Topology Representing Networks for Intrinsic Dimensionality Estimation

Abstract. In this paper we compare two methods for intrinsic dimensionality (ID) estimation based on optimally topology preserving maps (OTPMs). The rst one is a direct approach, where the intrinsic dimensionality is estimated directly from the OTPM. We argue that this approach su ers from both practical and theoretical pitfalls. The second is a new approach which combines OTPMs with an e cient local principal component analysis (PCA). Exploiting the OTPM, local PCA can be shown to have only linear time complexity w.r.t. the dimensionality of the input space (in contrast to the prohibitive cubic complexity of the conventional approach), and hence the method becomes applicable even for very high dimensional input spaces as frequently encountered in computer vision. A local ID estimate is then obtained as the local number of signi cant eigenvalues. In addition to ID estimation the local subspaces as revealed by our local PCA can be directly used for further data processing tasks includin...

• Type: Conference
• Year: 1997
• Where: ICANN
• Authors: Jörg Bruske, Gerald Sommer
• Keywords: ICANN 1997, Input Space, Intrinsic Dimensionality, Local Pca, Neural Networks