10 research outputs found
Building nonlinear data models with self-organizing maps
We study the extraction of nonlinear data models in high dimensional spaces with modified self-organizing maps. Our algorithm maps lower dimensional lattice into a high dimensional space without topology violations by tuning the neighborhood widths locally. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the
data. The performance of the algorithm is demonstrated for one- and two-dimensional principal manifolds and for sparse data sets
Nonlinear principal component analysis
We study the extraction of nonlinear data models in high-dimensional spaces with modified self-organizing maps. We present a general algorithm
which maps low-dimensional lattices into high-dimensional data manifolds without violation of topology. The approach is based on a new principle
exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. Moreover we present a second
algorithm for the extraction of generalized principal curves comprising disconnected and branching manifolds. The performance of the algorithm is
demonstrated for both one- and two-dimensional principal manifolds and also for the case of sparse data sets. As an application we reveal cluster
structures in a set of real world data from the domain of ecotoxicology
Building Nonlinear Data Models with Self-Organizing Maps
We study the extraction of nonlinear data models in high dimensional spaces with modified self-organizing maps. Our algorithm maps lower dimensional lattice into a high dimensional space without topology violations by tuning the neighborhood widths locally. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. The performance of the algorithm is demonstrated for one- and two-dimensional principal manifolds and for sparse data sets
Building nonlinear data models with self-organizing maps
We study the extraction of nonlinear data models in high dimensional spaces with modified self-organizing maps. Our algorithm maps lower dimensional lattice into a high dimensional space without topology violations by tuning the neighborhood widths locally. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the
data. The performance of the algorithm is demonstrated for one- and two-dimensional principal manifolds and for sparse data sets
An Algorithm for Generalized Principal Curves with Adaptive Topology in Complex Data Sets
Generalized principal curves are capable of representing complex
data structures as they may have branching points or may consist of
disconnected parts. For their construction using an unsupervised learning
algorithm the templates need to be structurally adaptive. The present
algorithm meets this goal by a combination of a competitive Hebbian
learning scheme and a self-organizing map algorithm. Whereas the Hebbian
scheme captures the main topological features of the data, in the
map the neighborhood widths are automatically adjusted in order to suppress
the noisy dimensions. It is noteworthy that the procedure which is
natural in prestructured Kohonen nets could be carried over to a neural
gas algorithm which does not use an initial connectivity. The principal
curve is then given by an averaging procedure over the critical
uctuations of the map exploiting noise-induced phase transitions in the neural
gas
Nonlinear principal component analysis
We study the extraction of nonlinear data models in high-dimensional spaces with modified self-organizing maps. We present a general algorithm
which maps low-dimensional lattices into high-dimensional data manifolds without violation of topology. The approach is based on a new principle
exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. Moreover we present a second
algorithm for the extraction of generalized principal curves comprising disconnected and branching manifolds. The performance of the algorithm is
demonstrated for both one- and two-dimensional principal manifolds and also for the case of sparse data sets. As an application we reveal cluster
structures in a set of real world data from the domain of ecotoxicology
Nonlinear principal component analysis
We study the extraction of nonlinear data models in high-dimensional spaces with modified self-organizing maps. We present a general algorithm
which maps low-dimensional lattices into high-dimensional data manifolds without violation of topology. The approach is based on a new principle
exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. Moreover we present a second
algorithm for the extraction of generalized principal curves comprising disconnected and branching manifolds. The performance of the algorithm is
demonstrated for both one- and two-dimensional principal manifolds and also for the case of sparse data sets. As an application we reveal cluster
structures in a set of real world data from the domain of ecotoxicology
An Algorithm for Generalized Principal Curves with Adaptive Topology in Complex Data Sets
Generalized principal curves are capable of representing complex
data structures as they may have branching points or may consist of
disconnected parts. For their construction using an unsupervised learning
algorithm the templates need to be structurally adaptive. The present
algorithm meets this goal by a combination of a competitive Hebbian
learning scheme and a self-organizing map algorithm. Whereas the Hebbian
scheme captures the main topological features of the data, in the
map the neighborhood widths are automatically adjusted in order to suppress
the noisy dimensions. It is noteworthy that the procedure which is
natural in prestructured Kohonen nets could be carried over to a neural
gas algorithm which does not use an initial connectivity. The principal
curve is then given by an averaging procedure over the critical
uctuations of the map exploiting noise-induced phase transitions in the neural
gas
Nonlinear Principal Component Analysis
We study the extraction of nonlinear data models in high-dimensional spaces with modified self-organizing maps. We present a general algorithm which maps low-dimensional lattices into high-dimensional data manifolds without violation of topology. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. Moreover we present a second algorithm for the extraction of generalized principal curves comprising disconnected and branching manifolds. The performance of the algorithm is demonstrated for both one- and two-dimensional principal manifolds and also for the case of sparse data sets. As an application we reveal cluster structures in a set of real world data from the domain of ecotoxicology