2. Piecewise-linear Function.

where the amplification factor inside the linear region of operation is assumed to be the unity.

3. Sigmoid Function. This s-shaped function is by far the most common form of activation function used. A typical expression is

where a is the slope parameter.

4. Hyperbolic Tangent Function. This is a form of sigmoid function but it produces values in the range [—1, +1] instead of [0,1]

Processing units (neurons) are linked to each other to form a network associated with a learning algorithm. A neural network can be formed with any kind of topology (architecture). In general, three kinds of network topologies are used [226]:

Single-layer feedforward networks include input layer of source nodes that projects onto an output layer of neurons (computation nodes), but not vice versa. They are also called feedforward or acyclic networks. Since the computation takes place only on the output layer nodes, the input layer does not count as a layer (Figure 4.18(a)).

Threshold Function

Piecewise-linear Function

Threshold Function

<p(u) |

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