Title :
A Bernoulli relational model for nonlinear embedding
Author :
Wang, Gang ; Zhang, Hui ; Zhang, Zhihua ; Lochovsky, Frederick H.
Author_Institution :
Dept. of Comput. Sci., Hong Kong Univ. of Sci. & Technol., China
Abstract :
The notion of relations is extremely important in mathematics. In this paper, we use relations to describe the embedding problem and propose a novel stochastic relational model for nonlinear embedding. Given some relation among points in a high-dimensional space, we start from preserving the same relation in a low embedded space and model the relation as probabilistic distributions over these two spaces, respectively. We illustrate that the stochastic neighbor embedding and the Gaussian process latent variable model can be derived from our relational model. Moreover we devise a new stochastic embedding model and refer to it as Bernoulli relational embedding (BRE). BRE´s ability in nonlinear dimensionality reduction is illustrated on a set of synthetic data and collections of bitmaps of handwritten digits and face images.
Keywords :
Gaussian processes; statistical distributions; Bernoulli relational model; Gaussian process latent variable model; high-dimensional space; nonlinear dimensionality reduction; nonlinear embedding; probabilistic distribution; stochastic embedding model; stochastic neighbor embedding; stochastic relational model; Automation; Computer science; Gaussian processes; Kernel; Machine learning; Mathematics; Pattern recognition; Principal component analysis; Space technology; Stochastic processes;
Conference_Titel :
Data Mining, Fifth IEEE International Conference on
Print_ISBN :
0-7695-2278-5
DOI :
10.1109/ICDM.2005.1