We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4. §

A variational level set method is developed for the supervised classification problem. Nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin-based loss and a geometric regularization term new to machine learning: the surface area of the decision boundary. This geometric level set classifier is analyzed i...

A frequent problem in density level-set estimation is the choice of the right features that give rise to compact and concise representations of the observed data. We present an efficient feature selection method for density level-set estimation where optimal kernel mixing coefficients and model parameters are determined simultaneously. Our approach generalizes one-class support vector machines ...

This paper initiates the study of sets in Euclidean space R (n ≥ 2) that are defined in terms of the dimensions of their elements. Specifically, given an interval I ⊆ [0, 1], we are interested in the connectivity properties of the set DIM consisting of all points in R whose (constructive Hausdorff) dimensions lie in the interval I. It is easy to see that the sets DIM and DIM(n−1,n] are totally ...