The dimension of the population genetics data produced by next-generation sequencing platforms is extremely high. However, the "intrinsic dimensionality" of sequence data, which determines the structure of populations, is much lower. This motivates us to use locally linear embedding (LLE) which projects high dimensional genomic data into low dimensional, neighborhood preserving embedding, as a ...

Clustering is the task of grouping a set of objects in such a way that objects in the same group (called cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). The dimension can be reduced by using some techniques of dimension reduction. Recently new non linear methods introduced for reducing the dimensionality of such data called Locally Li...

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 th...

Locally linear embedding is a popular manifold learning algorithm for nonlinear dimensionality reduction. However, the success of LLE depends greatly on an input parameter neighborhood size, and it is still an open problem how to find the optimal value for it. This paper focuses on this parameter, proposes that it should be self-tuning according to local density not a uniform value for all the ...

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...

Abstract The single-cell RNA sequencing (scRNA-seq) technique allows single cell level of gene expression measurements, but the scRNA-seq data often contain missing values, with a large proportion caused by technical defects failing to detect expressions, which is called dropout event. issue poses great challenge for analysis. In this chapter, we introduce method based on KNN-smoothing: LLE-KNN...

The liquid-liquid equilibrium (LLE) phase boundaries were determined experimentally for the ternary systems containing refined sunflower oil, methanol, and one of ten potential cosolvents at 308.2 K under atmospheric pressure by using cloud point method. n-Butylamine was found to be one of the best cosolvents, which could substantially enhance the miscibility between the oil and methanol. The L...

Subspace manifold learning represents a popular class of techniques in statistical image analysis and object recognition. Recent research in the field has focused on nonlinear representations; locally linear embedding (LLE) is one such technique that has recently gained popularity. We present and apply a generalization of LLE that introduces sample weights. We demonstrate the application of the...