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.

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.

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.

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.

Wavelet-Based Immune Fuzzy C-Means Algorithm

2014 ◽  
Vol 685 ◽  
pp. 638-641
Author(s):  
Zhi Xin Ma ◽  
Bin Bin Wen ◽  
Da Gan Nie
Keyword(s):  
Wavelet Transform ◽  
Fuzzy Clustering ◽  
Spatial Data ◽  
Reproductive Mode ◽  
Descent Direction ◽  
Fuzzy C Means ◽  
Objective Function Values ◽  
Data Objects ◽  
Fuzzy C Means Algorithm ◽  
Convergence Of Algorithm

Fuzzy clustering can express the ambiguity ofsample category, and better reflect the actual needs of datamining. By introducing wavelet transform and artificial immunealgorithm to fuzzy clustering, Wavelet-based Immune Fuzzy C-means Algorithm (WIFCM) is proposed for overcoming theimperfections of fuzzy clustering, such as falling easily into localoptimal solution, slower convergence speed and initialization-dependence of clustering centers. Innovations of WIFCM arethe elite extraction operator and the descent reproductive mode.Using the locality and multi-resolution of wavelet transform, theelite extraction operator explores the distribution and densityinformation of spatial data objects in multi-dimensional spaceto guide the search of cluster centers. Taking advantage ofthe relationship between the relative positions of elite centersand inferior centers, the descent reproductive mode obtains theapproximate fastest descent direction of objective function values,and assures fast convergence of algorithm. Compared to theclassic fuzzy C-means algorithm, experiments on 3 UCI data setsshow that WIFCM has obvious advantages in average numberof iterations and accuracy.

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.

Application of Hard C-Means and Fuzzy C-Means in Data Fusion

2012 ◽  
Vol 190-191 ◽  
pp. 265-268
Author(s):  
Ai Hong Tang ◽  
Lian Cai ◽  
You Mei Zhang
Keyword(s):  
Data Fusion ◽  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Large Data ◽  
Fcm Algorithm ◽  
Fuzzy C Means ◽  
Data Similarity ◽  
Fuzzy Clustering Algorithm ◽  
Fuzzy C Means Algorithm

This article describes two kinds of Fuzzy clustering algorithm based on partition,Fuzzy C-means algorithm is on the basis of the hard C-means algorithm, and get a big improvement, making large data similarity as far as possible together. As a result of Simulation, FCM algorithm has more reasonable than HCM method on convergence, data fusion, and so on.

scholarly journals Segmentasi Citra Ikan Tuna dengan Mahalanobis Histogram Thresholding dan Mahalanobis Fuzzy C-Means

2016 ◽  
Vol 7 (3) ◽  
Author(s):  
Andi Baso Kaswar ◽  
Agus Zainal Arifin ◽  
Arya Yudhi Wijaya
Keyword(s):  
Image Segmentation ◽  
Fuzzy Clustering ◽  
Mahalanobis Distance ◽  
Segmentation Result ◽  
Segmentation Method ◽  
Accuracy Improvement ◽  
Tuna Fish ◽  
Fuzzy C Means ◽  
Membership Value ◽  
Number Of Iterations

Abstract. Fuzzy C-Means segmentation algorithm based on Mahalanobis distance can be utilized to segment tuna fish image. However, initialization of pixels membership value and clusters centroid randomly cause the segmentation process become inefficient in terms of iteration and time of computation. This paper proposes a new method for tuna fish image segmentation by Mahalanobis Histogram Thresholding (M-HT) and Mahalanobis Fuzzy C-Means (MFCM). The proposed method consists of three main phases, namely: centroid initialization, pixel clustering and accuracy improvement. The experiment carried out obtained average of iteration amount is as many as 66 iteration with average of segmentation time as many as 162.03 second. While the average of Accuracy is 98.54%, average of Missclassification Error is 1.46%. The result shows that the proposed method can improve the efficiency of segmentation method in terms of number of iterations and time of segmentation. Besides that, the proposed method can give more accurate segmentation result compared with the conventional method.Keywords: Tuna Fish Image, Segmentation, Fuzzy Clustering, Histogram Thresholding, Mahalanobis Distance. Abstrak. Algoritma segmentasi Fuzzy C-Means berbasis jarak Mahalanobis dapat digunakan untuk mensegmentasi ikan tuna. Namun, inisialisasi derajat keanggotaan piksel dan centroid klaster secara random mengakibatkan proses segmentasi menjadi tidak efisien dalam hal iterasi dan waktu komputasi. Penelitian ini mengusulkan metode baru untuk segmentasi citra ikan tuna dengan Mahalanobis Histogram Thresholding (M-HT) dan Mahalanobis Fuzzy C-Means (MFCM). Metode ini terdiri atas tiga tahap utama, yaitu: inisialisasi centroid, pengklasteran piksel dan peningkatan akurasi. Berdasarkan hasil ekseprimen, diperoleh rata-rata jumlah iterasi sebanyak 66 iterasi dengan rata-rata waktu segmentasi 162,03 detik. Rata-rata Akurasi 98,54% dengan rata-rata tingkat Missclassification Error 1,46%. Hasil yang diperoleh menunjukkan bahwa metode yang diusulkan dapat meningkatkan efisiensi metode segmentasi dalam hal jumlah iterasi dan waktu segmentasi. Selain itu, metode yang diusulkan dapat memberikan hasil segmentasi yang lebih akurat dibandingkan dengan metode konvensional.Kata Kunci: Citra Ikan Tuna, Segmentasi, Fuzzy Clustering, Histogram Thresholding, Jarak Mahalanobis.

A thresholded fuzzy c-means algorithm for semi-fuzzy clustering

1991 ◽  
Vol 24 (9) ◽  
pp. 825-833 ◽  
Author(s):  
M.S. Kamel ◽  
Shokri Z. Selim
Keyword(s):  
Fuzzy Clustering ◽  
Fuzzy C Means ◽  
Fuzzy C Means Algorithm

scholarly journals Extended Single-Iteration Fuzzy C-Means, and Gustafson-Kessel Algorithms for Medium-Sized (106) Multisource Weber Problem

2019 ◽  
Vol 10 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Tarik Kucukdeniz ◽  
Sakir Esnaf ◽  
Engin Bayturk
Keyword(s):  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Cluster Center ◽  
Medium Size ◽  
Weber Problem ◽  
Solution Approach ◽  
Fuzzy C Means ◽  
Novel Approach ◽  
New Facilities

An uncapacitated multisource Weber problem involves finding facility locations for known customers. When this problem is restated as finding locations for additional new facilities, while keeping the current facilities, a new solution approach is needed. In this study, two new and cooperative fuzzy clustering algorithms are developed to solve a variant of the uncapacitated version of a multisource Weber problem (MWP). The first algorithm proposed is the extensive version of the single iteration fuzzy c-means (SIFCM) algorithm. The SIFCM algorithm assigns customers to existing facilities. The new extended SIFCM (ESIFCM), which is first proposed in this study, allocates discrete locations (coordinates) with the SIFCM and locates and allocates continuous locations (coordinates) with the original FCM simultaneously. If the SIFCM and the FCM, show differences between the successive cluster center values are still decreasing, share customer points among facilities. It is simply explained as single-iteration fuzzy c-means with fuzzy c-means. The second algorithm, also proposed here, runs like the ESIFCM. Instead of the FCM, a Gustafson-Kessel (GK) fuzzy clustering algorithm is used under the same framework. This algorithm is based on single-iteration (SIGK) and the GK algorithms. Numerical results are reported using two MWP problems in a class of a medium-size-data (106 bytes). Using clustering algorithms to locate and allocate the new facilities while keeping current facilities is a novel approach. When applied to the big problems, the speed of the proposed algorithms enable to find a solution while mathematical programming solution is not doable due to the great computational costs.

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