Abstract Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their observations. Such practice is needed atomistic simulations complex systems where even thousands degrees freedom are sampled. An abundance such makes gaining insight into a specific physical problem strenuous. Our primary aim this review to f...

Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. algorithms can discover a much lower-dimensional representation (embedding) high-dimensional dataset through non-linear transformations that preserve the most important structure original data. State-of-the-art manifold directly optimise embedding without mapping between space and discovered embedde...

Many learning situations involve multiple sets of training examples drawn from different but related underlying models. "Family dis-­ covery" is the task of discovering a parameterized family of models from this kind of training set. The task naturally arises in density estimation, classification, regression, manifold learning, reinforce­ ment learning, clustering, HMM learning, and other setti...

We propose motion manifold learning and motion primitive segmentation framework for human motion synthesis from motion-captured data. High dimensional motion capture date are represented using a low dimensional representation by topology preserving network, which maps similar motion instances to the neighborhood points on the low dimensional motion manifold. Nonlinear manifold learning between ...

In this paper, we propose a new multi-manifold metric learning (MMML) method for the task of face recognition based on image sets. Different from most existing metric learning algorithms that learn the distance metric for measuring single images, our method aims to learn distance metrics to measure the similarity between manifold pairs. In our method, each image set is modeled as a manifold and...

We look in this work at the problem of video-based face recognition in which both training and test sets are video sequences, and propose a novel approach based on manifold learning. The idea consists of first learning the intrinsic personal characteristics of each subject from the training video sequences by discovering the hidden low-dimensional nonlinear manifold of each individual. Then, a ...