Representing complex data using localized principal components with application to astronomical data

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex''. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds), Lecture Notes in Computational Science and Engineering, Springer, 2007, pp. 180--204, http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-

Overcoming the novelty effect in online gamified learning systems: an empirical evaluation of student engagement and performance

Learners in the Higher Education context who engage with computer-based gamified learning systems often experience the novelty effect: a pattern of high activity during the gamified system’s introduction followed by a drop in activity a few weeks later, once its novelty has worn off. We applied a two-tiered motivational, online gamified learning system over two years to a total number of 333 students. In a mixed methods research design, we used three-years’ worth of longitudinal data (333 students for the treatment group and 175 in the control group) to assess students’ engagement and performance in that period. Quantitative results established that students engaged and performed better in the gamified condition vis-à-vis the non- gamified. Furthermore, students exhibited higher levels of engagement in the second year compared to the first year of the gamified condition. Our qualitative data suggests that students in the second year of the gamified delivery exhibited sustained engagement, overcoming the novelty effect. Thus, our main contribution is in suggesting ways of making the engagement meaningful and useful for the students thus sustaining their engagement with computer-based gamified learning systems and overcoming the novelty effect

The Pathmox approach for PLS path modeling: Discovering which constructs differentiate segments

The problem of heterogeneity represents a very important issue in the decision-making process. Furthermore, it has become common practice in the context of marketing research to assume that different population parameters are possible depending on sociodemographic and psycho-demographic variables such as age, gender, and social status. In recent decades, numerous approaches have been proposed with the aim of involving heterogeneity in the parameter estimation procedures. In partial least squares path modeling, the common practice consists of achieving a global measurement of the differences arising from heterogeneity. This leaves the analyst with the important task of detecting, a posteriori, which are the causal relationships (ie, path coefficients) that produce changes in the model. This is the case in Pathmox analysis, which solves the heterogeneity problem by building a binary tree to detect those segments of population that cause the heterogeneity. In this article, we propose extending the same Pathmox methodology to asses which particular endogenous equation of the structural model and which path coefficients are responsible of the difference