Empty K-Means Skill-Set Profile Clustering in Educational Testing

• Activity Number: 479
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Nema Dean*+ and Rebecca Nugent and Elizabeth Ayers
• Companies: University of Glasgow and Carnegie Mellon University and University of California, Berkeley
• Keywords: Cognitive Diagnosis Models ; Empty K-Means Clustering ; Skill Set Profiling ; Educational Testing

Abstract

In cognitive diagnosis models the goal is to estimate students' skill masteries based on educational testing data. These models do not scale well to medium or high numbers of skills. As an alternative, skill set profile clustering attempts to group the students into clusters based on skill mastery estimates, for example, using k-means. Given d skills, there are 2^d possible true skill set profiles (assuming complete/zero mastery). However, in practice, not all possible profiles will be present. Moreover, clusters may not be centered exactly at these profiles. These profiles are useful as they provide natural starting centers. We modify the k means algorithm using the true profiles as starting centers to allow for the possibility of empty clusters. This empty k means method is flexible, quick and scales reasonably well. Results are shown on high dimensional on-line tutoring data.