Matrix recovery aims to learn a low-rank structure from high dimensional data, which arises in numerous learning applications. As a popular heuristic to matrix recovery, convex relaxation involves iterative calling of singular value decomposition (SVD). Riemannian optimization based method can alleviate such expensive cost in SVD for improved scalability, which however is usually degraded by the unknown rank. This paper proposes a novel algorithm RIST that exploits the algebraic variety of low-rank manifold for matrix recovery. Particularly, RIST utilizes an efficient scheme that automatically estimate the potential rank on the real algebraic variety and tracks the favorable Riemannian submanifold. Moreover, RIST utilizes the second-order geometric characterization and achieves provable superlinear convergence, which is superior to the linear convergence of most existing methods. Extensive comparison experiments demonstrate the accuracy and ef- ficiency of RIST algorithm.

Lifelike characters, or animated agents, provide a promising option for interface development because they allow us to draw on communication and interaction styles with which humans are already familiar. In this contribution, we revisit some of our past and ongoing projects to motivate an evolution of character-based presentation systems. This evolution starts from systems in which a character presents information content in the style of a TV presenter. It moves on with the introduction of presentation teams that convey information to the user by performing role plays. To explore new forms of active user involvement during a presentation, the next step can lead to systems that convey information in the style of interactive performances. From a technical point of view, this evaluation is mirrored in different approaches to determine the behavior of the employed characters. By means of concrete applications, we argue that a central planning component for automated agent scripting is not always a good choice, especially not in the case of interactive performances where the user might take on an active role as well.