SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
Multidimensional binary search trees used for associative searching
Communications of the ACM
Similarity Search in High Dimensions via Hashing
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Problems of learning on manifolds
Problems of learning on manifolds
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Face Recognition Using Laplacianfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Manifolds which are Isometric to Euclidean Space
Journal of Mathematical Imaging and Vision
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
The Journal of Machine Learning Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
SINOBIOMETRICS'04 Proceedings of the 5th Chinese conference on Advances in Biometric Person Authentication
Hi-index | 0.01 |
Data-driven non-parametric models, such as manifold learning algorithms, are promising data analysis tools. However, to fit an off-training-set data point in a learned model, one must first ''locate'' the point in the training set. This query has a time cost proportional to the problem size, which limits the model's scalability. In this paper, we address the problem of selecting a subset of data points as the landmarks helping locate the novel points on the data manifolds. We propose a new category of landmarks defined with the following property: the way the landmarks represent the data in the ambient Euclidean space should resemble the way they represent the data on the manifold. Given the data points and the subset of landmarks, we provide procedures to test whether the proposed property presents for the choice of landmarks. If the data points are organized with a neighbourhood graph, as it is often conducted in practice, we interpret the proposed property in terms of the graph topology. We also discuss the extent to which the topology is preserved for landmark set passing our test procedure. Another contribution of this work is to develop an optimization based scheme to adjust an existing landmark set, which can improve the reliability for representing the manifold data. Experiments on the synthetic data and the natural data have been done. The results support the proposed properties and algorithms.