation Based Attribute Selection Method for High Dimension...IJERA Editor
Attribute Selection is an important topic in Data Mining, because it is the effective way for reducing dimensionality, removing irrelevant data, removing redundant data, & increasing accuracy of the data. It is the process of identifying a subset of the most useful attributes that produces compatible results as the original entire set of attribute. Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group called a cluster are more similar in some sense or another to each other than to those in other groups (Clusters). There are various approaches & techniques for attribute subset selection namely Wrapper approach, Filter Approach, Relief Algorithm, Distributional clustering etc. But each of one having some disadvantages like unable to handle large volumes of data, computational complexity, accuracy is not guaranteed, difficult to evaluate and redundancy detection etc. To get the upper hand on some of these issues in attribute selection this paper proposes a technique that aims to design an effective clustering based attribute selection method for high dimensional data. Initially, attributes are divided into clusters by using graph-based clustering method like minimum spanning tree (MST). In the second step, the most representative attribute that is strongly related to target classes is selected from each cluster to form a subset of attributes. The purpose is to increase the level of accuracy, reduce dimensionality; shorter training time and improves generalization by reducing over fitting.
Hybrid Algorithm for Clustering Mixed Data SetsIOSR Journals
This document summarizes a hybrid algorithm for clustering mixed data sets that was proposed in reference [1]. The algorithm uses a genetic k-means approach to cluster both numeric and categorical data, overcoming limitations of other algorithms that can only handle one data type. It aims to minimize the total within-cluster variation to group similar objects. The selection operator uses proportional selection to determine the population for the next generation based on each solution's probability and fitness. The algorithm was reviewed, implemented in a prototype application, and found to improve performance compared to other related clustering algorithms like GKMODE and IGKA that also handle mixed data types.
ROLE OF CERTAINTY FACTOR IN GENERATING ROUGH-FUZZY RULEIJCSEA Journal
The generation of effective feature-based rules is essential to the development of any intelligent system. This paper presents an approach that integrates a powerful fuzzy rule generation algorithm with a rough set-assisted feature reduction method to generate diagnostic rule with a certainty factor. Certainty factor of each rule is calculated by considering both the membership value of each linguistic term introduced at time of fuzzyfication of data as well as possibility values, due to inconsistent data, generated by rough set theory at time of rule generation. In time of knowledge inferencing in an intelligent system, certainty factor of each rule will play an important role to find out the appropriate rule to be selected. Experimental results demonstrate the superiority of our approach.
ATTRIBUTE REDUCTION-BASED ENSEMBLE RULE CLASSIFIERS METHOD FOR DATASET CLASSI...csandit
Attribute reduction and classification task are an essential process in dealing with large data
sets that comprise numerous number of input attributes. There are many search methods and
classifiers that have been used to find the optimal number of attributes. The aim of this paper is
to find the optimal set of attributes and improve the classification accuracy by adopting
ensemble rule classifiers method. Research process involves 2 phases; finding the optimal set of
attributes and ensemble classifiers method for classification task. Results are in terms of
percentage of accuracy and number of selected attributes and rules generated. 6 datasets were
used for the experiment. The final output is an optimal set of attributes with ensemble rule
classifiers method. The experimental results conducted on public real dataset demonstrate that
the ensemble rule classifiers methods consistently show improve classification accuracy on the
selected dataset. Significant improvement in accuracy and optimal set of attribute selected is
achieved by adopting ensemble rule classifiers method.
Classification on multi label dataset using rule mining techniqueeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
CLUSTERING DICHOTOMOUS DATA FOR HEALTH CAREijistjournal
This document discusses clustering dichotomous health care data using the K-means algorithm after transforming the data using Wiener transformation. It begins with an introduction to dichotomous data and the challenges of clustering medical data. It then describes the K-means clustering algorithm and various distance measures used for binary data clustering. The document proposes using Wiener transformation to first transform binary data to real values before applying K-means clustering. It evaluates the results on a lens dataset using inter-cluster and intra-cluster distances, finding the transformed data yields better clusters than the original binary data according to these metrics.
Automatic Unsupervised Data Classification Using Jaya Evolutionary Algorithmaciijournal
In this paper we attempt to solve an automatic clustering problem by optimizing multiple objectives such as automatic k-determination and a set of cluster validity indices concurrently. The proposed automatic clustering technique uses the most recent optimization algorithm Jaya as an underlying optimization stratagem. This evolutionary technique always aims to attain global best solution rather than a local best solution in larger datasets. The explorations and exploitations imposed on the proposed work results to detect the number of automatic clusters, appropriate partitioning present in data sets and mere optimal values towards CVIs frontiers. Twelve datasets of different intricacy are used to endorse the performance of aimed algorithm. The experiments lay bare that the conjectural advantages of multi objective clustering optimized with evolutionary approaches decipher into realistic and scalable performance paybacks.
This document discusses classification and prediction. Classification predicts categorical class labels by classifying data based on a training set and class labels. Prediction models continuous values and predicts unknown values. Some applications are credit approval, marketing, medical diagnosis, and treatment analysis. Classification involves a learning step to describe classes and a classification step to classify new data. Prediction involves estimating accuracy by comparing test results to known labels. Issues with classification and prediction include data preparation, comparing methods, and decision tree induction algorithms.
IRJET- Ordinal based Classification Techniques: A SurveyIRJET Journal
This document summarizes and reviews various techniques for performing ordinal classification. Ordinal classification involves classifying data into categories that have an inherent ordering. The document discusses traditional approaches like regression and error-weighted classification. It also covers binary decomposition methods that split the problem into multiple binary classification problems. The majority of the document focuses on threshold modeling approaches, which learn thresholds between categories. These include cumulative link modeling, support vector machine methods, discriminant analysis, and augmented binary classification. Threshold modeling approaches generally perform better than traditional methods at maintaining the ordinal relationships between categories.
Automatic Unsupervised Data Classification Using Jaya Evolutionary Algorithmaciijournal
The document describes an automatic unsupervised data classification method using the Jaya evolutionary algorithm. It proposes using Jaya to optimize multiple cluster validity indices (CVIs) simultaneously to determine the optimal number of clusters and cluster assignments. Twelve real-world datasets from different domains are used to evaluate the method. The results show that the proposed AutoJAYA algorithm is able to accurately detect the number of clusters in each dataset and achieve good performance according to various CVIs, demonstrating its effectiveness at automatic unsupervised data classification.
Engineering Research Publication
Best International Journals, High Impact Journals,
International Journal of Engineering & Technical Research
ISSN : 2321-0869 (O) 2454-4698 (P)
www.erpublication.org
This document describes an expandable Bayesian network (EBN) approach for 3D object description from multiple images and sensor data. The key points are:
- EBNs can dynamically instantiate network structures at runtime based on the number of input images, allowing the use of a varying number of evidence features.
- EBNs introduce the use of hidden variables to handle correlation of evidence features across images, whereas previous approaches did not properly model this.
- The document presents an application of an EBN for building detection and description from aerial images using multiple views and sensor data. Experimental results showed the EBN approach provided significant performance improvements over other methods.
A comparative study of clustering and biclustering of microarray dataijcsit
There are subsets of genes that have similar behavior under subsets of conditions, so we say that they
coexpress, but behave independently under other subsets of conditions. Discovering such coexpressions can
be helpful to uncover genomic knowledge such as gene networks or gene interactions. That is why, it is of
utmost importance to make a simultaneous clustering of genes and conditions to identify clusters of genes
that are coexpressed under clusters of conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to approximate
this problem by finding suboptimal solutions. In this paper, we make a new survey on clustering and
biclustering of gene expression data, also called microarray data.
Vinayaka : A Semi-Supervised Projected Clustering Method Using Differential E...ijseajournal
- The document presents VINAYAKA, a semi-supervised projected clustering method using differential evolution.
- VINAYAKA uses a hybrid cluster validation index combining the Subspace Clustering Quality Estimate index (for internal validation) and Gini index gain (for external validation). Differential evolution optimizes this index to find optimal subspace cluster centers.
- The method is tested on the Wisconsin breast cancer dataset, and synthetic datasets are used to demonstrate that the hybrid index can identify the correct number of clusters more accurately than an internal index alone.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Assessment of Cluster Tree Analysis based on Data Linkagesjournal ijrtem
Abstract: Details linkage is a procedure which almost adjoins two or more places of data (surveyed or proprietary) from different companies to generate a value chest of information which can be used for further analysis. This allows for the real application of the details. One-to-Many data linkage affiliates an enterprise from the first data set with a number of related companies from the other data places. Before performs concentrate on accomplishing one-to-one data linkages. So formerly a two level clustering shrub known as One-Class Clustering Tree (OCCT) with designed in Jaccard Likeness evaluate was suggested in which each flyer contains team instead of only one categorized sequence. OCCT's strategy to use Jaccard's similarity co-efficient increases time complexness significantly. So we recommend to substitute jaccard's similarity coefficient with Jaro wrinket similarity evaluate to acquire the team similarity related because it requires purchase into consideration using positional indices to calculate relevance compared with Jaccard's. An assessment of our suggested idea suffices as approval of an enhanced one-to-many data linkage system.
Index Terms: Maximum-Weighted Bipartite Matching, Ant Colony Optimization, Graph Partitioning Technique
Multilevel techniques for the clustering problemcsandit
Data Mining is concerned with the discovery of interesting patterns and knowledge in data
repositories. Cluster Analysis which belongs to the core methods of data mining is the process
of discovering homogeneous groups called clusters. Given a data-set and some measure of
similarity between data objects, the goal in most clustering algorithms is maximizing both the
homogeneity within each cluster and the heterogeneity between different clusters. In this work,
two multilevel algorithms for the clustering problem are introduced. The multilevel
paradigm suggests looking at the clustering problem as a hierarchical optimization process
going through different levels evolving from a coarse grain to fine grain strategy. The clustering
problem is solved by first reducing the problem level by level to a coarser problem where an
initial clustering is computed. The clustering of the coarser problem is mapped back level-bylevel
to obtain a better clustering of the original problem by refining the intermediate different
clustering obtained at various levels. A benchmark using a number of data sets collected from a
variety of domains is used to compare the effectiveness of the hierarchical approach against its
single-level counterpart.
TWO PARTY HIERARICHAL CLUSTERING OVER HORIZONTALLY PARTITIONED DATA SETIJDKP
This document summarizes a research paper that proposes a two-party hierarchical clustering approach for horizontally partitioned data to enable privacy-preserving data mining. The key points are:
1) The paper presents an approach for applying hierarchical clustering across two parties that hold horizontally partitioned data, with the goal of preserving privacy.
2) Each party independently computes k-cluster centers on their own data and encrypts the distance matrices before sharing. Hierarchical clustering is then applied to merge the clusters.
3) An algorithm is provided for identifying the closest cluster for each data point based on the merged distance matrices.
4) The approach is analyzed and compared to other clustering techniques, demonstrating it has lower computational complexity
This document provides an overview of data mining techniques discussed in Chapter 3, including parametric and nonparametric models, statistical perspectives on point estimation and error measurement, Bayes' theorem, decision trees, neural networks, genetic algorithms, and similarity measures. Nonparametric techniques like neural networks, decision trees, and genetic algorithms are particularly suitable for data mining applications involving large, dynamically changing datasets.
IRJET- Optimal Number of Cluster Identification using Robust K-Means for ...IRJET Journal
This document discusses using a modified k-means algorithm to identify the optimal number of clusters in categorical sequence data. The traditional k-means algorithm requires the number of clusters to be predefined, which can impact performance. The proposed Robust K-means for Sequences algorithm aims to predict the optimal number of clusters by removing noise clusters. It evaluates cluster validation to assess clustering quality for categorical sequence data, where defining similarity is challenging. The algorithm combines a partition-based clustering method and a cluster validity index within a model selection process to determine the best number of clusters for categorical sequence sets.
A Survey on Constellation Based Attribute Selection Method for High Dimension...IJERA Editor
Attribute Selection is an important topic in Data Mining, because it is the effective way for reducing dimensionality, removing irrelevant data, removing redundant data, & increasing accuracy of the data. It is the process of identifying a subset of the most useful attributes that produces compatible results as the original entire set of attribute. Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group called a cluster are more similar in some sense or another to each other than to those in other groups (Clusters). There are various approaches & techniques for attribute subset selection namely Wrapper approach, Filter Approach, Relief Algorithm, Distributional clustering etc. But each of one having some disadvantages like unable to handle large volumes of data, computational complexity, accuracy is not guaranteed, difficult to evaluate and redundancy detection etc. To get the upper hand on some of these issues in attribute selection this paper proposes a technique that aims to design an effective clustering based attribute selection method for high dimensional data. Initially, attributes are divided into clusters by using graph-based clustering method like minimum spanning tree (MST). In the second step, the most representative attribute that is strongly related to target classes is selected from each cluster to form a subset of attributes. The purpose is to increase the level of accuracy, reduce dimensionality; shorter training time and improves generalization by reducing over fitting.
Hybrid Algorithm for Clustering Mixed Data SetsIOSR Journals
This document summarizes a hybrid algorithm for clustering mixed data sets that was proposed in reference [1]. The algorithm uses a genetic k-means approach to cluster both numeric and categorical data, overcoming limitations of other algorithms that can only handle one data type. It aims to minimize the total within-cluster variation to group similar objects. The selection operator uses proportional selection to determine the population for the next generation based on each solution's probability and fitness. The algorithm was reviewed, implemented in a prototype application, and found to improve performance compared to other related clustering algorithms like GKMODE and IGKA that also handle mixed data types.
ROLE OF CERTAINTY FACTOR IN GENERATING ROUGH-FUZZY RULEIJCSEA Journal
The generation of effective feature-based rules is essential to the development of any intelligent system. This paper presents an approach that integrates a powerful fuzzy rule generation algorithm with a rough set-assisted feature reduction method to generate diagnostic rule with a certainty factor. Certainty factor of each rule is calculated by considering both the membership value of each linguistic term introduced at time of fuzzyfication of data as well as possibility values, due to inconsistent data, generated by rough set theory at time of rule generation. In time of knowledge inferencing in an intelligent system, certainty factor of each rule will play an important role to find out the appropriate rule to be selected. Experimental results demonstrate the superiority of our approach.
ATTRIBUTE REDUCTION-BASED ENSEMBLE RULE CLASSIFIERS METHOD FOR DATASET CLASSI...csandit
Attribute reduction and classification task are an essential process in dealing with large data
sets that comprise numerous number of input attributes. There are many search methods and
classifiers that have been used to find the optimal number of attributes. The aim of this paper is
to find the optimal set of attributes and improve the classification accuracy by adopting
ensemble rule classifiers method. Research process involves 2 phases; finding the optimal set of
attributes and ensemble classifiers method for classification task. Results are in terms of
percentage of accuracy and number of selected attributes and rules generated. 6 datasets were
used for the experiment. The final output is an optimal set of attributes with ensemble rule
classifiers method. The experimental results conducted on public real dataset demonstrate that
the ensemble rule classifiers methods consistently show improve classification accuracy on the
selected dataset. Significant improvement in accuracy and optimal set of attribute selected is
achieved by adopting ensemble rule classifiers method.
Classification on multi label dataset using rule mining techniqueeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
CLUSTERING DICHOTOMOUS DATA FOR HEALTH CAREijistjournal
This document discusses clustering dichotomous health care data using the K-means algorithm after transforming the data using Wiener transformation. It begins with an introduction to dichotomous data and the challenges of clustering medical data. It then describes the K-means clustering algorithm and various distance measures used for binary data clustering. The document proposes using Wiener transformation to first transform binary data to real values before applying K-means clustering. It evaluates the results on a lens dataset using inter-cluster and intra-cluster distances, finding the transformed data yields better clusters than the original binary data according to these metrics.
Automatic Unsupervised Data Classification Using Jaya Evolutionary Algorithmaciijournal
In this paper we attempt to solve an automatic clustering problem by optimizing multiple objectives such as automatic k-determination and a set of cluster validity indices concurrently. The proposed automatic clustering technique uses the most recent optimization algorithm Jaya as an underlying optimization stratagem. This evolutionary technique always aims to attain global best solution rather than a local best solution in larger datasets. The explorations and exploitations imposed on the proposed work results to detect the number of automatic clusters, appropriate partitioning present in data sets and mere optimal values towards CVIs frontiers. Twelve datasets of different intricacy are used to endorse the performance of aimed algorithm. The experiments lay bare that the conjectural advantages of multi objective clustering optimized with evolutionary approaches decipher into realistic and scalable performance paybacks.
This document discusses classification and prediction. Classification predicts categorical class labels by classifying data based on a training set and class labels. Prediction models continuous values and predicts unknown values. Some applications are credit approval, marketing, medical diagnosis, and treatment analysis. Classification involves a learning step to describe classes and a classification step to classify new data. Prediction involves estimating accuracy by comparing test results to known labels. Issues with classification and prediction include data preparation, comparing methods, and decision tree induction algorithms.
IRJET- Ordinal based Classification Techniques: A SurveyIRJET Journal
This document summarizes and reviews various techniques for performing ordinal classification. Ordinal classification involves classifying data into categories that have an inherent ordering. The document discusses traditional approaches like regression and error-weighted classification. It also covers binary decomposition methods that split the problem into multiple binary classification problems. The majority of the document focuses on threshold modeling approaches, which learn thresholds between categories. These include cumulative link modeling, support vector machine methods, discriminant analysis, and augmented binary classification. Threshold modeling approaches generally perform better than traditional methods at maintaining the ordinal relationships between categories.
Automatic Unsupervised Data Classification Using Jaya Evolutionary Algorithmaciijournal
The document describes an automatic unsupervised data classification method using the Jaya evolutionary algorithm. It proposes using Jaya to optimize multiple cluster validity indices (CVIs) simultaneously to determine the optimal number of clusters and cluster assignments. Twelve real-world datasets from different domains are used to evaluate the method. The results show that the proposed AutoJAYA algorithm is able to accurately detect the number of clusters in each dataset and achieve good performance according to various CVIs, demonstrating its effectiveness at automatic unsupervised data classification.
Engineering Research Publication
Best International Journals, High Impact Journals,
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ISSN : 2321-0869 (O) 2454-4698 (P)
www.erpublication.org
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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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Index Terms: Maximum-Weighted Bipartite Matching, Ant Colony Optimization, Graph Partitioning Technique
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data mining applications for data analysis by finding data patterns. There is a number of clustering techniques and algorithms are
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Incremental learning from unbalanced data with concept class, concept drift a...IJDKP
Recently, stream data mining applications has drawn vital attention from several research communities.
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learning area has been developing learning algorithms that have certain assumptions on underlying
distribution of data such as data should have predetermined distribution. Such constraints on the problem
domain lead the way for development of smart learning algorithms performance is theoretically verifiable.
Real-word situations are different than this restricted model. Applications usually suffers from problems
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usual in real world applications, resulting in the “concept drift” which is related with data stream
examples. These issues have been separately addressed by the researchers, also, it is observed that joint
problem of class imbalance and concept drift has got relatively little research. If the final objective of
clever machine learning techniques is to be able to address a broad spectrum of real world applications,
then the necessity for a universal framework for learning from and tailoring (adapting) to, environment
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Classification By Clustering Based On Adjusted ClusterIOSR Journals
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This document compares hierarchical and non-hierarchical clustering algorithms. It summarizes four clustering algorithms: K-Means, K-Medoids, Farthest First Clustering (hierarchical algorithms), and DBSCAN (non-hierarchical algorithm). It describes the methodology of each algorithm and provides pseudocode. It also describes the datasets used to evaluate the performance of the algorithms and the evaluation metrics. The goal is to compare the performance of the clustering methods on different datasets.
Enhanced Clustering Algorithm for Processing Online DataIOSR Journals
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Principle Component Analysis Based on Optimal Centroid Selection Model for Su...ijtsrd
Clustering a large sparse and large scale data is an open research in the data mining. To discover the significant information through clustering algorithm stands inadequate as most of the data finds to be non actionable. Existing clustering technique is not feasible to time varying data in high dimensional space. Hence Subspace clustering will be answerable to problems in the clustering through incorporation of domain knowledge and parameter sensitive prediction. Sensitiveness of the data is also predicted through thresholding mechanism. The problems of usability and usefulness in 3D subspace clustering are very important issue in subspace clustering. . The Solutions is highly helpful benefit for police departments and law enforcement organisations to better understand stock issues and provide insights that will enable them to track activities, predict the likelihood. Also determining the correct dimension is inconsistent and challenging issue in subspace clustering .In this thesis, we propose Centroid based Subspace Forecasting Framework by constraints is proposed, i.e. must link and must not link with domain knowledge. Unsupervised Subspace clustering algorithm with inbuilt process like inconsistent constraints correlating to dimensions has been resolved through singular value decomposition. Principle component analysis is been used in which condition has been explored to estimate the strength of actionable to be particular attributes and utilizing the domain knowledge to refinement and validating the optimal centroids dynamically. An experimental result proves that proposed framework outperforms other competition subspace clustering technique in terms of efficiency, Fmeasure, parameter insensitiveness and accuracy. G. Raj Kamal | A. Deepika | D. Pavithra | J. Mohammed Nadeem | V. Prasath Kumar "Principle Component Analysis Based on Optimal Centroid Selection Model for SubSpace Clustering Model" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-4 , June 2020, URL: https://www.ijtsrd.com/papers/ijtsrd31374.pdf Paper Url :https://www.ijtsrd.com/computer-science/data-miining/31374/principle-component-analysis-based-on-optimal-centroid-selection-model-for-subspace-clustering-model/g-raj-kamal
Clustering and Classification Algorithms Ankita DubeyAnkita Dubey
Clustering is a process of partitioning a set of data (or objects) into a set of meaningful sub-classes, called clusters. Help users understand the natural grouping or structure in a data set. Used either as a stand-alone tool to get insight into data distribution or as a preprocessing step for other algorithms.
A survey on Efficient Enhanced K-Means Clustering Algorithmijsrd.com
Data mining is the process of using technology to identify patterns and prospects from large amount of information. In Data Mining, Clustering is an important research topic and wide range of unverified classification application. Clustering is technique which divides a data into meaningful groups. K-means clustering is a method of cluster analysis which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean. In this paper, we present the comparison of different K-means clustering algorithms.
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
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document provides an overview of different techniques for clustering categorical data. It discusses various clustering algorithms that have been used for categorical data, including K-modes, ROCK, COBWEB, and EM algorithms. It also reviews more recently developed algorithms for categorical data clustering, such as algorithms based on particle swarm optimization, rough set theory, and feature weighting schemes. The document concludes that clustering categorical data remains an important area of research, with opportunities to develop techniques that initialize cluster centers better.
A SURVEY ON OPTIMIZATION APPROACHES TO TEXT DOCUMENT CLUSTERINGijcsa
This document provides a survey of optimization approaches that have been applied to text document clustering. It discusses several clustering algorithms and categorizes them as partitioning methods, hierarchical methods, density-based methods, grid-based methods, model-based methods, frequent pattern-based clustering, and constraint-based clustering. It then describes several soft computing techniques that have been used as optimization approaches for text document clustering, including genetic algorithms, bees algorithms, particle swarm optimization, and ant colony optimization. These optimization techniques perform a global search to improve the quality and efficiency of document clustering algorithms.
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Building a Classifier Employing Prism Algorithm with Fuzzy Logic
1. International Journal of Data Mining & Knowledge Management Process (IJDKP) Vol.7, No.2, March 2017
DOI: 10.5121/ijdkp.2017.7204 51
BUILDING A CLASSIFIER EMPLOYING PRISM
ALGORITHM WITH FUZZY LOGIC
Ishrat Nahar Farhana, A.H.M. Sajedul Hoque , Rashed Mustafa and Mohammad
Sanaullah Chowdhury
Department of Computer Science and Engineering, University of Chittagong, Chittagong,
Bangladesh
ABSTRACT
Classification in data mining is receiving immense interest in recent times. As the knowledge is based on
historical data, classifications of data are essential for discovering the knowledge. To decrease the
classification complexity, the quantitative attributes of data need splitting. But the splitting using the
classical logic is less accurate. This can be overcome by the use of fuzzy logic. This paper illustrates how to
build up the classification rules using the fuzzy logic. The fuzzy classifier is built on by using the prism
decision tree algorithm. This classifier produces more realistic results than the classical one. The
effectiveness of this method is justified over a sample dataset.
KEYWORDS
Data Mining, Classification, Prism algorithm, Fuzzy logic , Membership Degree
1. INTRODUCTION
Data are big power for an organization to make better decisions. All knowledge of any
organization is hidden in its historical data. Data mining is the process of analyzing data from
different perspectives and summarizing it into useful information. We have a lot of raw data
around us which has no meaning or use until they are given into a form that is useful and familiar
to human. This helpful form is knowledge which can be derived from data and information. Thus
data mining is are necessary to discover that latent knowledge. Data mining has different
tasks.The primary data mining tasks are : Classification, Clustering, Regression, Summarization,
Dependency Modeling, Change and Deviation Detection [1]. Among those tasks, classification
assigns items in a collection to target classes and accurately predicts the target classes for each
case in the data [2] . Generally classification task generates a set of rules from training data set for
future prediction and decision tree is a widely used technique for that purpose. There are many
specific decision-tree algorithms, Prism algorithm is one of them. Prism algorithm is a rule based
algorithm that induces modular rules using ‘separate and conquer’ approach [3]. Training data set
may have both or either categorical or numerical attribute. For categorical attributes classification
model can be built easily. But if the data set has any numerical attribute, it should be converted
into categorical attribute by splitting the numeric range through classical logic or fuzzy logic.
Fuzzy logic refers to better performance due to the overestimation and under estimation problem
2. International Journal of Data Mining & Knowledge Management Process (IJDKP) Vol.7, No.2, March 2017
52
of classical logic which has been shown in this paper. Moreover, classical classifier assigns one
item in one and only one class, where fuzzy classifier supports multiple existence of one item
among different classes with some membership values. This paper describes the way of building
fuzzy classifier employing fuzzy logic on prism decision tree approach.
The rest of the paper is organized as follows. Section 2 provides a summary of related works.
Classification using prism algorithm is discussed in section 3. Section 4 illustrates classical Prism
algorithm. Generating rules using Fuzzy Prism classifier is presented in section 5. Section 6
illustrates the experimental result. Finally, section 7 concludes the paper.
2. RELATED WORK
The main objective of this research is to propose a new way of building classifiers using fuzzy
logic. We apply prism algorithm to classify training data set in fuzzy logic system. We focus on
building classifiers or rules using fuzzy logic which gives more accurate result than classical logic
system.
Some author proposed learning algorithm generates fuzzy rules from “soft” instances, which
differ from conventional instances in that they have class membership values [4].
On the other hand, some author proposed fuzzy decision tree induction method, which is based on
the reduction of classification ambiguity with fuzzy evidence [5]. Cognitive uncertainties
involved in classification problems are explicitly represented, measured, and incorporated into the
knowledge induction process according to them.
Methods of fuzzy k-means is used to overcome the problem of class overlap but their usefulness
maybe reduced when data sets are large and when the data include artefacts introduced by the
derivation of landform attributes from gridded digital elevation models. ‘High-resolution
landform classification using fuzzy k-means’ presents ways to overcome these limitations using
spatial sampling methods, statistical modelling of the derived stream topology, and fuzzy k-
means using the Distance metric [6].
Fuzzy decision trees represent classification knowledge more naturally to the way of human
thinking and are more robust in tolerating imprecise, conflict, and missing information.
3. CLASSIFICATION: A TASK OF DATA MINING
Data mining using classification goes through supervised learning approach where labelled
training data are used. The goal of classification is to accurately predict the target class for each
case in the data. Classification consists of two steps: building the classifier and using classifier
for classification [7]. Building the classifier phase trains the machine according to the given
classes in training data set. Then the second phase which is the testing phase tests the input data
from testing data set and put them into a class using classifier formed in first phase.
Different classification algorithms use different techniques for finding relationships. These
relationships are summarized in a model, which can then be applied to a different data set in
which the class assignments are unknown. Classification models are tested by comparing the
predicted values to known target values in a set of test data. Different techniques of data mining
are Decision Tree, Naive Bayes method, Support Vector Machine, Neural network, Kernel
3. International Journal of Data Mining & Knowledge Management Process (IJDKP) Vol.7, No.2, March 2017
53
Estimation. Different algorithms are used to produce modular classification rules to construct
regular decision tree. A decision tree is a flowchart-like structure in which each internal node
represents a "test" on an attribute, each branch represents the outcome of the test and each leaf
node represents a class label where decision is taken after computing all attributes. The paths
from root to leaf represent classification rules. Prism algorithms generate modular classification
rules that cannot necessarily be represented in the form of a decision tree and provide higher
classification accuracy [3].
Classification can be classified into two categories: Classical Classification and Fuzzy
Classification. Training data set may have vagueness which makes confusion to classify. That is it
seems an item may belong to different classes with some percentage. In that scenario, fuzzy
classification is used where an item can be classified into more than one class with some
membership degree.
4. CLASSICAL PRISM ALGORITHM
There are two general approaches to the induction of classification rules, the ‘divide and conquer’
approach, also known as TDIDT and the ‘separate and conquer’ approach. ‘Divide and conquer’
induces classification rules in the intermediate representation of a decision tree. ‘Separate and
conquer’ induces a set of IF..THEN rules. However the most notable development using the
‘separate and conquer’ approach is the Prism family of algorithms [8].
The prism algorithm was introduced by Cendrowska in 1987. The aim is to induce modular
classification rules directly from the training set. The algorithm assumes that all the attributes are
categorical. When there are continuous attributes they can first be converted to categorical one.
Alternatively the algorithm can be extended to deal with continuous attributes.Prism uses the
‘take the first rule fires’ conflict resolution strategy when the resulting rules are applied to the
unseen data, so it is important that as far as possible the most important rules are generated first.
The algorithm generates the rules concluding each of the possible classes in turn. Each rule is
generated term by term with each term of the form ‘attribute = value ’. The attribute/value pair
added at each step is chosen to maximize the probability of the target ‘outcome class ’ [9]. The
basic Prism algorithm is shown in Algorithm 1 [9].
Algorithm 1 (Classical Prism Algorithm)
Input: A training dataset with n classes Ci , i = 1,2,3.......n
Output: Generated rules for all classes
Method: The rules are generated in the following steps:
1. For each class Ci start with the complete training set each time
2. Compute the probability of each attribute/value pair for the class, Ci
3. Select the pair with the largest probability and create a subset of the training set
comprising all the instances with the selected attribute/value combination for each class, Ci
4. Repeat steps 2 and 3 for this subset until a subset is reached that contain only instances of
Ci.
5. The rule is induced by the conjunction of all the attribute/value pairs selected.
6. Remove all instances covered by this rule from the training set.
7. Repeat step 2 through 6 until all instances of Ci have been removed
8. Go to step 1 until all classes are examined.
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5. BUILDING CLASSIFIER USING FUZZY PRISM ALGORITHM
Researchers training data set may consist of categorical and numeric attributes. Building
classification model on numeric attribute is more complex than on categorical attribute. The
domain of numeric attribute is huge which increases the branch nodes of decision tree and
consequently increases the time complexity in testing phase. For example if the cardinality of any
numeric attribute is n, the space complexity and the time complexity of that attribute is O (n).
This problem refers to construct bins on the domain of that attribute. If the number of bins of any
numerical attribute is 3, then the complexity would be O (n/3). Constructing bins impose another
problem named vagueness. Some values may behave to be associated to more than one bin with
different membership degree. This problem can be solved by using fuzzy logic during the
construction of bins which ultimately implies fuzzy classifier. This section describes the process
of constructing fuzzy classifier step by step applying on Table 1.
Table 1. The Training Dataset
P_
ID
Age SpecRx Astigmatism
(angle in
degree)
Tear
Production
Rate(%)
Class
1 Young Myope 85 41 no contact lenses
2 Young Myope 80 78 soft contact lenses
3 Young Myope 95 45 no contact lenses
4 Young Myope 100 71 hard contact lenses
5 Young Hypermetrope 130 60 no contact lenses
6 Young Hypermetrope 120 61 hard contact lenses
7 Pre-presbyopic Myope 60 56 no contact lenses
8 Pre-presbyopic Myope 51 64 soft contact lenses
9 Pre-presbyopic Hypermetrope 75 50 no contact lenses
10 Pre-presbyopic Hypermetrope 90 73 soft contact lenses
11 Pre-presbyopic Hypermetrope 115 44 no contact lenses
12 Pre-presbyopic Hypermetrope 125 66 no contact lenses
13 Presbyopic Myope 105 53 no contact lenses
14 Presbyopic Myope 122 80 hard contact lenses
15 Presbyopic Hypermetrope 88 57 no contact lenses
16 Presbyopic Hypermetrope 110 47 no contact lenses
17 Presbyopic Hypermetrope 100 75 no contact lenses
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5.1 Fuzzy Prism Algorithm
Fuzzy logic is the multi-valued logic in which truth values of variables may have any real number
between 0 and 1, where for classical logic it would be either 0 or 1 [10]. For example, Age =
{(young,1), (young, .5), (middle aged, .5), (middle age,1), (middle aged, .1), (old, .4), (old, .7),
(old,1)}, where every Cartesian product consists of linguistic variables and membership degree.
The cardinality of the fuzzy set is computed by summing all membership values. So the
cardinality of Age is (1+.5+.5+1+.1+.4+.7+1) or 5.2. Similarly |young|, |middle aged| and |old| are
1.5, 1.6 and 2.1 respectively. The probability in Fuzzy Prism algorithm is calculated using this
cardinality shown in equation (1).
)1()(
AoftyCardinaaliTotal
LoftyCardinaaliTotal
LP AL =∈
Here L is a fuzzy linguistic term and A is the set of all linguistic terms. For instance, the
probability of young using eq. 1 will be
29.0
2.5
5.1
)( ==∈ youngP Ageyoung
The modified prism algorithm using fuzzy logic is shown in Algorithm 2.
Algorithm 2 (Fuzzy Prism Algorithm)
Input: A training dataset with n classes , Ci ,i = 1,2,3.......n
Output: Fuzzy Classifier
Method: The rules are generated in the following steps:
1. Map the given training data set into the fuzzy training set by employing fuzzy login on
numeric attribute.
2. For each class Ci start with the complete training set
each time.
3. Compute the probability of each attribute/value pair using equation 1 for the class, Ci
4. Select the pair with the largest probability and create a subset of the training set
comprising all the instances with the selected attribute/value combination for each class, Ci
5. Repeat steps 3 and 4 for this subset until a subset contains only instances of Ci or covers
all the attributes.
6. The rule is induced by the conjunction of all the attribute/value pairs selected.
7. Remove all instances covered by this rule from the training set.
8. Repeat step 3 through 7 until all instances of Ci have been removed
9. Go to step 2 until all classes are examined.
5.2 Constructing Bins
Due to the complexity of constructing decision tree on quantitative attributes: Astigmatism and
Tear Production Rate, these attributes must be split using either classical logic or fuzzy logic. The
constructed bins for Astigmatism is {Yes, No} and Tear Production Rate are is {Reduced,
Normal}. The range for Astigmatism is from 51 to 130 and for Tear Production Rate is from 41
to 80. If the intervals for Yes and No bins are from 51 to 90 and from 91 to 130, according to the
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classical logic each value under same interval has the same membership value that means either 0
or 1. For example, the membership degrees of 52 under Yes and No is 1 and 0 respectively.
Again for 92 it is vice versa. Here though the difference between 52 and 91 is 39, 52 and 91 both
belong to Yes. On the other hand, in spite of being 92 very closer to 91, it is associated to other
interval No. These are known as overestimation and underestimation problem in classical logic.
In order to remove these problems, fuzzy logic is applied. It needs to construct bins. This paper
addresses S-shaped membership function for No and Reduced and Z-shaped membership
function for Yes and Normal, which are shown in Figure 1.
Figure 1. S-shaped and Z-shaped membership function for No/Reduced and Yes/Normal
The mathematical equations for S and Z-shaped membership functions are also shown in (2) and
(3) respectively [11].
)2(cos
2
1
2
1
)( Π
−
−
+=
lbhb
xhb
xf S
)3(cos
2
1
2
1
)( Π
−
−
+=
lbhb
lbx
xf z
The classes are considered as:
Hard contact lens- Class 1(C1),
Soft contact lens- Class 2 (C2)
No contact lens- Class 3(C3).
5.3 Constructing Mapping Table
Using equation (2) and equation (3) on astigmatism and tear production the mapping Table 2 has
been constructed. Though astigmatism and tear production rate both have 2 intervals each, the
mapping table get 4 pairs for each data or each patient. Thus the total dataset of Table 1 which
holds 17 patient’s data is converted to the mapping table which holds 68 records, 4 instances for
each patient. Here the mapping table with 4 mapped records is shown partially in Table 2. The
Yes/NormalNo/Reduced
Min Max
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membership degree of a class is computed by taking the minimum membership value from all
fields of that record. In this way, the membership degrees for C3 in mapping table are 0.608,
0.392 and 0.
Table 2. The Partial Mapping Table
5.4 Generating Classification Rules
The steps from 2 to 9 of Algorithm 2 are now applied on Table 2 for each class. Here the
demonstration of constructing Rule 1 for class 1 has been shown. At first the probabilities of all
values of attributes are calculated using equation (1) is shown in Table 3.
Table 3. Probability of 68 instances
Attribute/Value Pair Total
Membership
Value for C1
Total Membership Value
of all 68 instances
Probability
Age =Young 8 24 0.33
Age = Pre-presbyopic 0 24 0
Age = presbyopic 4 20 0.2
SpecRx= Myope 8 32 0.25
SpecRx=
Hypermetrope
4 36 0.11
Astig=No 0.76 13.416 0.06
Astig=Yes 5.24 20.584 0.255
Tear= Reduced 1.212 17.544 0.07
Tear=Normal 4.788 16.456 0.291
Since the highest probability is 0.33 for the attribute value pair (Age =Young), it will be the first
term for Rule 1 is:
Rule 1 : (Age =Young) ^ ................... => C1
Subset S1 is created by picking those records whose has (Age =Young) pair over class C1 and
the constructed subset S1 = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24 }. All the probability for S1 is shown in Table 4.
P_ID R_ID Age SpecRx Astigmatism Tear Production
Rate
Class
(Members
hip value)
No Yes Reduced Normal
1 1 Young Myope 0.608 1 C3 (0.608)
2 Young Myope 0.392 1 C3 (0.392)
3 Young Myope 0.608 0 C3 (0)
4 Young Myope 0.392 0 C3 (0)
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Table 4 . Probability of 24 instances (S1)
Attribute/Value Pair Total
Membership
Value for C1
Total Membership
Value of all 68
instances
Probability
SpecRx= myope 4 16 0.125
SpecRx= Hypermetrope 4 8 0.5
Astig=No 0.71 4.154 0.17
Astig=Yes 3.29 7.846 0.42
Tear= Reduced 1.212 6.212 0.19
Tear = Normal 2.788 5.788 0.48
Here the highest probability is 0.5 for the attribute value pair ( SpecRx = Hypermetrope ) and this
is the 2nd
term for Rule 1 :
Rule 1 : ( Age =Young ) ^ ( SpecRx= Hypermetrope ) ^........ => C1
Again subset S2 is created by selecting those records which have the pair (Age =Young) and
(SpecRx= Hypermetrope) under class C1 and S2 ={17,18,19,20,21,22,23,24}. Like Table 4,
Table 5 has been formed on subset S2.
Table 5. Probability of 8 instances (S2)
Attribute/Value Pair Total Membership
Value for C1
Total Membership Value
of all 68 instances
Probability
Astig=No 0.039 0.039 1
Astig=Yes 1.922 3.922 0.49
Tear = Reduced 0.96 2 0.48
Tear = Normal 1.04 2 0.52
Similarly since the attribute value pair (Astig=No) has the highest probability 1 and is the 3rd
term of Rule 1 is :
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Rule 1:(Age =Young )^ (SpecRx= Hypermetrope) ^ (Astig=No).........=>C1
The constructed new subset S3 with (Age =Young), ( SpecRx = Hypermetrope ) and (Astig=No)
will be {17,19,21,23}. The next constructed probability over subset S3 is shown in Table 6.
Table 6. Probability of 4 instances (S3)
Attribute/Value
Pair
Total Membership Value
for C1
Total Membership
Value of all 68
instances
Probability
Tear = Reduced 0.48 1 0.48
Tear = Normal 0.52 1 0.52
From the Table 6, it is shown that the next attribute/value pair will be (Tear=Normal) which
probability is 0.52 is the 4th
term of Rule 1. The final generated Rule 1 is :
Rule 1: (Age =Young)^(SpecRx=Hypermetrope)^(Astig=No) ^(Tear=Normal) => C1
Then all records with pairs (Age =Young), (SpecRx= Hypermetrope), (Astig=No) and
(Tear=Normal) are deleted to generate rule 2.
In this manner, all the rules for class 1 (C1) is generated until all the instances labelled by class 1
(C1) are deleted from the mapping table. Similarly rules for class 2 (C2) and class 3 (C3) are
generated.
6. EXPERIMENTAL RESULT
According to the procedure described so far, the fuzzy classifier that has been found is shown in
Figure 2.
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Figure 2. Fuzzy Classifier
Here total 24 rules are generated for the training dataset of table 1 using fuzzy prism algorithm.
Some rule contains more than 1 class with a membership degree, which is not possible in
classical classifier. This is the beauty of fuzzy classifier. Here, if same rule has the different
membership degree in same class, the membership degree is aggregated by taking average values.
(Age =Young)^(SpecRx = Hypermetrope)^(Tear=Reduced)^(Astig=No) => C1 (0.039) , C3 (0)
(Age =Young)^(SpecRx = Hypermetrope)^(Tear=Reduced)^(Astig=Yes) => C1 (0.480) , C3 (0.520)
(Age =Young)^(SpecRx = Hypermetrope)^(Tear=Normal)^(Astig=No) => C1 (0.039) , C3 (0)
(Age =Young)^(SpecRx = Hypermetrope)^(Tear=Normal)^(Astig=Yes) => C1 (0.520) , C3 (0.480)
(Age =Young)^(SpecRx = Myope)^(Tear=Reduced)^(Astig=No) => C1 (0.126) , C2 (0.006) , C3 (0.510)
(Age =Young)^(SpecRx = Myope)^(Tear=Reduced)^(Astig=Yes) => C1 (0.126), C2 (0.006), C3 (0.491)
(Age =Young)^(SpecRx =Myope)^(Tear=Normal)^(Astig=Yes) => C1 (0.316), C2 (0.703), C3 (0.013)
(Age =Young)^(SpecRx = Myope)^(Tear=Normal)^(Astig=No) => C1 (0.684), C2 (0.297), C3 (0.013)
(Age = Presbyopic)^(SpecRx= Myope)^(Tear=Reduced)^(Astig=No) => C1 (0), C3 (0.227)
(Age = Presbyopic)^(SpecRx=Myope)^(Tear=Reduced)^(Astig=Yes) => C1 (0), C3(0.773)
(Age = Presbyopic)^(SpecRx=Myope)^(Tear=Normal)^(Astig=Yes) => C1 (0.025) , C3 (0.216)
(Age = Presbyopic)^(SpecRx= Myope)^(Tear=Normal)^(Astig=No) => C1 (0.025) , C3 (0.216)
(Age = Pre-presbyopic)^(SpecRx= Hypermetrope)^(Tear=Reduced)^(Astig=No) => C2 (0.077), C3 (0.295)
(Age = Pre-presbyopic)^(SpecRx= Hypermetrope)^(Tear=Reduced)^(Astig=Yes) => C2 (0.077) , C3 (0.470)
(Age = Pre-presbyopic)^(SpecRx= Hypermetrope)^(Tear=Normal)^(Astig=No) => C2(0.510) , C3 (0.050)
(Age = Pre-presbyopic)^(SpecRx= Hypermetrope)^(Tear=Normal)^(Astig=Yes)=> C2 (0.490) , C3 (0.285)
(Age = Pre-presbyopic)^(SpecRx= Myope)^(Tear=Reduced)^(Astig=No) => C2 (0.361) , C3 (0.677)
(Age = Pre-presbyopic)^(SpecRx=Myope)^(Tear=Reduced)^(Astig=Yes) => C2 (0) , C3 (0.032)
(Age = Pre-presbyopic)^(SpecRx=Myope)^(Tear=Normal)^(Astig=Yes) => C2 (0.639) , C3 (0.323)
(Age = Pre-presbyopic)^(SpecRx= Myope)^(Tear=Normal)^(Astig=No) => C2 (0) , C3 (0.032)
(Age = Presbyopic)^(SpecRx= Hypermetrope)^(Tear=Reduced)^(Astig=No) => C3 (0.247)
(Age = Presbyopic)^(SpecRx= Hypermetrope)^(Tear=Reduced)^(Astig=Yes) => C3 (0.447)
(Age = Presbyopic)^(SpecRx= Hypermetrope)^(Tear=Normal)^(Astig=Yes) => C3 (0.245)
(Age = Presbyopic)^(SpecRx= Hypermetrope)^(Tear=Normal)^(Astig=No) => C3 (0.367)
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7. CONCLUSION
In classical prism classifier, every rule belongs to one class only that means a rule either belongs
C1 or C2 or C3. So the classical result is not fully accurate. Because in real world, a single rule
cannot contain 100% characteristics of the features of a class. So it is not realistic. Because of
overestimation and underestimation problem testing data or patient (according to this paper)
contains some features of other classes but gives only one class as output, though it belongs more
than one class.
In this paper, Fuzzy classifier has been built using Prism algorithm successfully. It shows that a
single rule can contain more than one class with individual membership degree. So it gives more
accurate result than classical classification. It gives more realistic result than classical
classification by overcoming overestimation and underestimation problems of classical
classification. This fuzzy classifier has big application in industry. For example, bank authority
wants to give some incentive to the customers by classifying them into very committed,
committed and non committed customer. Some customer’s behavior is very confusing. Authority
cannot classify them in one class. It seems to the authority that those customers belong to
multiple classes with different percentage. In this circumstance, fuzzy classification is perfect.
The total calculation discussed in this paper has some difficulties. Fuzzy Prism classifier needs
huge calculation which increases time and space complexity. One can extend this work on Big
Data by inventing parallel algorithm on distributed computing platform such as hadoop or spark.
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