65,569 research outputs found
Hierarchical growing cell structures: TreeGCS
We propose a hierarchical clustering algorithm (TreeGCS) based upon the Growing Cell Structure (GCS) neural network of Fritzke. Our algorithm refines and builds upon the GCS base, overcoming an inconsistency in the original GCS algorithm, where the network topology is susceptible to the ordering of the input vectors. Our algorithm is unsupervised, flexible, and dynamic and we have imposed no additional parameters on the underlying GCS algorithm. Our ultimate aim is a hierarchical clustering neural network that is both consistent and stable and identifies the innate hierarchical structure present in vector-based data. We demonstrate improved stability of the GCS foundation and evaluate our algorithm against the hierarchy generated by an ascendant hierarchical clustering dendogram. Our approach emulates the hierarchical clustering of the dendogram. It demonstrates the importance of the parameter settings for GCS and how they affect the stability of the clustering
Neural Network architectures design by Cellular Automata evolution
4th Conference of Systemics Cybernetics and Informatics. Orlando, 23-26 July 2000The design of the architecture is a crucial step in the successful application of a neural network. However, the architecture design is basically, in most cases, a human experts job. The design depends heavily on both, the expert experience and on a tedious trial-and-error process. Therefore, the development of automatic methods to determine the architecture of feedforward neural networks is a field of interest in the neural network community. These methods are generally based on search techniques, as genetic algorithms, simulated annealing or evolutionary strategies. Most of the designed methods are based on direct representation of the parameters of the network. This representation does not allow scalability, so to represent large architectures very large structures are required. In this work, an indirect constructive encoding scheme is proposed to find optimal architectures of feed-forward neural networks. This scheme is based on cellular automata representations in order to increase the scalability of the method.Publicad
Emergence of scaling in random networks
Systems as diverse as genetic networks or the world wide web are best
described as networks with complex topology. A common property of many large
networks is that the vertex connectivities follow a scale-free power-law
distribution. This feature is found to be a consequence of the two generic
mechanisms that networks expand continuously by the addition of new vertices,
and new vertices attach preferentially to already well connected sites. A model
based on these two ingredients reproduces the observed stationary scale-free
distributions, indicating that the development of large networks is governed by
robust self-organizing phenomena that go beyond the particulars of the
individual systems.Comment: 11 pages, 2 figure
Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities
We study structure, eigenvalue spectra and diffusion dynamics in a wide class
of networks with subgraphs (modules) at mesoscopic scale. The networks are
grown within the model with three parameters controlling the number of modules,
their internal structure as scale-free and correlated subgraphs, and the
topology of connecting network. Within the exhaustive spectral analysis for
both the adjacency matrix and the normalized Laplacian matrix we identify the
spectral properties which characterize the mesoscopic structure of sparse
cyclic graphs and trees. The minimally connected nodes, clustering, and the
average connectivity affect the central part of the spectrum. The number of
distinct modules leads to an extra peak at the lower part of the Laplacian
spectrum in cyclic graphs. Such a peak does not occur in the case of
topologically distinct tree-subgraphs connected on a tree. Whereas the
associated eigenvectors remain localized on the subgraphs both in trees and
cyclic graphs. We also find a characteristic pattern of periodic localization
along the chains on the tree for the eigenvector components associated with the
largest eigenvalue equal 2 of the Laplacian. We corroborate the results with
simulations of the random walk on several types of networks. Our results for
the distribution of return-time of the walk to the origin (autocorrelator)
agree well with recent analytical solution for trees, and it appear to be
independent on their mesoscopic and global structure. For the cyclic graphs we
find new results with twice larger stretching exponent of the tail of the
distribution, which is virtually independent on the size of cycles. The
modularity and clustering contribute to a power-law decay at short return
times
Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces
We show that complex (scale-free) network topologies naturally emerge from
hyperbolic metric spaces. Hyperbolic geometry facilitates maximally efficient
greedy forwarding in these networks. Greedy forwarding is topology-oblivious.
Nevertheless, greedy packets find their destinations with 100% probability
following almost optimal shortest paths. This remarkable efficiency sustains
even in highly dynamic networks. Our findings suggest that forwarding
information through complex networks, such as the Internet, is possible without
the overhead of existing routing protocols, and may also find practical
applications in overlay networks for tasks such as application-level routing,
information sharing, and data distribution
Hierarchical growing neural gas
“The original publication is available at www.springerlink.com”. Copyright Springer.This paper describes TreeGNG, a top-down unsupervised learning method that produces hierarchical classification schemes. TreeGNG is an extension to the Growing Neural Gas algorithm that maintains a time history of the learned topological mapping. TreeGNG is able to correct poor decisions made during the early phases of the construction of the tree, and provides the novel ability to influence the general shape and form of the learned hierarchy
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