Nonlinear Projection with the Isotop Method

Isotopis a new neural method for nonlinear projection of high-dimensional data. Isotop builds the mapping between the data space and a projection space by means of topology preservation. Actually, the topology of the data to be projected is approximated by the use of neighborhoods between the neural units. Isotop is provided with a piecewise linear interpolator for the projection of generalization data after learning. Experiments on artificial and real data sets show the advantages of Isotop.

[1]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[2]  Stanley C. Ahalt,et al.  Competitive learning algorithms for vector quantization , 1990, Neural Networks.

[3]  I. Jolliffe.  Principal Component Analysis , 2002 .

[4]  Jeanny Hérault,et al.  Vector Quantization and Projection Neural Network , 1993, IWANN.

[5]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[6]  T. Kohonen.  Self-Organized Formation of Correct Feature Maps , 1982 .

[7]  Jeanny Hérault,et al.  Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets , 1997, IEEE Trans. Neural Networks.

[8]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[9]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.

[10]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[11]  Helge J. Ritter,et al.  Neural computation and self-organizing maps - an introduction , 1992, Computation and neural systems series.

[12]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[13]  R. Shepard.  The analysis of proximities: Multidimensional scaling with an unknown distance function. II , 1962 .

[14]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[15]  Amaury Lendasse,et al.  A robust nonlinear projection method , 2000 .

[16]  Roman Bek,et al.  Discourse on one way in which a quantum-mechanics language on the classical logical base can be built up , 1978, Kybernetika.

[17]  Yeuvo Jphonen,et al.  Self-Organizing Maps , 1995 .

[18]  R. Shepard.  The analysis of proximities: Multidimensional scaling with an unknown distance function. I. , 1962 .

[19]  C. Malsburg.  Self-organization of orientation sensitive cells in the striate cortex , 2004, Kybernetik.

[20]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.