Principal arc analysis on direct product manifolds

We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional representation of the manifold that can be used to find and visualize the principal modes of variation of the data, as Principal Component Analysis (PCA) does in linear spaces. The proposed method improves upon earlier manifold extensions of PCA by more concisely capturing important nonlinear modes. For the special case of data on a sphere, variation following nongeodesic arcs is captured in a single mode, compared to the two modes needed by previous methods. Several computational and statistical challenges are resolved. The development on spheres forms the basis of principal arc analysis on more complicated manifolds. The benefits of the method are illustrated by a data example using medial representations in image analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS370 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Infrastructure and Growth: Empirical Evidence

Investment in network infrastructure can boost long-term economic growth in OECD countries. Moreover, infrastructure investment can have a positive effect on growth that goes beyond the effect of the capital stock because of economies of scale, the existence of network externalities competition enhancing effects. This paper analyses the empirical relationship between infrastructure and economic growth. Time-series results reveal a positive impact of infrastructure investment on growth. They also show that this effect varies across countries and sectors and over time. In some cases, these results reveal evidence of possible over-investment. Bayesian model averaging of cross-section growth regressions confirms that infrastructure investment in telecommunications and the electricity sectors has a robust positive effect on long-term growth (but not in railways and road networks). Furthermore, this effect is highly nonlinear as the impact is stronger if the physical stock is lower.http://deepblue.lib.umich.edu/bitstream/2027.42/64356/1/wp957.pd

Validation of nonlinear PCA

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an independent test set, fail when applied to nonlinear PCA because of its inherent unsupervised characteristics. This paper presents a new approach for validating the complexity of nonlinear PCA models by using the error in missing data estimation as a criterion for model selection. It is motivated by the idea that only the model of optimal complexity is able to predict missing values with the highest accuracy. While standard test set validation usually favours over-fitted nonlinear PCA models, the proposed model validation approach correctly selects the optimal model complexity.Comment: 12 pages, 5 figure