Ensembles of landmark multidimensional scalings

Abstract

Landmark multidimensional scaling (LMDS) uses a subset of data (landmark points) to solve classical MDS, where the scalability is increased but the approximation is noise-sensitive. In this paper we present an ensemble of LMDSs, referred to as landmark MDS ensemble (LMDSE), where we use a portion of the input in a piecewise manner to solve classical MDS, combining individual LMDS solutions which operate on different partitions of the input. Ground control points (GCPs) that are shared by partitions considered in the ensemble, allow us to align individual LMDS solutions in a common coordinate system through affine transformations. LMDSE solution is determined by averaging aligned LMDS solutions. We show that LMDSE is less noise-sensitive while maintaining the scalability as well as the speed of LMDS. Experiments on synthetic data (noisy grid) and real-world data (similar image retrieval) confirm the high performance of the proposed LMDSE.