Pointed subspace approach to incomplete data

Incomplete data are often represented as vectors with filled missing attributes joined with flag vectors indicating missing components. In this paper, we generalize this approach and represent incomplete data as pointed affine subspaces. This allows to perform various affine transformations of data, such as whitening or dimensionality reduction. Moreover, this representation preserves the information, which coordinates were missing. To use our representation in practical classification tasks, we embed such generalized missing data into a vector space and define the scalar product of embedding space. Our representation is easy to implement, and can be used together with typical kernel methods. Performed experiments show that the application of SVM classifier on the proposed subspace approach obtains highly accurate results

Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study

We present a numerical study of the order-parameter probability density function (PDF) of the square Ising model for lattices with linear sizes $L=80-140$. A recent efficient entropic sampling scheme, combining the Wang-Landau and broad histogram methods and based on the high-levels of the Wang-Landau process in dominant energy subspaces is employed. We find that for large lattices there exists a stable window of the scaled order-parameter in which the full ansatz including the pre-exponential factor for the tail regime of the universal PDF is well obeyed. This window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal PDF. The probability densities are used to estimate the universal Privman-Fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime.Comment: 24 pages, 5 figure