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This paper presents a new approach for dimension reduction of data observed on spherical surfaces. Several dimension reduction techniques have been developed in recent years for non-euclidean data analysis. As a pioneer work, (Hauberg 2016) attempted to implement principal curves on Riemannian manifolds. However, this approach uses approximations to process data on Riemannian manifolds, resulting in distorted results. This study proposes a new approach to project data onto a continuous curve to construct principal curves on spherical surfaces. Our approach lies in the same line of (Hastie and Stuetzle et al. 1989) that proposed principal curves for data on euclidean space. We further investigate the stationarity of the proposed principal curves that satisfy the self-consistency on spherical surfaces. The results on the real data analysis and simulation examples show promising empirical characteristics of the proposed approach. [ABSTRACT FROM AUTHOR]

This study aims to explore the use of Instagram by the Centers for Disease Control and Prevention, one of the representative public health authorities in the United States. For this aim, all of the photos uploaded on the Centers for Disease Control and Prevention Instagram account were crawled and the content of them were analyzed using Microsoft Azure Cognitive Services. Also, engagement was measured by the sum of numbers of likes and comments to each photo, and sentiment analysis of comments was conducted. Results suggest that the photos that can be categorized into "text" and "people" took the largest share in the Centers for Disease Control and Prevention Instagram photos. And it was found that the Centers for Disease Control and Prevention's major way of delivering messages on Instagram was to imprint key messages that call for actions for better health on photos and to provide the source of complementary information on text component of each post. It was also found that photos with more and bigger human faces had lower level of engagement than the others, and happiness and neutral emotions expressed on the faces in photos were negatively associated with engagement. The features whose high value would make the photos look splendid and gaudy were negatively correlated with engagement, but sharpness was positively correlated. [ABSTRACT FROM AUTHOR]