The exploration of domain knowledge to improve the mining process begins to give its first results. For example, the use of domaindriven constraints allows the focusing of the discovery process on more useful patterns, from the user’s point of view. Semi-supervised clustering is a technique that partitions unlabeled data by making use of domain knowledge, usually expressed as pairwise constrain...

We prove optimality principles for semicontinuous bounded viscosity solutions of HamiltonJacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems. This result is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equations. We define the appr...

Prepositions are very common and very ambiguous, and understanding their sense is critical for understanding the meaning of the sentence. Supervised corpora for the preposition-sense disambiguation task are small, suggesting a semi-supervised approach to the task. We show that signals from unannotated multilingual data can be used to improve supervised prepositionsense disambiguation. Our appro...

In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally provides a detailed, transparent, and easily understood expression of the learning process in terms of graph flows. As a result, one can visualize and inter...

The (PS)-weak lower semicontinuity property has been introduced in Vasiliu and Yan [10] for general continuously differentiable functionals on Sobolev spaces in connection with the Ekeland variational principle and the direct method of calculus of variations. In this paper, we give a necessary and sufficient condition of this property for the functionals in one-dimension of the simple type I(u)...

In [2], Billera proved that the R-algebra of continuous piecewise polynomial functions (C0 splines) on a d-dimensional simplicial complex 1 embedded in Rd is a quotient of the Stanley–Reisner ring A1 of 1. We derive a criterion to determine which elements of the Stanley–Reisner ring correspond to splines of higher-order smoothness. In [5], Lau and Stiller point out that the dimension of C k (1)...

For every segmentation task, prior knowledge about the object that shall be segmented has to be incorporated. This is typically performed either automatically by using labeled data to train the used algorithm, or by manual adaptation of the algorithm to the specific application. For the segmentation of 3D data, the generation of training sets is very tedious and time consuming, since in most ca...