Results 1  10
of
268,229
An Algorithm for Intrinsic Dimensionality Estimation
, 1997
"... . In this paper a new method for analyzing the intrinsic dimensionality (ID) of low dimensional manifolds in high dimensional feature spaces is presented. The basic idea is to first extract a lowdimensional representation that captures the intrinsic topological structure of the input data and then ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. In this paper a new method for analyzing the intrinsic dimensionality (ID) of low dimensional manifolds in high dimensional feature spaces is presented. The basic idea is to first extract a lowdimensional representation that captures the intrinsic topological structure of the input data
An evaluation of intrinsic dimensionality estimators
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... only holds if we consider the whole set &. If more information about the curves are given, e.g. if fiducial points are given, then it might be possible to construct invariants which are nonconstant and continuThus the euclidean nature of image distorsion and the projective nature of camera geo ..."
Abstract

Cited by 49 (1 self)
 Add to MetaCart
only holds if we consider the whole set &. If more information about the curves are given, e.g. if fiducial points are given, then it might be possible to construct invariants which are nonconstant and continuThus the euclidean nature of image distorsion and the projective nature of camera geometry do not interact well. It is possible that one could construct projective invariants which are continuous with respect to some other metric, but would this metric be relevant? ous. ACKNOWLEDGEMENTS I would like to thank my supervisor Gunnar Sparr for inspiration and guidance. I would also like to thank my fellow students Anders
Optic Flow Statistics and Intrinsic Dimensionality
 Proc. of Brain Inspired Cognitive Systems
, 2004
"... Different kinds of visual substructures can be distinguished by the intrinsic dimensionality of the local signals. The concept of intrinsic dimensionality has been mostly exercised using discrete formulations. A recent work (Kruger and Felsberg, 2003; Felsberg and Kruger, 2003) introduced a cont ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Different kinds of visual substructures can be distinguished by the intrinsic dimensionality of the local signals. The concept of intrinsic dimensionality has been mostly exercised using discrete formulations. A recent work (Kruger and Felsberg, 2003; Felsberg and Kruger, 2003) introduced a
The intrinsic dimensionality of graphs
 IN STOC
, 2003
"... We resolve the following conjecture raised by Levin together with Linial, London, and Rabinovich [16]. For a graph G, let dim(G) be the smallest d such that G occurs as a (not necessarily induced) subgraph of Z d ∞, the infinite graph with vertex set Z d and an edge (u, v) whenever u − v ∞ = 1. ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
ρG). For several special families of graphs (e.g., planar graphs), we salvage the strong form, showing that dim(G) = O(ρG). Our results extend to a variant of the conjecture for finitedimensional Euclidean spaces posed by Linial [15] and independently by Benjamini and Schramm [22].
Intrinsic dimensionality estimation of submanifolds in rd
 In ICML
, 2005
"... We present a new method to estimate the intrinsic dimensionality of a submanifold M in Rd from random samples. The method is based on the convergence rates of a certain Ustatistic on the manifold. We solve at least partially the question of the choice of the scale of the data. Moreover the proposed ..."
Abstract

Cited by 39 (3 self)
 Add to MetaCart
We present a new method to estimate the intrinsic dimensionality of a submanifold M in Rd from random samples. The method is based on the convergence rates of a certain Ustatistic on the manifold. We solve at least partially the question of the choice of the scale of the data. Moreover
Estimating the Intrinsic Dimensionality of Hyperspectral Images
 Proc. Of European Symposium on Artificial Neural Networks (ESANN’99), D facto publications
, 1999
"... Abstract. Estimating the intrinsic dimensionality (ID) of an intrinsically low (d) dimensional data set embedded in a high (n) dimensional input space by conventional Principal Component Analysis (PCA) is computationally hard because PCA scales cubic (O(n 3)) with the input dimension [11]. Besides ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
Abstract. Estimating the intrinsic dimensionality (ID) of an intrinsically low (d) dimensional data set embedded in a high (n) dimensional input space by conventional Principal Component Analysis (PCA) is computationally hard because PCA scales cubic (O(n 3)) with the input dimension [11
Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... A new method for analyzing the intrinsic dimensionality (ID) of low dimensional manifolds in high dimensional feature spaces is presented. The basic idea is to first extract a lowdimensional representation that captures the intrinsic topological structure of the input data and then to analyze this ..."
Abstract

Cited by 47 (3 self)
 Add to MetaCart
A new method for analyzing the intrinsic dimensionality (ID) of low dimensional manifolds in high dimensional feature spaces is presented. The basic idea is to first extract a lowdimensional representation that captures the intrinsic topological structure of the input data and then to analyze
A Probabilistic Definition of Intrinsic Dimensionality for Images
 th DAGM Symposium
, 2003
"... In this paper we address the problem of appropriately representing the intrinsic dimensionality of image neighborhoods. This dimensionality describes the degrees of freedom of a local image patch and it gives rise to some of the most often applied corner and edge detectors. ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
In this paper we address the problem of appropriately representing the intrinsic dimensionality of image neighborhoods. This dimensionality describes the degrees of freedom of a local image patch and it gives rise to some of the most often applied corner and edge detectors.
Intrinsic Dimensionality of Extracellular Action Potentials
"... Abstract — Linear approaches to lowdimensional feature extraction may not be appropriate when statistical data are generated by a nonlinear interaction of parameters. Equally inadequate are linear methods for determining the dimension of the feature space. This article estimates the intrinsic dime ..."
Abstract
 Add to MetaCart
Abstract — Linear approaches to lowdimensional feature extraction may not be appropriate when statistical data are generated by a nonlinear interaction of parameters. Equally inadequate are linear methods for determining the dimension of the feature space. This article estimates the intrinsic
The Intrinsic Dimensionality of Graphs (Extended Abstract)
 STOC'03
, 2003
"... We resolve the following conjecture raised by Levin together with Linial, London, and Rabinovich [16]. Let Z be the infinite graph whose vertex set is Z and which has an edge (u, v) whenever uv# = 1. Let dim(G) be the smallest d such that G occurs as a (not necessarily induced) subgraph ..."
Abstract
 Add to MetaCart
We resolve the following conjecture raised by Levin together with Linial, London, and Rabinovich [16]. Let Z be the infinite graph whose vertex set is Z and which has an edge (u, v) whenever uv# = 1. Let dim(G) be the smallest d such that G occurs as a (not necessarily induced) subgraph . The growth rate of G, denoted #G , is the minimum # such that every ball of radius r > 1 in G contains at most vertices. By simple volume arguments, dim(G) = # #G ). Levin conjectured that this lower bound is tight, i.e., that dim(G) = O(#G) for every graph G. Previously,
Results 1  10
of
268,229