Isometric projection

Deng Cai, Xiaofei He, Jiawei Han

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recently the problem of dimensionality reduction has received a lot of interests in many fields of information processing. We consider the case where data is sampled from a low dimensional manifold which is embedded in high dimensional Euclidean space. The most popular manifold learning algorithms include Locally Linear Embedding, ISOMAP, and Laplacian Eigenmap. However, these algorithms are nonlinear and only provide the embedding results of training samples. In this paper, we propose a novel linear dimensionality reduction algorithm, called Isometric Projection. Isometric Projection constructs a weighted data graph where the weights are discrete approximations of the geodesic distances on the data manifold. A linear subspace is then obtained by preserving the pairwise distances. In this way, Isometric Projection can be defined everywhere. Comparing to Principal Component Analysis (PCA) which is widely used in data processing, our algorithm is more capable of discovering the intrinsic geometrical structure. Specially, PCA is optimal only when the data space is linear, while our algorithm has no such assumption and therefore can handle more complex data space. Experimental results on two real life data sets illustrate the effectiveness of the proposed method.

Original languageEnglish (US)
Title of host publicationAAAI-07/IAAI-07 Proceedings
Subtitle of host publication22nd AAAI Conference on Artificial Intelligence and the 19th Innovative Applications of Artificial Intelligence Conference
Pages528-533
Number of pages6
StatePublished - Nov 28 2007
EventAAAI-07/IAAI-07 Proceedings: 22nd AAAI Conference on Artificial Intelligence and the 19th Innovative Applications of Artificial Intelligence Conference - Vancouver, BC, Canada
Duration: Jul 22 2007Jul 26 2007

Publication series

NameProceedings of the National Conference on Artificial Intelligence
Volume1

Other

OtherAAAI-07/IAAI-07 Proceedings: 22nd AAAI Conference on Artificial Intelligence and the 19th Innovative Applications of Artificial Intelligence Conference
CountryCanada
CityVancouver, BC
Period7/22/077/26/07

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence

Fingerprint Dive into the research topics of 'Isometric projection'. Together they form a unique fingerprint.

Cite this