Since the introduction of LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al., 2000), a large number of non-linear dimensionality reduction techniques (manifold learners) have been proposed. Many of these non-linear techniques can be viewed as instantiations of Kernel PCA; they employ a cleverly designed kernel matrix that preserves local data structure in the “feature space” (Bengio et al...

Liquid-liquid extraction-thin layer chromatography (LLE-TLC) has been a common and routine combined method for detection of drugs in biological materials. Solid-phase extraction (SPE) is gradually replacing the traditional LLE method. High performance thin layer chromatography (HPTLC) has several advantages over TLC. The present work studied the higher efficiency of a new SPE-HPTLC method over ...

In this paper, Locally Linear Embedding (LLE) has been implemented for unsupervised non-linear dimension reduction that computes low dimensional, neighborhood preserving embeddings of high dimensional data. Inputs are mapped into a single global coordinate system of lower dimensionality, and its optimizations though capable of generating highly nonlinear embeddings but local minima are not invo...

R. M. Shiffrin, R. Ratcliff, K. Murnane, and P. Nobel (1993) claimed that TODAM (a theory of distributed associative memory) is unable simultaneously to predict an absent (or negative) liststrength effect (LSE) and a positive list-length effect (LLE). However, Shiffrin et al. failed to distinguish between situations in which lag (number of items intervening between study and test) is controlled...

We present a new and effective approach for Hyperspectral Image (HSI) classification and clutter detection, overcoming a few long-standing challenges presented by HSI data characteristics. Residing in a high-dimensional spectral attribute space, HSI data samples are known to be strongly correlated in their spectral signatures, exhibit nonlinear structure due to several physical laws, and contai...

The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. Here we describe locally linear embedding (LLE), an unsupervised learning algorithm that computes low dimensional, neighborhood preserving embeddings of high dimensional data. The data, assum...

Locally linear embedding (LLE) is a nonlinear dimensionality reduction method proposed recently. It can reveal the intrinsic distribution of data, which cannot be provided by classical linear dimensionality reduction methods. The application of LLE, however, is limited because of its lack of a parametric mapping between the observation and the low-dimensional output. And the large data set to b...

We show that the thermodynamic entropy density is proportional to the largest Lyapunov exponent (LLE) of a discrete hydrodynamical system, a deterministic two-dimensional lattice gas automaton. The definition of the LLE for cellular automata is based on the concept of Boolean derivatives and is formally equivalent to that of continuous dynamical systems. This relation is justified using a Marko...

Low-loss electron (LLE) imaging in the scanning electron microscope (SEM) is based on the collection of backscattered electrons that have undergone minimal elastic interactions within a sample and therefore carry high-resolution, surface-specific information. Oliver Wells credits the concept of filtering the high-energy emitted electrons in the SEM to a statement made by McMullan [2], that the ...

Within a quantum molecular dynamics model we calculate the largest Lyapunov exponent (LLE), density fluctuation and mass distribution of fragments for a series of nuclear systems at different initial temperatures. It is found that the LLE peaks at the temperature (”critical temperature”) where the density fluctuation reaches a maximal value and the mass distribution of fragments is best fitted ...