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Dimensionality-Reduction Methods

  • Dimensionality reduction: In some situations, it is more effective to construct a new space instead of using some subspaces of the original data

  • Ex. To cluster the points in the following figure, any subspace of the original one, X and Y, cannot help, since all the three clusters will be projected into the overlapping areas in X and Y axes.

    • Construct a new dimension as the dashed one, the three clusters become apparent when the points projected into the new dimension
  • Dimensionality reduction methods
    • Feature selection and extraction: But may not focus on clustering structure finding
    • Spectral clustering: Combining feature extraction and clustering (i.e., use the spectrum of the similarity matrix of the data to perform dimensionality reduction for clustering in fewer dimensions)
      • Normalized Cuts (Shi and Malik, CVPR’97 or PAMI’2000)
      • The Ng-Jordan-Weiss algorithm (NIPS’01)

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