The hypersphere neuron

نویسندگان

  • Vladimir Banarer
  • Christian Perwass
  • Gerald Sommer
چکیده

In this paper a special higher order neuron, the hypersphere neuron, is introduced. By embedding Euclidean space in a conformal space, hyperspheres can be expressed as vectors. The scalar product of points and spheres in conformal space, gives a measure for how far a point lies inside or outside a hypersphere. It will be shown that a hypersphere neuron may be implemented as a perceptron with two bias inputs. By using hyperspheres instead of hyperplanes as decision surfaces, a reduction in computational complexity can be achieved for certain types of problems. Furthermore, in this setup, a reliability measure can be associated with data points in a straight forward way.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Design of a Multilayered Feed-Forward Neural Network Using Hypersphere Neurons

In this paper a special higher order neuron, the hypersphere neuron, is introduced. By embedding Euclidean space in a conformal space, hyperspheres can be expressed as vectors. The scalar product of points and spheres in conformal space, gives a measure for how far a point lies inside or outside a hypersphere. It will be shown that a hypersphere neuron may be implemented as a perceptron with tw...

متن کامل

Spherical Decision Surfaces Using Conformal Modelling

In this paper a special higher order neuron, the hypersphere neuron, is introduced. By embedding Euclidean space in a conformal space, hyperspheres can be expressed as vectors. The scalar product of points and spheres in conformal space, gives a measure for how far a point lies inside or outside a hypersphere. It will be shown that a hypersphere neuron may be implemented as a perceptron with tw...

متن کامل

An approach for construction of Boolean neural networks based on geometrical expansion

We propose a fast covering learning algorithm (FCLA) for construction of Boolean neural networks. We visualize a neuron in terms of a hypersphere. To expand this hypersphere, we introduce three di0erent radii. The construction process makes use of three concentric hyperspheres based on these radii, and is illustrated using an example. FCLA results in a simple neural network; further the resulti...

متن کامل

Hyperplane Training of a Hypersphere Classifier

A novel classifier architecture is introduced which belongs to both hyperplane and hypersphere families. The basic computational unit in the architecture is a perceptron whose input is augmented by its squared length. Traditional methods of training hyperplane classifiers (perceptron training algorithm, backpropagation, etc.) function in the augmented input space, and induce hyperspherical deci...

متن کامل

A Short Note on The Volume of Hypersphere

In this note, a new method for deriving the volume of hypersphere is proposed by using probability theory. The explicit expression of the multiple times convolution of the probability density functions we should use is very complicated. But in here, we don’t need its whole explicit expression. We just need the only a part of information and this fact make it possible to derive the general expre...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003