Clustering of Handwritten Mathematical Expressions for Computer-Assisted Marking

Vu-Tran-Minh KHUONG; Khanh-Minh PHAN; Huy-Quang UNG; Cuong-Tuan NGUYEN; Masaki NAKAGAWA

doi:10.1587/transinf.2020EDP7087

Clustering of Handwritten Mathematical Expressions for Computer-Assisted Marking

Vu-Tran-Minh KHUONG, Khanh-Minh PHAN, Huy-Quang UNG, Cuong-Tuan NGUYEN, Masaki NAKAGAWA

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Many approaches enable teachers to digitalize students' answers and mark them on the computer. However, they are still limited for supporting marking descriptive mathematical answers that can best evaluate learners' understanding. This paper presents clustering of offline handwritten mathematical expressions (HMEs) to help teachers efficiently mark answers in the form of HMEs. In this work, we investigate a method of combining feature types from low-level directional features and multiple levels of recognition: bag-of-symbols, bag-of-relations, and bag-of-positions. Moreover, we propose a marking cost function to measure the marking effort. To show the effectiveness of our method, we used two datasets and another sampled from CROHME 2016 with synthesized patterns to prepare correct answers and incorrect answers for each question. In experiments, we employed the k-means++ algorithm for each level of features and considered their combination to produce better performance. The experiments show that the best combination of all the feature types can reduce the marking cost to about 0.6 by setting the number of answer clusters appropriately compared with the manual one-by-one marking.

Publication: IEICE TRANSACTIONS on Information Vol.E104-D No.2 pp.275-284

Publication Date: 2021/02/01

Publicized: 2020/11/24

Online ISSN: 1745-1361

DOI: 10.1587/transinf.2020EDP7087

Type of Manuscript: PAPER

Category: Educational Technology

Authors

Vu-Tran-Minh KHUONG
  Tokyo University of Agriculture and Technology
Khanh-Minh PHAN
  Tokyo University of Agriculture and Technology
Huy-Quang UNG
  Tokyo University of Agriculture and Technology
Cuong-Tuan NGUYEN
  Tokyo University of Agriculture and Technology
Masaki NAKAGAWA
  Tokyo University of Agriculture and Technology

Keyword

clustering, handwritten mathematical answers, computer-assisted marking, offline handwritten mathematical expressions

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Vu-Tran-Minh KHUONG, Khanh-Minh PHAN, Huy-Quang UNG, Cuong-Tuan NGUYEN, Masaki NAKAGAWA, "Clustering of Handwritten Mathematical Expressions for Computer-Assisted Marking" in IEICE TRANSACTIONS on Information, vol. E104-D, no. 2, pp. 275-284, February 2021, doi: 10.1587/transinf.2020EDP7087.
Abstract: Many approaches enable teachers to digitalize students' answers and mark them on the computer. However, they are still limited for supporting marking descriptive mathematical answers that can best evaluate learners' understanding. This paper presents clustering of offline handwritten mathematical expressions (HMEs) to help teachers efficiently mark answers in the form of HMEs. In this work, we investigate a method of combining feature types from low-level directional features and multiple levels of recognition: bag-of-symbols, bag-of-relations, and bag-of-positions. Moreover, we propose a marking cost function to measure the marking effort. To show the effectiveness of our method, we used two datasets and another sampled from CROHME 2016 with synthesized patterns to prepare correct answers and incorrect answers for each question. In experiments, we employed the k-means++ algorithm for each level of features and considered their combination to produce better performance. The experiments show that the best combination of all the feature types can reduce the marking cost to about 0.6 by setting the number of answer clusters appropriately compared with the manual one-by-one marking.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2020EDP7087/_p

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@ARTICLE{e104-d_2_275,
author={Vu-Tran-Minh KHUONG, Khanh-Minh PHAN, Huy-Quang UNG, Cuong-Tuan NGUYEN, Masaki NAKAGAWA, },
journal={IEICE TRANSACTIONS on Information},
title={Clustering of Handwritten Mathematical Expressions for Computer-Assisted Marking},
year={2021},
volume={E104-D},
number={2},
pages={275-284},
abstract={Many approaches enable teachers to digitalize students' answers and mark them on the computer. However, they are still limited for supporting marking descriptive mathematical answers that can best evaluate learners' understanding. This paper presents clustering of offline handwritten mathematical expressions (HMEs) to help teachers efficiently mark answers in the form of HMEs. In this work, we investigate a method of combining feature types from low-level directional features and multiple levels of recognition: bag-of-symbols, bag-of-relations, and bag-of-positions. Moreover, we propose a marking cost function to measure the marking effort. To show the effectiveness of our method, we used two datasets and another sampled from CROHME 2016 with synthesized patterns to prepare correct answers and incorrect answers for each question. In experiments, we employed the k-means++ algorithm for each level of features and considered their combination to produce better performance. The experiments show that the best combination of all the feature types can reduce the marking cost to about 0.6 by setting the number of answer clusters appropriately compared with the manual one-by-one marking.},
keywords={},
doi={10.1587/transinf.2020EDP7087},
ISSN={1745-1361},
month={February},}

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TY - JOUR
TI - Clustering of Handwritten Mathematical Expressions for Computer-Assisted Marking
T2 - IEICE TRANSACTIONS on Information
SP - 275
EP - 284
AU - Vu-Tran-Minh KHUONG
AU - Khanh-Minh PHAN
AU - Huy-Quang UNG
AU - Cuong-Tuan NGUYEN
AU - Masaki NAKAGAWA
PY - 2021
DO - 10.1587/transinf.2020EDP7087
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E104-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 2021
AB - Many approaches enable teachers to digitalize students' answers and mark them on the computer. However, they are still limited for supporting marking descriptive mathematical answers that can best evaluate learners' understanding. This paper presents clustering of offline handwritten mathematical expressions (HMEs) to help teachers efficiently mark answers in the form of HMEs. In this work, we investigate a method of combining feature types from low-level directional features and multiple levels of recognition: bag-of-symbols, bag-of-relations, and bag-of-positions. Moreover, we propose a marking cost function to measure the marking effort. To show the effectiveness of our method, we used two datasets and another sampled from CROHME 2016 with synthesized patterns to prepare correct answers and incorrect answers for each question. In experiments, we employed the k-means++ algorithm for each level of features and considered their combination to produce better performance. The experiments show that the best combination of all the feature types can reduce the marking cost to about 0.6 by setting the number of answer clusters appropriately compared with the manual one-by-one marking.
ER -