Manifold Alignment

1. Overview

Most data sets can be modeled by manifolds. Manifold alignment aligns their underlying structures and transfers knowledge across data sets.
Sample applications include cross-lingual retrieval, automatic machine translation, representation and control transfer, image interpretation, improving advertisement/search, and social network analysis.
Manifold Alignment

  • Chang Wang, Peter Krafft, and Sridhar Mahadevan
    Manifold Alignment
    This is a chapter for the book of "Manifold Learning: Theory and Applications". It summarizes our work together with the other related work in this area.

    2. Different Approaches on Manifold Alignment

    Existing manifold alignment approaches can be categorized into two types: two-step alignment and one-step alignment. In two step alignment, the data instances in each data set are first mapped to lower dimensional spaces reflecting their intrinsic geometries using a standard (linear like LPP or nonlinear like Laplacian eigenmaps dimensionality reduction approach. Alignment of two manifolds can be achieved by removing some components (like rotational and scaling components) from one manifold leaving another untouched.

    Manifold alignment can be done at two levels: instance-level and feature-level. In text mining, examples of instances can be documents in English, Arabic, etc; examples of features can be English words/topics, Arabic words/topics, etc. Instance-level alignment computes nonlinear embeddings for alignment, but such an alignment result is defined only on known instances, and difficult to generalize to new instances. Feature-level alignment builds mappings between features, and is more suited for knowledge transfer applications than instance-level alignment.

    3. Some Papers on Manifold Alignment

    I might miss some recent papers in this area. Let me know if you think some other papers should also be included here.

    One-Step Manifold Alignment

  • J. Ham, D. Lee, and L. Saul.
    Semisupervised alignment of manifolds. [One of the pioneering papers in this area. instance-level]
    In Proceddings of the International Workshop on Artificial Intelligence and Statistics, pages 120-127, 2005.

  • Chang Wang, Sridhar Mahadevan
    A General Framework for Manifold Alignment. [feature-level or instance-level, preserving local geometry] [Code]
    AAAI Fall Symposium on Manifold Learning and its Applications, 2009. (AAAI FS 2009)

  • Chang Wang, Sridhar Mahadevan
    Manifold Alignment Preserving Global Geometry. [feature-level or instance-level, preserving global geometry] [Code]
    The 23rd International Joint conference on Artificial Intelligence (IJCAI 2013).

  • L. Xiong, F. Wang, and C. Zhang.
    Semi-definite manifold alignment. [using seme-definite programming framework to solve the problem]
    In Proceedings of the 18th European Conference on Machine Learning, 2007.

  • Chang Wang, Sridhar Mahadevan
    Heterogeneous Domain Adaptation using Manifold Alignment. [feature-level or instance-level, using labels to align manifolds]
    The 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011).

  • Chang Wang, Sridhar Mahadevan
    Manifold Alignment without Correspondence. [feature-level or instance-level, unsupervised alignment] [Code]
    The 21st International Joint Conference on Artificial Intelligence (IJCAI 2009).

  • Chang Wang, Sridhar Mahadevan
    Multiscale Manifold Alignment [feature-level or instance-level, multiscale alignment]
    Univ. of Massachusetts TR UM-CS-2010-049, 2010.

    Two-Step Manifold Alignment

  • S. Lafon, Y. Keller, and R. Coifman.
    Data fusion and multicue data matching by dision maps. [feature-level or instance-level]
    IEEE transactions on Pattern Analysis and Machine Intelligence, 28(11):1784-1797, 2006.

  • Chang Wang, Sridhar Mahadevan.
    Manifold Alignment using Procrustes Analysis. [feature-level or instance-level] [Code]
    The 25th International Conference on Machine Learning (ICML 2008). pages 1120-1127, Helsinki, Finland, July 2008.
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    Chang Wang,
    Oct 19, 2015, 6:48 PM
    Chang Wang,
    Jun 21, 2015, 5:40 PM
    Chang Wang,
    Mar 22, 2015, 6:38 PM