Learning and Design of Principal Curves

By Balázs Kégl, Adam Krzyzak, Tamás Linder, Kenneth Zeger. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000

391 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/4bd817f9455b3470727aa6be240a8dd3ae5068bb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Distance Metric Learning: A Comprehensive Survey (2006, background): “The goal is to find principal surfaces passing through the middle of data, for example, the principal curves [42, 43].”
Nonlinear Dimensionality Reduction with Local Spline Embedding (2009, methodology): “…structures, algorithms that can generate nonlinear mappings [40] have also been developed [31], such as self-organizing map [29], autoencoder neural network [1], generative topographic map [4], principal curve and manifold [24], [49], [28], [46], [21], [15], [20], and kernel PCA [42], [35].”
Sample Complexity of Testing the Manifold Hypothesis (2010, background): “A different definition of a principal curve was proposed by [12], where they attempted to find piecewise linear curves of bounded length which minimize the expected squared distance to a random point from a distribution.”
Regularized Principal Manifolds (1999, methodology): “it is equivalent to the algorithm proposed in [21].”
Another Look at Principal Curves and Surfaces (2001, background): “Ke gl, Krzyz* ak, Linder and Zeger [18] introduce the concept of principal curves with a fixed length.”
K-Profiles: A Nonlinear Clustering Method for Pattern Detection in High Dimensional Data (2015, background): “Fourth, given the high dimensions, computationally expensive methods, for example, principal curves [13, 14], are hard to be adopted even though they can model nonlinear relationships.”
Incremental nonlinear dimensionality reduction by manifold learning (2006, background): “Over time, different nonlinear mapping techniques have been proposed, such as selforganizing maps (SOM) [29], principal curve and its extensions [24], [28], [45], [47], auto-encoder neural networks [1], [15], generative topographic maps (GTM) [6], and kernel principal component analysis [42].”
Testing the Manifold Hypothesis (2013, background): “We refer the interested reader to a limited set of papers associated with this field; see [3, 8, 9, 11, 16, 20, 26, 31, 32, 41, 43, 47, 50, 52, 55] and the references therein.”
Underground operation of the ICARUS T600 LAr-TPC: first results (2011, methodology): “A dedicated reconstruction program based on the polygonal line algorithm [10] for 3D reconstruction, and on neural network for particle identification was used to this purpose.”
Riemannian Manifold Learning (2008, background): “The purpose of dimensionality reduction is to map a set of highdimensional data into a low-dimensional space while preserving the intrinsic structure in the data.”