Transcript Neural Networks - University of Southern Mississippi

Data Mining:
Concepts and Techniques
— Chapter 6 —
July 17, 2015
Data Mining: Concepts and
Techniques
1
Chapter 6. Classification and
Prediction
•
•
What is classification? What is
•
Support Vector Machines (SVM)
prediction?
•
Lazy learners (or learning from
and prediction
•
your neighbors)
Issues regarding classification
•
Frequent-pattern-based
classification
Classification by decision tree
induction
•
Other classification methods
•
Bayesian classification
•
Prediction
•
Rule-based classification
•
Accuracy and error measures
•
Classification by back
•
Ensemble methods
propagation
•
Model selection
July 17, 2015
Data Mining: Concepts
and
• Summary
Techniques
2
What are Neural Networks?
• Models of the brain and nervous system
• Highly parallel
– Process information much more like the brain than a serial
computer
• Learning
• Very simple principles
• Very complex behaviours
• Applications
– As powerful problem solvers
– As biological models
Biological Neural Nets
• Pigeons as art experts (Watanabe et al. 1995)
– Experiment:
• Pigeon in Skinner box
• Present paintings of two different artists (e.g. Chagall / Van
Gogh)
• Reward for pecking when presented a particular artist (e.g. Van
Gogh)
• Pigeons were able to discriminate between Van
Gogh and Chagall with 95% accuracy (when
presented with pictures they had been trained on)
• Discrimination still 85% successful for previously
unseen paintings of the artists
• Pigeons do not simply memorise the pictures
• They can extract and recognise patterns (the ‘style’)
• They generalise from the already seen to make
predictions
• This is what neural networks (biological and artificial)
are good at (unlike conventional computer)
ANNs – The basics
• ANNs incorporate the two fundamental components
of biological neural nets:
1. Neurones (nodes)
2. Synapses (weights)
• Neurone vs. Node
• Structure of a node:
•
Squashing function limits node output:
• Synapse vs. weight
Feed-forward nets
• Information flow is unidirectional
• Data is presented to Input layer
• Passed on to Hidden Layer
• Passed on to Output layer
• Information is distributed
• Information processing is parallel
Internal representation (interpretation) of data
• Feeding data through the net:
n
net   wi xi
i 0
 1 
o   (net)  
net 
1 e 
(1  0.25) + (0.5  (-1.5)) = 0.25 + (-0.75) = - 0.5
Squashing:
1
 0.3775
0.5
1 e
• Data is presented to the network in the form of
activations in the input layer
• Data usually requires preprocessing
– Analogous to senses in biology
Defining a Network Topology
• First decide the network topology:
– # of units in the input layer,
– # of hidden layers (if > 1),
– # of units in each hidden layer,
– and # of units in the output layer
• Normalizing the input values for each attribute measured in
the training tuples to [0.0—1.0]
• One input unit per domain value
• Output, if for classification and more than two classes, one
output unit per class is used
July 17, 2015
Data Mining: Concepts and
Techniques
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•# of units in the input layer,
•# of hidden layers (if > 1),
•# of units in each hidden layer,
•and # of units in the output
layer
n
net   wi xi
i 0
 1 
o   (net)  
net 
1 e 
• Weight settings determine the behaviour of a network
 How can we find the right weights?
Training the Network - Learning
• Backpropagation
– Requires training set (input / output pairs)
– Starts with small random weights
– Error is used to adjust weights (supervised learning)
 Gradient descent on error landscape
Backpropagation
• Iteratively process a set of training tuples & compare the network's
prediction with the actual known target value
• For each training tuple, the weights are modified to minimize the
mean squared error between the network's prediction and the actual
target value
• Modifications are made in the “backwards” direction: from the output
layer, through each hidden layer down to the first hidden layer, hence
“backpropagation”
• Steps
– Initialize weights (to small random #s) and biases in the network
– Propagate the inputs forward (by applying activation function)
– Backpropagate the error (by updating weights and biases)
– Terminating condition (when error is very small, etc.)
July 17, 2015
Data Mining: Concepts and
Techniques
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n
net   wi xi
i 0
 1 
o   (net)  
net 
1

e


 k  ok (1  ok )(tk  ok )
 h  oh (1  oh )
wji  wji  wji
w
koutputs

kh k
where wji   j x ji
Termination Conditions
• Fixed number of iterations
• Error on training examples falls below threshold
• Error on validation set meets some criteria
Example
1
4
2
6
5
3
•Learning rate l=0.9 and class label=1
Avoiding overfitting
• Weight decay
– Decrease weights by small factor during each
iteration
– Stay away from complex surfaces
• Validation Data
– Train with training set
– Get error with validation set
– Keep best weights so far on validation data
• Cross-validation to determine best number of
iterations