A non-negative matrix factorization analysis of a multiple-choice education test

• Activity Number: 120
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kumer Das*+ and Jay Powell and Myron Katzoff
• Companies: Lamar University and Better Schooling Systems and
• Keywords: Contingency Table ; Principal Component Analysis ; Singular Value Decomposition ; Non-negative matrix factorization ; Alternative scoring procedures

Abstract

Educational questionnaires serve a number of purposes, one of which is to better understand the performance of students so that education delivery can be improved. Principal components analysis, PCA, is often used to help examine a large number of variables to better understand the relationships among them and to summarize into a relatively few ``score" the information in the data set. Singular value decomposition, SVD, can also be employed to reduce the size of a big data matrix. Our idea is to contrast a relatively new matrix factorization method, non-negative matrix factorization, NMF, with PCA and SVD with the goal of pointing to individualized education. We show that NMF offers interpretive advantages.