Construct Concept Structure for Linear Algebra Based on Cognition Diagnosis and Clustering with Mahalanobis Distances

2011 ◽  
Vol 211-212 ◽  
pp. 756-760
Author(s):  
Chin Chun Chen ◽  
Yuan Horng Lin ◽  
Jeng Ming Yih ◽  
Shu Yi Juan
Keyword(s):  
Linear Algebra ◽  
Mahalanobis Distance ◽  
Euclidean Distance ◽  
Clustering Algorithms ◽  
Knowledge Structure ◽  
Interpretive Structural Modeling ◽  
Mahalanobis Distances ◽  
Fuzzy C Means ◽  
Euclidean Distance Function ◽  
Fuzzy C Means Algorithm

Euclidean distance function based fuzzy clustering algorithms can only be used to detect spherical structural clusters. The purpose of this study is improved Fuzzy C-Means algorithm based on Mahalanobis distance to identify concept structure for Linear Algebra. In addition, Concept structure analysis (CSA) could provide individualized knowledge structure. CSA algorithm is the major methodology and it is based on fuzzy logic model of perception (FLMP) and interpretive structural modeling (ISM). CSA could display individualized knowledge structure and clearly represent hierarchies and linkage among concepts for each examinee. Each cluster of data can easily describe features of knowledge structures. The results show that there are five clusters and each cluster has its own cognitive characteristics. In this study, the author provide the empirical data for concepts of linear algebra from university students. To sum up, the methodology can improve knowledge management in classroom more feasible. Finally, the result shows that Algorithm based on Mahalanobis distance has better performance than Fuzzy C-Means algorithm.

Construct Knowledge Structure of Linear Algebra

2011 ◽  
Vol 211-212 ◽  
pp. 793-797
Author(s):  
Chin Chun Chen ◽  
Yuan Horng Lin ◽  
Jeng Ming Yih ◽  
Sue Fen Huang
Keyword(s):  
Knowledge Management ◽  
Linear Algebra ◽  
Fuzzy Clustering ◽  
Mahalanobis Distance ◽  
Clustering Algorithms ◽  
Knowledge Structure ◽  
Interpretive Structural Modeling ◽  
Cognitive Characteristics ◽  
Fuzzy C Means ◽  
Fuzzy C Means Algorithm

Apply interpretive structural modeling to construct knowledge structure of linear algebra. New fuzzy clustering algorithms improved fuzzy c-means algorithm based on Mahalanobis distance has better performance than fuzzy c-means algorithm. Each cluster of data can easily describe features of knowledge structures individually. The results show that there are six clusters and each cluster has its own cognitive characteristics. The methodology can improve knowledge management in classroom more feasible.

Identifying the Mastery Concepts in Linear Algebra by Using FCM-CM Algorithm

2010 ◽  
Vol 44-47 ◽  
pp. 3897-3901
Author(s):  
Hsiang Chuan Liu ◽  
Yen Kuei Yu ◽  
Jeng Ming Yih ◽  
Chin Chun Chen
Keyword(s):  
Objective Function ◽  
Linear Algebra ◽  
Fuzzy Clustering ◽  
Distance Function ◽  
Mahalanobis Distance ◽  
Euclidean Distance ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Euclidean Distance Function ◽  
Fuzzy C Means Algorithm

Euclidean distance function based fuzzy clustering algorithms can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters by employing Mahalanobis distance in objective function, however, both of them need to add some constrains for Mahalanobis distance. In this paper, the authors’ improved Fuzzy C-Means algorithm based on common Mahalanobis distance (FCM-CM) is used to identify the mastery concepts in linear algebra, for comparing the performances with other four partition algorithms; FCM-M, GG, GK, and FCM. The result shows that FCM-CM has better performance than others.

Management of Abstract Algebra Concepts Based on Knowledge Structure

2013 ◽  
Vol 284-287 ◽  
pp. 3537-3542
Author(s):  
Chin Chun Chen ◽  
Yuan Horng Lin ◽  
Jeng Ming Yih
Keyword(s):  
Mahalanobis Distance ◽  
Clustering Algorithm ◽  
Fuzzy Theory ◽  
Clustering Algorithms ◽  
Knowledge Structures ◽  
Interpretive Structural Modeling ◽  
Fuzzy C Means ◽  
Integrated Method ◽  
Combined Algorithm ◽  
Fuzzy C Means Algorithm

Knowledge Management of Mathematics Concepts was essential in educational environment. The purpose of this study is to provide an integrated method of fuzzy theory basis for individualized concept structure analysis. This method integrates Fuzzy Logic Model of Perception (FLMP) and Interpretive Structural Modeling (ISM). The combined algorithm could analyze individualized concepts structure based on the comparisons with concept structure of expert. Fuzzy clustering algorithms are based on Euclidean distance function, which can only be used to detect spherical structural clusters. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-M) was proposed to improve those limitations of GG and GK algorithms, but it is not stable enough when some of its covariance matrices are not equal. A new improved Fuzzy C-Means algorithm based on a Normalized Mahalanobis distance (FCM-NM) is proposed. Use the best performance of clustering Algorithm FCM-NM in data analysis and interpretation. Each cluster of data can easily describe features of knowledge structures. Manage the knowledge structures of Mathematics Concepts to construct the model of features in the pattern recognition completely. This procedure will also useful for cognition diagnosis. To sum up, this integrated algorithm could improve the assessment methodology of cognition diagnosis and manage the knowledge structures of Mathematics Concepts easily.

Analysis of Segmentation Parameters Effect towards Parallel Processing Time on Fuzzy C Means Algorithm

2018 ◽  
Vol 1 (4) ◽  
pp. 99
Author(s):  
Cepi Ramdani ◽  
Indah Soesanti ◽  
Sunu Wibirama
Keyword(s):  
Parallel Processing ◽  
Processing Time ◽  
Color Image ◽  
Clustering Algorithms ◽  
Fuzzy C Means ◽  
Sequential Processing ◽  
Processing Times ◽  
Parameter Values ◽  
Fuzzy C Means Algorithm ◽  
Segmentation Parameters

Fuzzy C Means algorithm or FCM is one of many clustering algorithms that has better accuracy to solve problems related to segmentation. Its application is almost in every aspects of life and many disciplines of science. However, this algorithm has some shortcomings, one of them is the large amount of processing time consumption. This research conducted mainly to do an analysis about the effect of segmentation parameters towards processing time in sequential and parallel. The other goal is to reduce the processing time of segmentation process using parallel approach. Parallel processing applied on Nvidia GeForce GT540M GPU using CUDA v8.0 framework. The experiment conducted on natural RGB color image sized 256x256 and 512x512. The settings of segmentation parameter values were done as follows, weight in range (2-3), number of iteration (50-150), number of cluster (2-8), and error tolerance or epsilon (0.1 – 1e-06). The results obtained by this research as follows, parallel processing time is faster 4.5 times than sequential time with similarity level of image segmentations generated both of processing types is 100%. The influence of segmentation parameter values towards processing times in sequential and parallel can be concluded as follows, the greater value of weight parameter then the sequential processing time becomes short, however it has no effects on parallel processing time. For iteration and cluster parameters, the greater their values will make processing time consuming in sequential and parallel become large. Meanwhile the epsilon parameter has no effect or has an unpredictable tendency on both of processing time.

scholarly journals A Generalization of Possibilistic Fuzzy C-Means Method for Statistical Clustering of Data

2021 ◽  
Vol 15 ◽  
pp. 1759-1765
Author(s):  
Souad Azzouzi ◽  
Amal Hjouji ◽  
Jaouad EL- Mekkaoui ◽  
Ahmed EL Khalfi
Keyword(s):  
Euclidean Distance ◽  
Dimensional Space ◽  
Noisy Data ◽  
High Accuracy ◽  
Cluster Center ◽  
Fuzzy C Means ◽  
Clustering And Classification ◽  
The Comparative Study ◽  
Fuzzy C Means Algorithm ◽  
Statistical Clustering

The Fuzzy C-means (FCM) algorithm has been widely used in the field of clustering and classification but has encountered difficulties with noisy data and outliers. Other versions of algorithms related to possibilistic theory have given good results, such as Fuzzy C- Means(FCM), possibilistic C-means (PCM), Fuzzy possibilistic C-means (FPCM) and possibilistic fuzzy C- Means algorithm (PFCM).This last algorithm works effectively in some environments but encountered more shortcomings with noisy databases. To solve this problem, we propose in this manuscript, a new algorithm named Improved Possibilistic Fuzzy C-Means (ImPFCM) by combining the PFCM algorithm with a very powerful statistical method. The properties of this new ImPFCM algorithm show that it is not only applicable on clusters of spherical shapes, but also on clusters of different sizes and densities. The results of the comparative study with very recent algorithms indicate the performance and the superiority of the proposed approach to easily group the datasets in a large-dimensional space and to use not only the Euclidean distance but more sophisticated standards norms, capable to deal with much more complicated problems. On the other hand, we have demonstrated that the ImPFCM algorithm is also capable of detecting the cluster center with high accuracy and performing satisfactorily in multiple environments with noisy data and outliers.

Comparative study on textual data set using fuzzy clustering algorithms

Kybernetes ◽  
2016 ◽  
Vol 45 (8) ◽  
pp. 1232-1242 ◽  
Author(s):  
Rjiba Sadika ◽  
Moez Soltani ◽  
Saloua Benammou
Keyword(s):  
Comparative Study ◽  
Clustering Algorithms ◽  
Fuzzy Model ◽  
Data Sets ◽  
Data Set ◽  
Content Type ◽  
Fuzzy C Means ◽  
Textual Data ◽  
Tunisian Revolution ◽  
Fuzzy C Means Algorithm

Purpose The purpose of this paper is to apply the Takagi-Sugeno (T-S) fuzzy model techniques in order to treat and classify textual data sets with and without noise. A comparative study is done in order to select the most accurate T-S algorithm in the textual data sets. Design/methodology/approach From a survey about what has been termed the “Tunisian Revolution,” the authors collect a textual data set from a questionnaire targeted at students. Five clustering algorithms are mainly applied: the Gath-Geva (G-G) algorithm, the modified G-G algorithm, the fuzzy c-means algorithm and the kernel fuzzy c-means algorithm. The authors examine the performances of the four clustering algorithms and select the most reliable one to cluster textual data. Findings The proposed methodology was to cluster textual data based on the T-S fuzzy model. On one hand, the results obtained using the T-S models are in the form of numerical relationships between selected keywords and the rest of words constituting a text. Consequently, it allows the authors to interpret these results not only qualitatively but also quantitatively. On the other hand, the proposed method is applied for clustering text taking into account the noise. Originality/value The originality comes from the fact that the authors validate some economical results based on textual data, even if they have not been written by experts in the linguistic fields. In addition, the results obtained in this study are easy and simple to interpret by the analysts.

scholarly journals Fuzzy Clustering Algorithms for Image Segmentation

2011 ◽  
Author(s):  
Alberto Rey ◽  
Alfonso Castro ◽  
Bernardino Arcay
Keyword(s):  
Fuzzy Clustering ◽  
Euclidean Distance ◽  
Spatial Information ◽  
Multicore Processors ◽  
Clustering Algorithms ◽  
Source Code ◽  
Spatial Constraints ◽  
3D Images ◽  
Fuzzy C Means ◽  
The Membership Function

In this document we present the implementation of three fuzzy clustering algorithms using the Insight Toolkit ITK. Firstly, we developed the conventional Fuzzy C-Means that will serve as the basis for the rest of the proposed algorithms. The next algorithms are the FCM with spatial constraints based on kernel-induced distance and the Modified Spatial Kernelized Fuzzy C-Means. Both of these introduce a Kernel function, replacing the Euclidean distance of the FCM, and spatial information into the membership function.These algorithms have been implemented in a threaded version to take advantage of the multicore processors. Moreover, providing an useful implementation make it possible that classes work with 2D/3D images, different kernels and spatial shapes.We included the source code as well as different 2D/3D examples, using several input parameters for the algorithms and obtaining the results generated on 2D/3D CT lung studies.

Kernelised Rough Sets Based Clustering Algorithms Fused With Firefly Algorithm for Image Segmentation

2019 ◽  
Vol 8 (4) ◽  
pp. 25-38
Author(s):  
Srujan Sai Chinta
Keyword(s):  
Image Segmentation ◽  
Euclidean Distance ◽  
Firefly Algorithm ◽  
Clustering Algorithms ◽  
Kernel Functions ◽  
Gaussian Kernel ◽  
Clustering Methods ◽  
Fuzzy C Means ◽  
Intuitionistic Fuzzy ◽  
Radial Basis

Data clustering methods have been used extensively for image segmentation in the past decade. In one of the author's previous works, this paper has established that combining the traditional clustering algorithms with a meta-heuristic like the Firefly Algorithm improves the stability of the output as well as the speed of convergence. It is well known now that the Euclidean distance as a measure of similarity has certain drawbacks and so in this paper we replace it with kernel functions for the study. In fact, the authors combined Rough Fuzzy C-Means (RFCM) and Rough Intuitionistic Fuzzy C-Means (RIFCM) with Firefly algorithm and replaced Euclidean distance with either Gaussian or Hyper-tangent or Radial basis Kernels. This paper terms these algorithms as Gaussian Kernel based rough Fuzzy C-Means with Firefly Algorithm (GKRFCMFA), Hyper-tangent Kernel based rough Fuzzy C-Means with Firefly Algorithm (HKRFCMFA), Gaussian Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (GKRIFCMFA) and Hyper-tangent Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (HKRIFCMFA), Radial Basis Kernel based rough Fuzzy C-Means with Firefly Algorithm (RBKRFCMFA) and Radial Basis Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (RBKRIFCMFA). In order to establish that these algorithms perform better than the corresponding Euclidean distance-based algorithms, this paper uses measures such as DB and Dunn indices. The input data comprises of three different types of images. Also, this experimentation varies over different number of clusters.

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