Perceptron Problem in Neural Network



NEURAL NETWORK

Perceptron

Dang Xuan Tho

2010

Perceptron Problem

Consider a perceptron shown in Fig 9.1. The input data x = [x₁,x₂]^T

Figure 9.1: Perceptron with two-dimensional input data:

- see in printed version -

...

The data x is randomly sample in both classes, and applied to the perceptron. The connection weights are updated following

d (n)= ...

- see in printed version -

The inner product of w and x and an angle θ, shown in Fig. 9.3 between them are related by

- see in printed version -

Figure 9.3: Relation between inner product of two vectors and angle between them

    Please show the regions, where the final weight vector w can locate, in the following two cases. The regions should be indicated by an angle.

a. η is large.
b. η is very small.

And answer some question

1. Obtain the region, where optimum connection weight can locate.
2. Direction of adjustment.

The input potential v can be expressed by

- see in printed version -

 

[....]

1 Schröder, Burkhard + Claudia: Die Online-Durchsuchung, Telepolis, 2008.
2 Vgl. http://www.burks.de/burksblog/category/die-online-durchsuchung, Zugriff: 19.12.09.
3 Zit.: http://www.rbb-online.de/kontraste/beitrag/2007/wanze_im_wohnzimmer.html, Zugriff: 19.12.09.
4 Vgl. http://www.compliancemagazin.de/gesetzestandards/deutschland/bundestagbundesregierung/
deutscherbundestag251007.html, Zugriff: 19.12.09.
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6 Vgl, http://juris.bundesgerichtshof.de/cgi-bin/rechtsprechung/document.py?Gericht=bgh&Art=en&Datum=
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