An Iterative Locally Linear Embedding Algorithm
نویسندگان
چکیده
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 propose to iterate the two steps in LLE repeatedly to improve the results. Extensive experiment results show that iterative LLE algorithm significantly improves both classification and clustering results.
منابع مشابه
Supervised Locally Linear Embedding
Locally linear embedding (LLE) is a recently proposed method for unsupervised nonlinear dimensionality reduction. It has a number of attractive features: it does not require an iterative algorithm, and just a few parameters need to be set. Two extensions of LLE to supervised feature extraction were independently proposed by the authors of this paper. Here, both methods are unified in a common f...
متن کاملCoupling Nonlinear Element Free Galerkin and Linear Galerkin Finite Volume Solver for 2D Modeling of Local Plasticity in Structural Material
This paper introduces a computational strategy to collaboratively develop the Galerkin Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free Galerkin met...
متن کاملUnsupervised Locally Linear Embedding for Dimension Reduction
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...
متن کاملLinear Sphericity Testing of 3-Connected Single Source Digraphs
It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3-connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $O(n)$ time.
متن کاملAn accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations
In this paper, an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed. The convergence analysis of the algorithm is investigated. We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions. Finally, some numerical examples are given to demons...
متن کامل