In this paper, we use the CUR matrix factorization as a means of dimension reduction to identify important subsequences in electrocardiogram (ECG) time series. As opposed to other factorizations typically used in dimension reduction that characterize data in terms of abstract representatives (for example, an orthogonal basis), the CUR factorization describes the data in terms of actual instances within the original data set. Therefore, the CUR characterization can be directly related back to the clinical setting. We apply CUR to a synthetic ECG data set as well as to data from the MIT-BIH Arrhythmia, MGH-MF, and Incart databases using the discrete empirical interpolation method (DEIM) and an incremental QR factorization. In doing so, we demonstrate that CUR is able to identify beat morphologies that are representative of the data set, including rare-occurring beat events, providing a robust summarization of the ECG data. We also see that using CUR-selected beats to label the remaining unselected beats via 1-nearest neighbor classification produces results comparable to those presented in other works. While the electrocardiogram is of particular interest here, this work demonstrates the utility of CUR in detecting representative subsequences in quasiperiodic physiological time series.
Undergraduate learning in STEM is enhanced by participation in tractable and relevant research projects. Simultaneously, it is challenging to design meaningful research opportunities that remain affordable, engage students in most aspects of the scientific process, and offer opportunities for transformative learning experiences. We designed a collaborative 12-week undergraduate research project based on the quantification of litter along two urban streams in the Oklahoma City (United States) metropolitan area, addressing a regional issue with global implications. This study engaged six undergraduate students at a low cost with commonly available equipment. Three faculty involved brought expertise in physical stream characterization, ecology, statistics, and mathematical modeling, allowing students to approach data analysis from multidisciplinary and collaborative perspectives. Students participated in nearly all stages of scientific research, including a brief literature survey, data collection and analysis toward addressing research questions, interpretation of results, and presentation at a scientific meeting. Post-project surveys revealed that students held highly favorable perceptions in relation to overarching project goals, including improvements in data management and quantitative analysis, in comprehension of scientific abstracts, in grasping the scientific process, and in skill development toward future career goals. Student perceptions regarding the importance of participation in generating data, interest in future data analysis, and the importance of receiving financial compensation for participation were less favorable and varied. Despite increased interest in conducting future field work, interest in pursuing a career in research was slightly diminished after participation in the project. Evidence of transformative learning existed in the targeted areas of scholarly activity and health and wellness. We discuss the benefits of our study design, including suggestions for improvement and the adaptability of this study for other educational contexts.
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