Embed-to-control (E2C) [17] is a model for solving high-dimensional optimal control problems by combining variational autoencoders with locally-optimal controllers. However, the current E2C model suffers from two major drawbacks: 1) its objective function does not correspond to the likelihood of the data sequence and 2) the variational encoder used for embedding typically has large variational ...

The existing nonlinear local methods for dimensionality reduction yield impressive results in data embedding and manifold visualization. However, they also open up the problem of how to define a unified projection from new data to the embedded subspace constructed by the training samples. Thinking globally and fitting locally, we present a new linear embedding approach, called Locally Embedded ...

Locally linear embedding (LLE) is a recently proposed unsupervised procedure for mapping high-dimensional data nonlinearly to a lower-dimensional space. In this paper, a supervised variation on LLE is proposed. This mapping, when combined with simple classifiers such as the nearest mean classifier, is shown to yield remarkably good classification results in experiments. Furthermore, a number of...

A model of a rigid-plastic rate-independent polycrystalline aggregate wherein subaggregates are represented as the nodes of a binary tree is proposed. The lowest nodes of the binary tree represent grains. Higher binary tree nodes represent increasingly larger sub-aggregates of grains, culminating with the root of the tree, which represents the entire polycrystalline aggregate. Planar interfaces...

Recently, a new method intended to realize conformal mappings has been published. Called Locally Linear Embedding (LLE), this method can map high-dimensional data lying on a manifold to a representation of lower dimensionality that preserves the angles. Although LLE is claimed to solve problems that are usually managed by neural networks like Kohonen’s Self-Organizing Maps (SOMs), the method re...

A number of manifold learning algorithms have been recently proposed, including locally linear embedding (LLE). These algorithms not only merely reduce data dimensionality, but also attempt to discover a true low dimensional structure of the data. The common feature of the most of these algorithms is that they operate in a batch or offline mode. Hence, when new data arrive, one needs to rerun t...