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Machine Learning
Neural Networks
Slides mostly adapted from Tom
Mithcell, Han and Kamber

Artificial Neural Networks
 Computational models inspired by the human
brain:
 Algorithms that try to mimic the brain.
 Massively parallel, distributed system, made up of
simple processing units (neurons)
 Synaptic connection strengths among neurons are
used to store the acquired knowledge.
 Knowledge is acquired by the network from its
environment through a learning process

History
 late-1800's - Neural Networks appear as an
analogy to biological systems
 1960's and 70's – Simple neural networks appear
 Fall out of favor because the perceptron is not
effective by itself, and there were no good algorithms
for multilayer nets
 1986 – Backpropagation algorithm appears
 Neural Networks have a resurgence in popularity
 More computationally expensive

Applications of ANNs
 ANNs have been widely used in various domains
for:
 Pattern recognition
 Function approximation
 Associative memory

Properties
 Inputs are flexible
 any real values
 Highly correlated or independent
 Target function may be discrete-valued, real-valued, or
vectors of discrete or real values
 Outputs are real numbers between 0 and 1
 Resistant to errors in the training data
 Long training time
 Fast evaluation
 The function produced can be difficult for humans to
interpret

When to consider neural networks
 Input is high-dimensional discrete or raw-valued
 Output is discrete or real-valued
 Output is a vector of values
 Possibly noisy data
 Form of target function is unknown
 Human readability of the result is not important
Examples:
 Speech phoneme recognition
 Image classification
 Financial prediction

November 14, 2022 Data Mining: Concepts and Techniques 7
A Neuron (= a perceptron)
 The n-dimensional input vector x is mapped into variable y by
means of the scalar product and a nonlinear function mapping
t
-
f
weighted
sum
Input
vector x
output y
Activation
function
weight
vector w

w0
w1
wn
x0
x1
xn
)
sign(
y
e
For Exampl
n
0
i
t
x
w i
i 
 


Perceptron
 Basic unit in a neural network
 Linear separator
 Parts
 N inputs, x1 ... xn
 Weights for each input, w1 ... wn
 A bias input x0 (constant) and associated weight w0
 Weighted sum of inputs, y = w0x0 + w1x1 + ... + wnxn
 A threshold function or activation function,
 i.e 1 if y > t, -1 if y <= t

Artificial Neural Networks (ANN)
 Model is an assembly of
inter-connected nodes
and weighted links
 Output node sums up
each of its input value
according to the weights
of its links
 Compare output node
against some threshold t

X1
X2
X3
Y
Black box
w1
t
Output
node
Input
nodes
w2
w3
)
( t
x
w
I
Y
i
i
i 
 
Perceptron Model
)
( t
x
w
sign
Y
i
i
i 
 
or

Types of connectivity
 Feedforward networks
 These compute a series of
transformations
 Typically, the first layer is the input
and the last layer is the output.
 Recurrent networks
 These have directed cycles in their
connection graph. They can have
complicated dynamics.
 More biologically realistic.
hidden units
output units
input units

Different Network Topologies
 Single layer feed-forward networks
 Input layer projecting into the output layer
Input Output
layer layer
Single layer
network

 Multi-layer feed-forward networks
 One or more hidden layers. Input projects only from
previous layers onto a layer.
Input Hidden Output
layer layer layer
2-layer or
1-hidden layer
fully connected
network

 Multi-layer feed-forward networks
Input Hidden Output
layer layers layer

 Recurrent networks
 A network with feedback, where some of its inputs
are connected to some of its outputs (discrete time).
Input Output
layer layer
Recurrent
network

Algorithm for learning ANN
 Initialize the weights (w0, w1, …, wk)
 Adjust the weights in such a way that the output
of ANN is consistent with class labels of training
examples
 Error function:
 Find the weights wi’s that minimize the above error
function
 e.g., gradient descent, backpropagation algorithm
 2
)
,
(
 

i
i
i
i X
w
f
Y
E

Optimizing concave/convex function
 Maximum of a concave function = minimum of a
convex function
Gradient ascent (concave) / Gradient descent (convex)
Gradient ascent rule

Decision surface of a perceptron
 Decision surface is a hyperplane
 Can capture linearly separable classes
 Non-linearly separable
 Use a network of them

Multi-layer Networks
 Linear units inappropriate
 No more expressive than a single layer
 „Introduce non-linearity
 Threshold not differentiable
 „Use sigmoid function

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.)

How A Multi-Layer Neural Network Works?
 The inputs to the network correspond to the attributes measured for
each training tuple
 Inputs are fed simultaneously into the units making up the input layer
 They are then weighted and fed simultaneously to a hidden layer
 The number of hidden layers is arbitrary, although usually only one
 The weighted outputs of the last hidden layer are input to units making
up the output layer, which emits the network's prediction
 The network is feed-forward in that none of the weights cycles back to
an input unit or to an output unit of a previous layer
 From a statistical point of view, networks perform nonlinear regression:
Given enough hidden units and enough training samples, they can
closely approximate any function

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, each initialized to 0
 Output, if for classification and more than two classes, one
output unit per class is used
 Once a network has been trained and its accuracy is
unacceptable, repeat the training process with a different
network topology or a different set of initial weights

Backpropagation and Interpretability
 Efficiency of backpropagation: Each epoch (one interation through the
training set) takes O(|D| * w), with |D| tuples and w weights, but # of
epochs can be exponential to n, the number of inputs, in the worst case
 Rule extraction from networks: network pruning
 Simplify the network structure by removing weighted links that have the
least effect on the trained network
 Then perform link, unit, or activation value clustering
 The set of input and activation values are studied to derive rules
describing the relationship between the input and hidden unit layers
 Sensitivity analysis: assess the impact that a given input variable has on a
network output. The knowledge gained from this analysis can be
represented in rules

Neural Network as a Classifier
 Weakness
 Long training time
 Require a number of parameters typically best determined empirically,
e.g., the network topology or “structure.”
 Poor interpretability: Difficult to interpret the symbolic meaning behind
the learned weights and of “hidden units” in the network
 Strength
 High tolerance to noisy data
 Ability to classify untrained patterns
 Well-suited for continuous-valued inputs and outputs
 Successful on a wide array of real-world data
 Algorithms are inherently parallel
 Techniques have recently been developed for the extraction of rules from
trained neural networks

Artificial Neural Networks (ANN)
X1 X2 X3 Y
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
0 0 1 0
0 1 0 0
0 1 1 1
0 0 0 0

X1
X2
X3
Y
Black box
0.3
0.3
0.3 t=0.4
Output
node
Input
nodes









otherwise
0
true
is
if
1
)
(
where
)
0
4
.
0
3
.
0
3
.
0
3
.
0
( 3
2
1
z
z
I
X
X
X
I
Y

A Multi-Layer Feed-Forward Neural Network
Output layer
Input layer
Hidden layer
Output vector
Input vector: X
wij
ij
k
i
i
k
j
k
j x
y
y
w
w )
ˆ
( )
(
)
(
)
1
(






General Structure of ANN
Activation
function
g(Si )
Si
Oi
I1
I2
I3
wi1
wi2
wi3
Oi
Neuron i
Input Output
threshold, t
Input
Layer
Hidden
Layer
Output
Layer
x1 x2 x3 x4 x5
y
Training ANN means learning
the weights of the neurons

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