M-Isomap : Orthogonal Constrained Marginal Isomap for Nonlinear Dimensionality Reduction

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

92 Scopus Citations
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Author(s)

  • Zhao Zhang
  • Tommy W. S. Chow
  • Mingbo Zhao

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)1-12
Journal / PublicationIEEE Transactions on Cybernetics
Volume43
Issue number1
Publication statusPublished - Feb 2013

Abstract

Isomap is a well-known nonlinear dimensionality reduction (DR) method, aiming at preserving geodesic distances of all similarity pairs for delivering highly nonlinear manifolds. Isomap is efficient in visualizing synthetic data sets, but it usually delivers unsatisfactory results in benchmark cases. This paper incorporates the pairwise constraints into Isomap and proposes a marginal Isomap (M-Isomap) for manifold learning. The pairwise Cannot-Link and Must-Link constraints are used to specify the types of neighborhoods. M-Isomap computes the shortest path distances over constrained neighborhood graphs and guides the nonlinear DR through separating the interclass neighbors. As a result, large margins between both inter- and intraclass clusters are delivered and enhanced compactness of intracluster points is achieved at the same time. The validity of M-Isomap is examined by extensive simulations over synthetic, University of California, Irvine, and benchmark real Olivetti Research Library, YALE, and CMU Pose, Illumination, and Expression databases. The data visualization and clustering power of M-Isomap are compared with those of six related DR methods. The visualization results show that M-Isomap is able to deliver more separate clusters. Clustering evaluations also demonstrate that M-Isomap delivers comparable or even better results than some state-of-the-art DR algorithms.

Research Area(s)

  • Isomap, Manifold learning, Nonlinear dimensionality reduction (DR), Pairwise constraints (PCs), Visualization

Citation Format(s)

M-Isomap: Orthogonal Constrained Marginal Isomap for Nonlinear Dimensionality Reduction. / Zhang, Zhao; Chow, Tommy W. S.; Zhao, Mingbo.
In: IEEE Transactions on Cybernetics, Vol. 43, No. 1, 02.2013, p. 1-12.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review