We study the existence of multi-graphs which are immersed in E3(κ, τ), having constant mean curvatureH, where E3(κ, τ) is a homogeneous, simply connected 3-manifold whose isometry group has dimension 4.

despite recent advances in video inpainting techniques, reconstructing large missing regions of a moving subject while its scale changes remains an elusive goal. in this paper, we have introduced a scale-change invariant method for large missing regions to tackle this problem. using this framework, first the moving foreground is separated from the background and its scale is equalized. then, a ...

In this paper, we propose a sentence ordering algorithm using a semi-supervised sentence classification and historical ordering strategy. The classification is based on the manifold structure underlying sentences, addressing the problem of limited labeled data. The historical ordering helps to ensure topic continuity and avoid topic bias. Experiments demonstrate that the method is effective.

Manifold learning based methods have been widely used for non-linear dimensionality reduction (NLDR). However, in many practical settings, the need to process streaming data is a challenge for such methods, owing to the high computational complexity involved. Moreover, most methods operate under the assumption that the input data is sampled from a single manifold, embedded in a high dimensional...

Multi-view data clustering attracts more attention than their single view counterparts due to the fact that leveraging multiple independent and complementary information from multi-view feature spaces outperforms the single one. Multi-view Spectral Clustering aims at yielding the data partition agreement over their local manifold structures by seeking eigenvalue-eigenvector decompositions. Amon...

Many real-world control applications, from economics to robotics, are characterized by the presence of multiple conflicting objectives. In these problems, the standard concept of optimality is replaced by Pareto–optimality and the goal is to find the Pareto frontier, a set of solutions representing different compromises among the objectives. Despite recent advances in multi–objective optimizati...

We introduce BranchGAN , a novel training method that enables unconditioned generative adversarial networks (GANs) to learn image manifolds at multiple scales. What is unique about BranchGAN is that it is trained in multiple branches, progressively covering both the breadth and depth of the network, as resolutions of the training images increase to reveal finer-scale features. Specifically, eac...

In this paper, we study the problem of face identification from only one training sample per person(OSPP). For a face identification system, the most critical obstacles towards real-world applications are often caused by the disguised, corrupted and varying illuminated images in limited sample sets. Meanwhile, storing fewer training samples would essentially reduce the cost for collecting, stor...

High-dimensional data are ubiquitous in many areas of science and engineering, such as machine learning, signal and image processing, computer vision, pattern recognition, bioinformatics, etc. Often, high-dimensional data are not distributed uniformly in the ambient space; instead they lie in or close to a union of low-dimensional manifolds. Recovering such low-dimensional structures in the dat...