### K-separability

Wlodzislaw Duch

^{1}Department of Informatics,
Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland, and

^{2}School of Computer Engineering,
Nanyang Technological University, Singapore.

Abstract.

Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane.
For complex data with multimodal distributions this transformation is difficult to learn.
Projection on more than two line segments is the simplest extension of linear separability, defining much easier goal for the learning process. The difficulty of learning non-linear data distributions is shifted to separation of line intervals, making the main part of the transformation much simpler.

For classification of difficult Boolean problems, such as the parity problem, linear projection combined with k-separability seems to be sufficient.

Preprint for comments in PDF, 430 KB.

Reference: W. Duch,
K-separability.
Lecture Notes in Computer Science 4131 (2006) 188-197

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