Laplacian Eigenmaps Dimensionality Reduction Based on Clustering-Adjusted Similarity
نویسندگان
چکیده
منابع مشابه
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a lowdimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections ...
متن کاملA Laplacian Eigenmaps Based Semantic Similarity Measure between Words
The measurement of semantic similarity between words is very important in many applicaitons. In this paper, we propose a method based on Laplacian eigenmaps to measure semantic similarity between words. First, we attach semantic features to each word. Second, a similarity matrix ,which semantic features are encoded into, is calculated in the original high-dimensional space. Finally, with the ai...
متن کاملContinuous nonlinear dimensionality reduction by kernel Eigenmaps
We equate nonlinear dimensionality reduction (NLDR) to graph embedding with side information about the vertices, and derive a solution to either problem in the form of a kernel-based mixture of affine maps from the ambient space to the target space. Unlike most spectral NLDR methods, the central eigenproblem can be made relatively small, and the result is a continuous mapping defined over the e...
متن کاملDiscrete Hessian Eigenmaps method for dimensionality reduction
For a given set of data points lying on a low-dimensional manifold embedded in a high-dimensional space, the dimensionality reduction is to recover a low-dimensional parametrization from the data set. The recently developed Hessian Eigenmaps is a mathematically rigorous method that also sets a theoretical framework for the nonlinear dimensionality reduction problem. In this paper, we develop a ...
متن کاملConvergence of Laplacian Eigenmaps
Geometrically based methods for various tasks of data analysis have attracted considerable attention over the last few years. In many of these algorithms, a central role is played by the eigenvectors of the graph Laplacian of a data-derived graph. In this paper, we show that if points are sampled uniformly at random from an unknown submanifold M of RN , then the eigenvectors of a suitably const...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algorithms
سال: 2019
ISSN: 1999-4893
DOI: 10.3390/a12100210