Pattern Recognition Techniques - Biomedical Signal Analysis: Contemporary Methods and Applications - page 213

Tabl e 6 . 5
Comparing statistical, Syntactical and neural pattern recognition approaches.
Statistical

Syntactic Neural

Pattern
Generation
Basis

Probabilistic
Models

Formal
Grammars

Stable State or
Weight Matrix

Pattern
Classification
Basis

Neural
Network
Properties

Estimation or
Decision Theory Parsing

Feature
Organization

Structural
Relations

Input Vector Input Vector

Training Mechanism

Determining
Neural Network
Parameters

Density
Estimation

Forming
Grammars Supervised

Unsupervised Clustering Clustering Clustering

Learning
Structural
Rules

Structural
Information

Semantic
Information Limitations

EXERCISES

1. Consider a biased input of the form

τ t ( i )=
k

a t ( i ) w ik + b

and a logistic activation function. What bias b is necessary for
f (0) = 0? Does this also hold for the algebraic sigmoid function?
Hint : The logistic function is defined as f ( x )=

1

1+exp−αx with
α being a slope parameter. The algebraic sigmoid function is given
as f ( x )=

x
√ 1+v 2

.
2. For f ( τ j )givenas

1

f ( τ j )= ,

τ j −θ j

1+exp −{

θ 0 }

a) Determine and plot f ( τ j )for τ j =0and θ 0 = 10.
b) Repeat this for τ j =0, θ 0 = 100, and θ 0 =0 . 1.
3. Show that if the output activation is given by