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International Conference on Computational Science and Its Applications

ICCSA 2017: Computational Science and Its Applications – ICCSA 2017 pp 203–216Cite as

Q-matrix Extraction from Real Response Data Using Nonnegative Matrix Factorizations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10404))

Abstract

In this paper we illustrate the use of Nonnegative Matrix Factorization (NMF) to analyze real data derived from an e-learning context. NMF is a matrix decomposition method which extracts latent information from data in such a way that it can be easily interpreted by humans. Particularly, the NMF of a score matrix can automatically generate the so called Q-matrix. In an e-learning scenario, the Q-matrix describes the abilities to be acquired by students to correctly answer evaluation exams. An example on real response data illustrates the effectiveness of this factorization method as a tool for EDM.

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Notes

  1. 1.

    The actual values of W and H have been normalized to allow the heatmap representation.

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Acknowledgements

This work has been supported in part by the GNCS (Gruppo Nazionale per il Calcolo Scientifico) of Istituto Nazionale di Alta Matematica Francesco Severi, P.le Aldo Moro, Roma, Italy.

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Authors and Affiliations

  1. Department of Informatics, University of Bari Aldo Moro, 70125, Bari, Italy

    Gabriella Casalino, Ciro Castiello & Corrado Mencar

  2. Department of Mathematics, University of Bari Aldo Moro, 70125, Bari, Italy

    Nicoletta Del Buono & Flavia Esposito

Authors
  1. Gabriella Casalino
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  2. Ciro Castiello
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  3. Nicoletta Del Buono
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  4. Flavia Esposito
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  5. Corrado Mencar
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Corresponding author

Correspondence to Gabriella Casalino .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

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Casalino, G., Castiello, C., Del Buono, N., Esposito, F., Mencar, C. (2017). Q-matrix Extraction from Real Response Data Using Nonnegative Matrix Factorizations. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10404. Springer, Cham. https://doi.org/10.1007/978-3-319-62392-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-62392-4_15

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  • Print ISBN: 978-3-319-62391-7

  • Online ISBN: 978-3-319-62392-4

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