DR2011

DR2011 - 4/21/2011 Introduction to Dimension Reduction...

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4/21/2011 1 Introduction to Dimension Reduction Starting from PCA, Diffusion maps, … Need of Dimension Reduction Real-world data (speech signals, digital photographs, or fMRI scans) usually has a high dimensionality. In order to handle such real-world data adequately, its dimensionality needs to be reduced. Dimensionality reduction is the transformation of high-dimensional data into a meaningful representation of reduced dimensionality.
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2 Meaningful? Ideally, the reduced representation should have a dimensionality that corresponds to the intrinsic dimensionality of the data. The intrinsic dimensionality of data is the minimum number of parameters needed to account for the observed properties of the data. In mathematical terms, intrinsic dimensionality means that the points in dataset X are lying on or near a manifold with dimensionality d that is embedded in the D-dimensional space. Examples of manifolds
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DR2011 - 4/21/2011 Introduction to Dimension Reduction...

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