Algorithms for clustering data
Algorithms for clustering data
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
An Evaluation of Intrinsic Dimensionality Estimators
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dimension reduction by local principal component analysis
Neural Computation
Intrinsic Dimensionality Estimation With Optimally Topology Preserving Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Independent component analysis: algorithms and applications
Neural Networks
Self-Organizing Maps
Introduction to Algorithms
Estimating the Intrinsic Dimension of Data with a Fractal-Based Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Stroke Segmentation of Chinese Characters Using Markov Random Fields
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
An Algorithm for Finding Intrinsic Dimensionality of Data
IEEE Transactions on Computers
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
IEEE Transactions on Signal Processing
Mining interlacing manifolds in high dimensional spaces
Proceedings of the 2011 ACM Symposium on Applied Computing
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The discovery of structures hidden in high-dimensional data space is of great significance for understanding and further processing of the data. Real world datasets are often composed of multiple low dimensional patterns, the interlacement of which may impede our ability to understand the distribution rule of the data. Few of the existing methods focus on the detection and extraction of the manifolds representing distinct patterns. Inspired by the nonlinear dimensionality reduction method ISOmap, in this paper we present a novel approach called Multi-Manifold Partition to identify the interlacing low dimensional patterns. The algorithm has three steps: first a neighborhood graph is built to capture the intrinsic topological structure of the input data, then the dimensional uniformity of neighboring nodes is analyzed to discover the segments of patterns, finally the segments which are possibly from the same low-dimensional structure are combined to obtain a global representation of distribution rules. Experiments on synthetic data as well as real problems are reported. The results show that this new approach to exploratory data analysis is effective and may enhance our understanding of the data distribution.