Characterization of liquid-liquid equilibrium (LLE) in system containing ionic liquids (ILs) is important in evaluating ILs as candidates for replacing traditional extraction and separation solvents. Though an increasing amount of experimental LLE data is becoming available, comprehensive coverage of ternary liquid-phase behavior via experimental observation is impossible. Therefore, it is impo...

The local linear embedding algorithm (LLE) is a widely used nonlinear dimension-reducing algorithm. However, its large sample properties are still not well understood. In this paper we present new theoretical results for LLE based on the way that LLE computes its weight vectors. We show that LLE’s weight vectors are computed from the high-dimensional neighborhoods and are thus highly sensitive ...

Linear Linkage Encoding (LLE) is a representational scheme proposed for Genetic Algorithms (GA). LLE is convenient to be used for grouping problems and it doesn’t suffer from the redundancy problem that exists in classical encoding schemes. Any number of groups can be represented in a fixed length chromosome in this scheme. However, the length of the chromosome in LLE is determined by the numbe...

We introduce Locally Linear Embedding (LLE) to the astronomical community as a new classification technique, using SDSS spectra as an example data set. LLE is a nonlinear dimensionality reduction technique which has been studied in the context of computer perception. We compare the performance of LLE to wellknown spectral classification techniques, e.g. principal component analysis and line-rat...

The capabilities of learning and memory in parents are presumably transmitted to their offsprings, in which genetic codes and epigenetic regulations are thought as molecular bases. As neural plasticity occurs during memory formation as cellular mechanism, we aim to examine the correlation of activity strengths at cortical glutamatergic and GABAergic neurons to the transgenerational inheritance ...

This paper considers a recently proposed method for unsupervised learning and dimensionality reduction, locally linear embedding (LLE). LLE computes a compact representation of highdimensional data combining the major advantages of linear methods (computational efficiency, global optimality, and flexible asymptotic convergence guarantees) with the advantages of non-linear approaches (flexibilit...

Locally Linear embedding (LLE) is a popular dimension reduction method. In this paper, we systematically improve the two main steps of LLE: (A) learning the graph weights W, and (B) learning the embedding Y. We propose a sparse nonnegative W learning algorithm. We propose a weighted formulation for learning Y and show the results are identical to normalized cuts spectral clustering. We further ...

LLE is a well-known method to nonlinear dimensionality reduction. In this short paper, we present an alternative way to formulate LLE. The alignment technique is exploited to align the local coordinates on the local patches of manifolds to be the global ones. The efficient computation of embedding coordinates of LLE automatically appears in the proposed framework. 2006 Pattern Recognition Socie...

The Landau-Lifshitz equation (LLE) governing the flow of magnetic spin in a ferromagnetic material is a PDE with a noncanonical Hamiltonian structure. In this paper we derive a number of new formulations of the LLE as a partial differential equation on a multisymplectic structure. Using this form we show that the standard central spatial discretization of the LLE gives a semi-discrete multisymp...