ICONIP’07 Tutorial on Clifford Neural Networks, 13-16 Nov., Japan

14th International Conference on Neural Information Processing

13-16 November, 2007, Kitakyushu, Japan

Title of Tutorial: Introduction to Theory, Construction and Application of Clifford Neural Networks

Speaker: Dr. Sven Buchholz, Senior Researcher, Cognitive Systems Group, Institute of Computer Science,
Christian-Albrechts-University Kiel, Christian-Albrechts-Platz 4, D-24118 Kiel, Germany

Abstract: This tutorial aims to give an introduction to neural computation with Clifford Geometric Algebra (GA) and to show how to apply the framework e.g. to the fields of signal processing, geometric analysis of climate data and molecular conformation. Clifford NNs are unrivaled in geometrically correct representation and computation with multi-dimensional geometric data. Attendants will learn to represent problems in GA, construct Clifford MLPs, and interpret the results. Recommended for everyone dealing with multi-dimensional data, the mathematical background will be explained.

In the beginning an introduction to the basics of GA will be given that shows how GA generalizes number systems like complex numbers and quaternions. The basics will be taught in a very interactive manner using dedicated visualization software.

The main part treats the foundations of GA-neural computation: the construction of basic and spinor Clifford neurons, and of Clifford MLPs with real- and Clifford-valued activation functions. The advantages for processing, optimization, and interpretation of data as (geometric) objects by Clifford NNs are demonstrated.

Finally an overview of practical applications of GA-NNs to geometric data analysis will round off the tutorial. This will illustrate how naturally
and interpretatively GA-NNs can be used to represent and analyze geometric objects and their relationships. Some explicit examples will be introduced from diverse fields like biochemistry and meteorology.

Keywords: Clifford geometric algebra, multidimensional Neural Networks, GA-valued Neurons, Clifford MLP, Self Organizing Maps, geometric interpretation, molecular conformation, climate extremes

Time: 120 minutes


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