Entropic graphs for intrinsic dimension estimation in manifold learning

2004 ◽  
Author(s):  
J.A. Costa ◽  
A.O. Hero
Keyword(s):  
Manifold Learning ◽  
Intrinsic Dimension ◽  
Dimension Estimation ◽  
Entropic Graphs

Intrinsic dimension estimation of manifolds by incising balls

2009 ◽  
Vol 42 (5) ◽  
pp. 780-787 ◽  
Author(s):  
Mingyu Fan ◽  
Hong Qiao ◽  
Bo Zhang
Keyword(s):  
Intrinsic Dimension ◽  
Dimension Estimation

An Improved Noise Reduction Algorithm Based on Manifold Learning and Its Application to Signal Noise Reduction

2010 ◽  
Vol 26-28 ◽  
pp. 653-656 ◽  
Author(s):  
Guang Bin Wang ◽  
Liang Pei Huang
Keyword(s):  
Noise Reduction ◽  
Manifold Learning ◽  
Estimation Method ◽  
Vibration Signal ◽  
Reduction Algorithm ◽  
Intrinsic Dimension ◽  
Reduction Effect ◽  
Dimension Space ◽  
Space Data ◽  
Noise Reduction Algorithm

In the noise reduction algorithm based on manifold learning, phase space data may be distorted and reduction targets are chosen at random, it made efficiency and effect of noise reduction lower.To solve this problem, a improved noise reducation method (local tangent space mean reconstruction) was proposed.The process of global array by affine transformation will be replaced with mean reconstruction,and the intrinsic dimension was estimate as dimension of reduction targets by using maximum likehood estimation method, the data in addition to intrinsic dimension space will be eliminated.Noise reduction experiment to fan vibration signal with noise shows this method had better noise reduction effect.

scholarly journals Intrinsic dimension estimation for locally undersampled data

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Vittorio Erba ◽  
Marco Gherardi ◽  
Pietro Rotondo
Keyword(s):  
State Of The Art ◽  
High Contrast ◽  
Challenging Problem ◽  
Intrinsic Dimension ◽  
Dimension Estimation ◽  
Correlation Integral ◽  
Curved Manifolds ◽  
The Core ◽  
Invariant Object Recognition ◽  
Undersampled Data

AbstractIdentifying the minimal number of parameters needed to describe a dataset is a challenging problem known in the literature as intrinsic dimension estimation. All the existing intrinsic dimension estimators are not reliable whenever the dataset is locally undersampled, and this is at the core of the so called curse of dimensionality. Here we introduce a new intrinsic dimension estimator that leverages on simple properties of the tangent space of a manifold and extends the usual correlation integral estimator to alleviate the extreme undersampling problem. Based on this insight, we explore a multiscale generalization of the algorithm that is capable of (i) identifying multiple dimensionalities in a dataset, and (ii) providing accurate estimates of the intrinsic dimension of extremely curved manifolds. We test the method on manifolds generated from global transformations of high-contrast images, relevant for invariant object recognition and considered a challenge for state-of-the-art intrinsic dimension estimators.

scholarly journals On Local Intrinsic Dimension Estimation and Its Applications

2010 ◽  
Vol 58 (2) ◽  
pp. 650-663 ◽  
Author(s):  
K.M. Carter ◽  
R. Raich ◽  
A.O. Hero
Keyword(s):  
Intrinsic Dimension ◽  
Dimension Estimation

scholarly journals Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA

2011 ◽  
Vol 32 (14) ◽  
pp. 1706-1713 ◽  
Author(s):  
Charles Bouveyron ◽  
Gilles Celeux ◽  
Stéphane Girard
Keyword(s):  
Maximum Likelihood ◽  
Intrinsic Dimension ◽  
Dimension Estimation ◽  
Probabilistic Pca
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