Limitations of Perceptrons
A Solution : multiple layers- Perceptrons have a monotinicity property: - If a link has positive weight, activation can only increase as the corresponding input value increase (irrespective of other input values)
- Can't represent functions where input interactions can cancel one another's effect (e.g. XOR)
- Can represent only linearly separable functions.
Power / Expressiveness of Multi-layer Networks
- Can represent interactions among inputs
- Two layer networks can represent any Boolean function, and continuous functions (within a tolerance) as long as the number of hidden units is sufficient and appropriate activation functions used
- Learning algorithms exist, but weaker guarantees than perceptron learning algorithms
Multilayer Network
Two-layer back-propagation neural network
The back-propagation training algorithm
- Step 1: Installation
- Set all the weights and threshold levels of the network to random numbers uniformly distributed inside a small range
Backprop
Initialization
- Set all the weights and threshold levels of the network to random numbers uniformly distributed inside a small range
Forward computing :
- Apply an input vector x to input units- Compute activation / output vector z on hidden layer
zj = Φ (∑i 𝒱ij𝒳i)
- Compute the output vector y on output layer
yk = Φ (∑i 𝒲ik𝒳j)
y is the result of the computation
Learning for BP Nets
- Update of weights in W (between output and hidden layers): - delta rule
- Not applicable to updating V (between input and hidden ) - don't know the target values for hidden units z1, z2, ..., zp
- Solution : Propagate errors at output units to hidden units to drive the update of weight in V (again by delta rule) (error BACK-PROPAGATION learning)
- Error back propagation can be continued downward if the net has more than one hidden layer.
- How to compute errors on hidden units?
thank you for the valuable information giving on data science it is very helpful.
ReplyDeleteData Science Training in Hyderabad
Great Article
ReplyDeleteIEEE final year projects on machine learning
JavaScript Training in Chennai
Final Year Project Centers in Chennai
JavaScript Training in Chennai
Thank you because you have been willing to share information with us. we will always appreciate all you have done here because I know you are very concerned with our. network wiring companies
ReplyDelete