Construct Concept Structure for Linear Algebra Based on Cognition Diagnosis and Clustering with Mahalanobis Distances
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.
C. C. Chen et al., "Construct Concept Structure for Linear Algebra Based on Cognition Diagnosis and Clustering with Mahalanobis Distances", Advanced Materials Research, Vols. 211-212, pp. 756-760, 2011