Fractals in Cellular Systems as Solutions for Cognitive Problems

Loocke, Philip Van

doi:10.1142/s0218348x00000032

Cited by 3 publications

(2 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, different types of random discrimination methods for classi cation have been studied (Kleinberg, 1996(Kleinberg, , 2000Ho, 1995;Berlind, 1994;Van Loocke, 2000, 2001. Such methods generate a huge number of elementary functions (which correspond to units in the present context) to de ne a classi cation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fields as Limit Functions of Stochastic Discrimination and Their Adaptability

Loocke

2002

Neural Computation

View full text Add to dashboard Cite

For a particular type of elementary function, stochastic discrimination is shown to have an analytic limit function. Classifications can be performed directly by this limit function instead of by a sampling procedure. The limit function has an interpretation in terms of fields that originate from the training examples of a classification problem. Fields depend on the global configuration of the training points. The classification of a point in input space is known when the contributions of all fields are summed. Two modifications of the limit function are proposed. First, for nonlinear problems like high-dimensional parity problems, fields can be quantized. This leads to classification functions with perfect generalization for high-dimensional parity problems. Second, fields can be provided with adaptable amplitudes. The classification corresponding to a limit function is taken as an initialization; subsequently, amplitudes are adapted until an error function for the test set reaches minimal value. It is illustrated that this increases the performance of stochastic discrimination. Due to the nature of the fields, generalization improves even if the amplitude of every training example is adaptable.

show abstract

Section: Introductionmentioning

confidence: 99%

“…InVan Loocke (2000, 2001, elementary functions of a sigmoid type have been shown to be ef cient at nonlinear problems such as high-dimensional parity problems. These functions were applied to binary problems only.…”

mentioning

confidence: 99%

Fields as Limit Functions of Stochastic Discrimination and Their Adaptability

Loocke

2002

Neural Computation

View full text Add to dashboard Cite

show abstract

Untitled

Loocke

2001

Artificial Intelligence Review

View full text Add to dashboard Cite

Study of Fractals Derived From Ifs-Fractals by Metric Procedures

Mol

2005

Fractals

View full text Add to dashboard Cite

It is a well-known fact that when visualizing an IFS-attractor through the chaos game, it is possible that the first points mapped will come closer to but stay visibly different from the attractor. This simple fact will be analyzed in more detail, through visualizations of different aspects of this convergence process. It will be shown that, in applying on every point in a 2D-plane the same sequence of mappings and coloring each point according to convergence distance, neighboring points form structures which resemble the attractor itself. Further, it is in this way possible to generate boundaries of the attractor that vary between small and coarse-grained. Using these results, it will be shown that it is possible to, starting with an IFS-attractor, construct fractals of which this IFS-attractor is a subset.

show abstract

Fractals in Cellular Systems as Solutions for Cognitive Problems

Cited by 3 publications

References 2 publications

Fields as Limit Functions of Stochastic Discrimination and Their Adaptability

Fields as Limit Functions of Stochastic Discrimination and Their Adaptability

Untitled

Study of Fractals Derived From Ifs-Fractals by Metric Procedures

Contact Info

Product

Resources

About