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Publications [#243804] of Mauro Maggioni

Papers Published

  1. Little, AV; Lee, J; Jung, Y-M; Maggioni, M, Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD, IEEE Workshop on Statistical Signal Processing Proceedings (2009), pp. 85-88 [doi]
    (last updated on 2017/12/12)

    Abstract:
    The problem of estimating the intrinsic dimensionality of certain point clouds is of interest in many applications in statistics and analysis of high-dimensional data sets. Our setting is the following: the points are sampled from a manifold M of dimension k, embedded in ℝD, with k < D, and corrupted by D-dimensional noise. When M is a linear manifold (hy-perplane), one may analyse this situation by SVD, hoping the noise would perturb the rank k covariance matrix. When M is a nonlinear manifold, SVD performed globally may dramatically overestimate the intrinsic dimensionality. We discuss a multiscale version SVD that is useful in estimating the intrinsic dimensionality of nonlinear manifolds. © 2009 IEEE.

 

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