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Introduction to Neural Networks
Simon Durrant
Quantitative Methods
December 15th
A Typical Artificial Neural Network
Neurons may also
have a threshold or
bias input (not shown).
Outputs
1
5
2

Neurons have transfer
functions which
change the signals and
then give outputs.
Hidden
-3
3
2
-4
1

Inputs get multiplied
by the weights and
summed before
entering neurons.
Inputs
-1

A neural network
consists of neurons
connected by weights.
-2

2
But what are they for?
-2.47
The Family of Neural Networks



Many types of network; some common subdivisions.
Supervised learning:
– we have a set of exemplars for which we have known target outputs.
– The network learns by adjusting weights to better achieve the target outputs.
Unsupervised learning:
– We aim to find groups and subdivisions within our data
– Weights are adjusted such that neurons with similar weight patterns are made
even more similar, while others are made more distinct. Each set of similar
neurons comes to represent a particular subgroup in the data, and responds
most strongly to inputs from the subgroup.
Neural Networks
Supervised
Regression
Classification
Time Series
Unsupervised
Clustering
Dimensionality
Reduction
Classification with ANNs

Two classes (red and blue), two-dimensional data (i.e. each data point is
defined by two values, such as length and width).

We want a model that can separate the two classes, and will be able to tell
us which class a new data point belongs to.

http://lcn.epfl.ch/tutorial/english/mlp/html/index.html
Classification with ANNs

Two classes (red and blue), two-dimensional data (i.e. each data point is
defined by two values, such as length and width).

We want a model that can separate the two classes, and will be able to tell
us which class a new data point belongs to.

http://lcn.epfl.ch/tutorial/english/mlp/html/index.html
Regression with ANNs

We want to predict Boston house prices. We have measured 13
different variables associated with 500+ houses in Boston for which
we know the price.

We want a model that will use the relevant information from our
inputs in whatever complex combination gives the best outcome.

We will use the Matlab Neural Network Toolbox for this demo.

Our chosen network is a multi-layer perceptron.
Regression with ANNs

Our network has learned to predict the correct price for houses that
it was not trained on (the test set) – it has generalised.

The strong performance (r ranges between 0 and 1, where 1 is a
perfect score; we have r=0.948 for the unseen test data) is greater
than the maximum that can be achieved with multiple linear
regression.
Cluster Visualisation with ANNs

We have taken four different measurements from different types of
iris flowers: sepal length, sepal width, petal length, petal width.

We want to know if there are subgroups of irises.

A Self-Organising Map is the type of neural network we use here.

It adjusts weights to group similar items using a Mexican hat.

We will use the Matlab Neural Network Toolbox for this demo.
Cluster Visualisation with ANNs

Weights have
evolved to cover
the input space.

Looking at
weight distances
in the grid, we
see clear
subdivisions
within the data.

This is reflected
in the number of
hits for
neighborouging
neurons.
Cluster Visualisation with ANNs

Another demo (from http://www.ai-junkie.com/ann/som/som5.html): selforganisation of small coloured blocks on the basis of their RGB colour
values.

It can be used for practical purposes in mapping world poverty, for example,
when measured by a complex series of variables (e.g. health, nutrition,
education, water supply etc.)

All of these are forms of dimensionality reduction – take complex
multivariate data and reduce it to two (or N) dimensions.
Advantages of Neural Networks

Can handle many different statistical requirements
(regression, classification, clustering, time series
analysis, pattern analysis etc.).

Can handle nonlinear data without any special
measures.

Are somewhat model-free, i.e. you do not need to know
in advance whether to use a linear model, polynomial
model etc..

Seamlessly provide generalisation, i.e. can be applied
to novel inputs and give a useful and meaningful output.

Provide graceful degradation; if you break part of the
model, it does not fall apart entirely.
…and Disadvantages

Can be something of a black box.

Requires selection of particularly type of network.

Requires choice of network architectural features (such
as the number of neurons within a layer).

Setting free parameter values in order to achieve good
performance can sometimes be difficult.
But if treated with care, artificial neural networks
can offer a set of very powerful statistical
techniques without requiring a large knowledge of
statistics.
Applications of Neural Networks

Sales forecasting.

Industrial control systems.

Robot navigation.

Stock price prediction.

Medical image analysis.

Musical instrument classification.

Modelling human cognition.

Consumer behaviour data mining.

…and 100s more.
Thanks for Listening!
Any Questions?