Subset selection in dimension reduction methods

Dimension reduction methods play an important role in multivariate statistical analysis, in particular with high-dimensional data. Linear methods can be seen as a linear mapping from the original feature space to a dimension reduction subspace. The aim is to transform the data so that the essential structure is more easily understood. However, highly correlated variables provide redundant information, whereas some other feature may be irrelevant, and we would like to identify and then discard both of them while pursuing dimension reduction. Here we propose a greedy search algorithm, which avoids the search over all possible subsets, for ranking subsets of variables based on their ability to explain variation in the dimension reduction variates.Dimension reduction methods, Linear mapping, Subset selection, Greedy search

Clustering multivariate spatial data based on local measures of spatial autocorrelation.

A growing interest in clustering spatial data is emerging in several areas, from local economic development to epidemiology, from remote sensing data to environment analyses. However, methods and procedures to face such problem are still lacking. Local measures of spatial autocorrelation aim at identifying patterns of spatial dependence within the study region. Mapping these measures provide the basic building block for identifying spatial clusters of units. If this may work satisfactorily in the univariate case, most of the real problems have a multidimensional nature. Thus, we need a clustering method based on both the multivariate data information and the spatial distribution of units. In this paper we propose a procedure for exploring and discover patterns of spatial clustering. We discuss an implementation of the popular partitioning algorithm known as K-means which incorporates the spatial structure of the data through the use of local measures of spatial autocorrelation. An example based on a set of variables related to the labour market of the Italian region Umbria is presented and deeply discussed.

On the effective action of stable non-BPS branes

We study the world-volume effective action of stable non-BPS branes present in Type II theories compactified on K3. In particular, by exploiting the conformal description of these objects available in the orbifold limit, we argue that their world-volume effective theory can be chiral. The resulting anomalies are cancelled through the usual inflow mechanism provided there are anomalous couplings, similar to those of BPS branes, to the twisted R-R fields. We also show that this result is in agreement with the conjectured interpretation of these non-BPS configurations as BPS branes wrapped on non-supersymmetric cycles of the K3.Comment: 12 pages, LaTex, no figure

Thermodynamics of vortex lines in layered superconductors

We study the dissipative thermodynamics of vortex lines in layered superconductors within a simple string model in the dilute limit of negligible vortex interactions and compute the specific heat $C_v$ in presence of arbitrary dissipation. The interplay of dissipation, inertia and elasticity is shown to control the qualitative thermodynamical behavior and their relative amount determines two very distinct regimes for the specific heat. In the dissipation dominated case we find a behavior $C_v \sim \sqrt{T}$ for a large interval of temperature below $T_c$.Comment: 10 pages, RevTe