Grading Problem-Solving for Clustering Students' Score Using Dynamic Programming Procedure in The Context of Dynamic Time Warping

Clustering is the solution for grouping a plenty of data when there is no knowledge of the classes. Clustering is typically a well-known algorithm in the origins of machine learning or artificial intelligence. However, artificial intelligence is, unfortunately, relatively hard to understand for some reasons, hence, followed by the rise of explainable artificial intelligence research. In this paper, we propose an alternative approach to grouping problem-solving by using a dynamic programming procedure in the context of dynamic time warping. We conduct a cluster analysis in stagewise optimization with the following four steps; (1) define an optimal value function, (2) formulate recurrence relation, (3) set the boundary condition, and (4) answer is given by. We also demonstrate a numerical example along with its table-filling solution in the case of grading students' scores into
$k$
clusters. The results conclude that dynamic time warping algorithm may have preferences to be an alternative solution for certain machine learning tasks beyond traditional unsupervised methods instead.