|
|||||
|
|
Intrinsic dimensionality estimation based on manifold assumption |
|
| Affiliation: | 1. State Key Laboratory of Software Engineering, School of Computer, Wuhan University, Wuhan, Hubei 430072, China;2. Key Laboratory of Knowledge Processing and Networked Manufacture, Hunan University of Science and Technology, Xiangtan 411201, China;1. Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin N.T., Hong Kong;2. Hong Kong Applied Science and Technology Research Institute (ASTRI), Shatin N.T., Hong Kong;1. School of Computer Science and Technology, Southwest University of Science and Technology, Mianyang 621010, China;2. Department of Computer Science, University of Central Arkansas, Conway, AR 72035, USA;3. IT Research and Development Group, University of Arkansas for Medical Sciences, Little Rock, AR 72205, USA;4. School of Information and Engineering, Southwest University of Science and Technology, Mianyang 621010, China;1. Department of Electrical and Computer Engineering, Concordia University, Montréal, QC H3G 2W1, Canada;2. Concordia Institute for Information Systems Engineering, Concordia University, Montréal, QC H3G 2W1, Canada |
| Abstract: | Dimensionality reduction is an important tool and has been widely used in many fields of data mining and machine learning. Intrinsic dimension of data sets is a key parameter for dimensionality reduction. In this paper, a new intrinsic dimension estimation method based on geometrical relationship between manifold intrinsic dimension and data neighborhood geodesic distances is presented. The estimator is derived by manifold sampling assumption. On a densely sampled manifold, the number of samples that fall into a ball is equal to the volume times the density of the ball. The radius of the ball is calculated by graph distance which is approximation of geodesic distance on manifold. Then the intrinsic dimension is estimated on each sample. Experiments conducted on synthetic and real world data set show that the performance of our new method is robust and comparable to other works. |
| Keywords: | Intrinsic dimension estimation Dimensionality reduction Graph distance Geodesic distance Manifold assumption Geometric relation Local neighborhood Data analysis |
| 本文献已被 ScienceDirect 等数据库收录！ | |
