Large-scale data mining and retrieval applications have increasingly turned to compact binary data representations as a way to achieve both fast queries and efficient data storage; many algorithms have been proposed for learning effective binary encodings. Most of these algorithms focus on learning a set of projection hyperplanes for the data and simply binarizing the result from each hyperplan...

Suppose that for a set H of n unknown hyperplanes in the Euclidean d-dimensional space, a line probe is available which reports the set of intersection points of a query line with the hyperplanes. Under this model, this paper investigates the complexity to nd a generic line for H and further to determine the hyperplanes in H. This problem arises in factoring the u-resultant to solve systems of ...

In this paper, an imprecise data classification is considered using new version of Fisher discriminator, namely interval Fisher. In the conventional formulation of Fisher, elements of within-class scatter matrix (related to covariance matrix between clusters) and between-class scatter matrix (related to covariance matrix of centers of clusters) have single values; but in the interval Fisher, th...

We prove that, for each Banach space X which is isomorphic to its hyperplanes, the Lipschitz-free spaces over and sphere are isomorphic.