Differential Priors for Elastic Nets

The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns.

An adaptive and dynamic dimensionality reduction method for high-dimensional indexing

The notorious "dimensionality curse" is a well-known phenomenon for any multi-dimensional indexes attempting to scale up to high dimensions. One well-known approach to overcome degradation in performance with respect to increasing dimensions is to reduce the dimensionality of the original dataset before constructing the index. However, identifying the correlation among the dimensions and effectively reducing them are challenging tasks. In this paper, we present an adaptive Multi-level Mahalanobis-based Dimensionality Reduction (MMDR) technique for high-dimensional indexing. Our MMDR technique has four notable features compared to existing methods. First, it discovers elliptical clusters for more effective dimensionality reduction by using only the low-dimensional subspaces. Second, data points in the different axis systems are indexed using a single B+-tree. Third, our technique is highly scalable in terms of data size and dimension. Finally, it is also dynamic and adaptive to insertions. An extensive performance study was conducted using both real and synthetic datasets, and the results show that our technique not only achieves higher precision, but also enables queries to be processed efficiently. Copyright Springer-Verlag 2005

Motivations for group membership: The role of subjective importance and uncertainty reduction

An experiment was conducted to investigate the idea that an important motive for identifying with social groups is to reduce subjective uncertainty, particularly uncertainty on subjectively important dimensions that have implications for the self-concept (e.g., Hogg, 1996; Hogg & Mullin, 1999). When people are uncertain on a dimension that is subjectively important, they self-categorize in terms of an available social categorization and, thus, exhibit group behaviors. To test this general hypothesis, group membership, task uncertainty, and task importance were manipulated in a 2 x 2 x 2 between-participants design (N = 128), under relatively minimal group conditions. Ingroup identification and desire for consensual validation of specific attitudes were the key dependent measures, but we also measured social awareness. All three predictions were supported. Participants identified with their group (H1), and desired to obtain consensual validation from ingroup members (H2) when they were uncertain about their judgments on important dimensions, indicating that uncertainty reduction motivated participants towards embracing group membership. In addition, identification mediated the interactive effect of the independent variables on consensual validation (H3), and the experimental results were not associated with an increased sense of social awareness and, therefore, were unlikely to represent only behavioral compliance with generic social norms. Some implications of this research in the study of cults and totalist groups and the explication of genocide and group violence are discussed.