Graph-based manifold-ranking methods have been successfully applied to topic-focused multi-document summarization. This paper further proposes to use the multi-modality manifold-ranking algorithm for extracting topic-focused summary from multiple documents by considering the within-document sentence relationships and the cross-document sentence relationships as two separate modalities (graphs)....

We propose a view-constrained latent variable model for multi-view facial expression classification. In this model, we first learn a discriminative manifold shared by multiple views of facial expressions, followed by the expression classification in the shared manifold. For learning, we use the expression data from multiple views, however, the inference is performed using the data from a single...

Contemporary organizations recognize the importance of lean and green production to realize ecological economic benefits. Compared with existing optimization methods, multi-task multi-objective reinforcement learning (MT-MORL) offers an attractive means address dynamic, multi-target process-optimization problems associated Energy-Flexible Machining (EFM). Despite recent advances in learning, re...

The rigidity theorem of Witten-Bott-Taubes-Hirzebruch [W, BT, H] tells us that, if the circle group acts on a closed almost complex (or more generally unitary) manifold whose first Chern class is divisible by a positive integer N greater than 1, then its equivariant elliptic genus of level N is rigid. Applying this to a non-singular compact toric variety we see that its elliptic genus of level ...

Motivated by recent developments in manifold-valued regression we propose a family of nonparametric kernel-smoothing estimators with metric-space valued output including several robust versions. Depending on the choice of the output space and the metric the estimator reduces to partially well-known procedures for multi-class classification, multivariate regression in Euclidean space, regression...

In many multi-dimensional tracking problems, the quantities of interest are restricted to a manifold in observation space. Learning the manifold shape is a necessary step for dimensionality reduction, which in turn allows faster and more robust tracking performance. For manifolds with arbitrary topology, learning the shape from noisy scattered data is not trivial. This paper presents a geometri...

In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.