Linear-Space Algorithms for Distance Preserving Embedding
نویسندگان
چکیده
The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in 2-dimensional Euclidean space so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then principal coordinate analysis can solve it in polynomial time. A serious disadvantage is its quadratic space requirement. In this paper we develop linear-space algorithms for this problem. A key idea is to partition a set of n objects into disjoint subsets (clusters) of size O( √ n) such that the minimum inter cluster distance is maximized among all possible such partitions.
منابع مشابه
A linear-space algorithm for distance preserving graph embedding
The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in d-dimensional Euclidean space for a constant d so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then multi-dimensional ...
متن کاملEmbedding normed linear spaces into $C(X)$
It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can ...
متن کاملOrthogonal Tensor Sparse Neighborhood Preserving Embedding for Two-dimensional Image
Orthogonal Tensor Neighborhood Preserving Embedding (OTNPE) is an efficient dimensionality reduction algorithm for two-dimensional images. However, insufficiencies of the robustness performance and deficiencies of supervised discriminant information are remained. Motivated by the sparse learning, an algorithm called Orthogonal Tensor Sparse Neighborhood Embedding (OTSNPE) for two-dimensional im...
متن کاملBinary Embedding: Fundamental Limits and Fast Algorithm
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary N distinct points in S, our goal is to encode each point using mdimensional binary strings such that we can reconstruct their geodesic distance up to δ uniform distortion. Existing bina...
متن کاملIsometric Projection by Deng Cai , Xiaofei He , and
Recently the problem of dimensionality reduction has received a lot of interests in many fields of information processing, including data mining, information retrieval, and pattern recognition. We consider the case where data is sampled from a low dimensional manifold which is embedded in high dimensional Euclidean space. The most popular manifold learning algorithms include Locally Linear Embe...
متن کامل