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 selecti
on, 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.
How are people linked in a highly connected society? Since in many networks a power-law (scale-free) node-degree distribution can be observed, power-law might be seen as a universal characteristics of networks. But this study of communication in the
Flickr social online network reveals that power-law node-degree distributions are restricted to only sparsely connected networks. More densely connected networks, by contrast, show an increasing divergence from power-law. This work shows that this observation is consistent with the classic idea from social sciences that similarity is the driving factor behind communication in social networks. The strong relation between communication strength and node similarity could be confirmed by analyzing the Flickr network. It also is shown that node similarity as a network formation model can reproduce the characteristics of different network densities and hence can be used as a model for describing the topological transition from weakly to strongly connected societies.
