The locally linear embedding (LLE) algorithm belongs to a group of manifold learning methods that not only merely reduce data dimensionality, but also attempt to discover a true low dimensional structure of the data. In this paper, we propose an incremental version of LLE and experimentally demonstrate its advantages in terms of topology preservation. Also compared to the original (batch) LLE, ...

Locally Linear Embedding (LLE) is a widely used non-linear dimensionality reduction (NLDR) method that projects multi-dimensional data into a low-dimensional embedding space while attempting to preserve object adjacencies from the original high-dimensional feature space. A limitation of LLE, however, is the presence of free parameters, changing the values of which may dramatically change the lo...

Locally linear embedding (Lle) is a powerful approach for mapping high-dimensional data nonlinearly to a lower-dimensional space. However, when the training examples are not densely sampled, Lle often returns invalid results. In this paper, the Nle (Neighbor Line-based Lle) approach is proposed, which generates some virtual examples with the help of neighbor line such that the Lle learning can ...

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...

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...

liquid-liquid equilibria for the (water + lactic acid + benzyl alcohol or p-xylene) ternary systems were investigated at atmospheric pressure and in the temperature range from 298.15-318.15 k. the studied systems exhibit two types of liquid-liquid equilibrium (lle) behavior. the system consisting of benzyl alcohol displays type-1 lle behavior, while a type-2 behavior is exhibited by the other s...

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...

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...