Intrinsic dimension estimation of manifolds by incising balls

Authors:
Mingyu Fan;Hong Qiao;Bo Zhang
Affiliations:
Graduate School, Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China;Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China;LSEC, Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China
Venue:
Pattern Recognition
Year:
2009

Citing 10
Cited 6

An Evaluation of Intrinsic Dimensionality Estimators

IEEE Transactions on Pattern Analysis and Machine Intelligence
Understanding nonlinear dynamics

Understanding nonlinear dynamics
Intrinsic Dimensionality Estimation With Optimally Topology Preserving Maps

IEEE Transactions on Pattern Analysis and Machine Intelligence
Intrinsic Dimension Estimation of Data: An Approach Based on Grassberger–Procaccia's Algorithm

Neural Processing Letters
Estimating the Intrinsic Dimension of Data with a Fractal-Based Method

IEEE Transactions on Pattern Analysis and Machine Intelligence
Laplacian Eigenmaps for dimensionality reduction and data representation

Neural Computation
Intrinsic dimensionality estimation of submanifolds in Rd

ICML '05 Proceedings of the 22nd international conference on Machine learning
An Algorithm for Finding Intrinsic Dimensionality of Data

IEEE Transactions on Computers
An Intrinsic Dimensionality Estimator from Near-Neighbor Information

IEEE Transactions on Pattern Analysis and Machine Intelligence
Geodesic entropic graphs for dimension and entropy estimation in manifold learning

IEEE Transactions on Signal Processing

Estimating intrinsic dimensionality using the multi-criteria decision weighted model and the average standard estimator

Information Sciences: an International Journal
An improved local tangent space alignment method for manifold learning

Pattern Recognition Letters
Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA

Pattern Recognition Letters
Intrinsic dimension induced similarity measure for clustering

ADMA'11 Proceedings of the 7th international conference on Advanced Data Mining and Applications - Volume Part II
Dimension estimation of image manifolds by minimal cover approximation

Neurocomputing
Intrinsic dimension estimation via nearest constrained subspace classifier

Pattern Recognition

Quantified Score

Hi-index	0.01

Visualization

Abstract

Dimensionality reduction is a very important tool in data mining. Intrinsic dimension of data sets is a key parameter for dimensionality reduction. However, finding the correct intrinsic dimension is a challenging task. In this paper, a new intrinsic dimension estimation method is presented. The estimator is derived by finding the exponential relationship between the radius of an incising ball and the number of samples included in the ball. The method is compared with the previous dimension estimation methods. Experiments have been conducted on synthetic and high dimensional image data sets and on data sets of the Santa Fe time series competition, and the results show that the new method is accurate and robust.