Low Bias Local Intrinsic Dimension Estimation from Expected Simplex Skewness
Författare
Summary, in English
In exploratory high-dimensional data analysis, local intrinsic dimension estimation can sometimes be used in order to discriminate between data sets sampled from different low-dimensional structures. Global intrinsic dimension estimators can in many cases be adapted to local estimation, but this leads to problems with high negative bias or high variance. We introduce a method that exploits the curse/blessing of dimensionality and produces local intrinsic dimension estimators that have very low bias, even in cases where the intrinsic dimension is higher than the number of data points, in combination with relatively low variance. We show that our estimators have a very good ability to classify local data sets by their dimension compared to other local intrinsic dimension estimators; furthermore we provide examples showing the usefulness of local intrinsic dimension estimation in general and our method in particular for stratification of real data sets.
Avdelning/ar
Publiceringsår
2015
Språk
Engelska
Sidor
196-202
Publikation/Tidskrift/Serie
IEEE Transactions on Pattern Analysis and Machine Intelligence
Volym
37
Issue
1
Dokumenttyp
Artikel i tidskrift
Förlag
IEEE - Institute of Electrical and Electronics Engineers Inc.
Ämne
- Mathematics
Nyckelord
- Eigenvalues and eigenfunctions
- Calibration
- Estimation
- Dimension
- Manifolds
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 1939-3539