Introduction to Matlab for Cognitive Programming

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Introduction to Matlabfor Cognitive Programming

• Scott Bolland
• School of Information Technology and Electrical
  Engineering

2
Introduction

• Matlab is a Matrix Laboratory software package
  that can be used as an interactive programming
  environment.
• One of Matlabs main strengths lies in its
  ability to handle numeric computations involving
  matrices and vectors in a succinct and intuitive
  manner.
• The aim of this Workshop is to provide an
  hands-on introduction to Matlabs interface and
  programming language
• Furthermore, the Workshop also offers the option
  to explore implementations of various cognitive
  models, from simple cellular automata, to genetic
  algorithms and neural networks

3
What is a Matrix

• A matrix is defined as being a rectangular array
  of numbers, containing a number of rows and
  columns

Columns
23 2 4 1.2 1 87
A 3 Row by 2 Column Matrix
Rows
4
Why are Matrices Interesting?

• They Can Represent Experiment Data

Scores
21. 1.7 1.6 1.5 NaN 1.9 1.8 1.5 5.1 1.8 1.4 2.2
1.6 1.8
Data
Heart Rate Weight Exercise Hours
72 134 3.2 81 201 3.5 69 156 7.1 82 148 2.8
Patient 1 2 3 4
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Why are Matrices Interesting?

• They Can Represent Cellular Automata

0
Pattern
1
6
Why are Matrices Interesting?

• They Can Represent A Population for a GA

Individuals
Population
1 0 1 1 1 0 1 1
0 0 0 1 1 0 1 1
1 0 1 1 0 0 1 1
1 1 1 1 1 0 1 1
1 0 1 1 1 1 1 1
1 0 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 0 1 1 1 0 1 1
Genome
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Why are Matrices Interesting?

• They Can Represent Weights of a Neural Network

Single Layer Feedforward Network
To Unit
From Unit
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Benefits of Using Matlab

• Matrices are easily loaded, or generated

gtgt data load(experiment2.txt) data 2.1
1.7 1.6 1.5 NaN 1.9 1.8 1.5 5.1 1.8 1.4 2.2 gtgt
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Benefits of Using Matlab

• Matrices are easily loaded, or generated

gtgt population round(rand(5,10)) population
0 0 0 0 1 1 0 1
0 1 0 0 1 1 0 1
1 0 1 0 1 1 0 1
1 0 0 1 1 0 0 0
1 0 0 0 1 1 1 0
0 0 0 1 1 0 0 1 1
1 gtgt
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Benefits of Using Matlab

• Matrices are easily transformed

gtgt data load(experiment2.txt) data 2.1
1.7 1.6 1.5 NaN 1.9 1.8 1.5 5.1 1.8 1.4 2.2 gtgt
data data(finite(data)) data 2.1 1.7 1.6 1.5
1.9 1.8 1.5 5.1 1.8 1.4 2.2 gtgt mu mean(data),
sigma std(data) m 2.0545 s
1.0405 gtgt
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Benefits of Using Matlab

• Matlab provides powerful graphing functions

gtgt X,Y meshgrid(-8.58) gtgt R sqrt(X.2
Y.2) eps gtgt Z sin(R)./R gtgt
mesh(X,Y,Z,'EdgeColor','black') gtgt
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Benefits of Using Matlab

• Matlab provides powerful graphing functions

gtgt X,Y meshgrid(-8.58) gtgt R sqrt(X.2
Y.2) eps gtgt Z sin(R)./R gtgt
mesh(X,Y,Z,'EdgeColor','black') gtgt
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Benefits of Using Matlab

• Matlab provides simple, yet powerful programming
  language

global keys global values global width keys
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0
1 1 1 values 0 0 0 0 0 0 0 1 width
21 height 10 startPattern
round(rand(1,width)) totalPattern
startPattern for (x 2height) lastRow
totalPattern(end,) newRow for (y
1width) newRow(1,y) getBit(lastRow,y)
end totalPattern totalPattern newRow end
image(totalPattern63) colormap(gray) axis
off
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Benefits of Using Matlab

• Matlab provides simple, yet powerful programming
  language

global keys global values global width keys
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0
1 1 1 values 0 0 0 0 0 0 0 1 width
21 height 10 startPattern
round(rand(1,width)) totalPattern
startPattern for (x 2height) lastRow
totalPattern(end,) newRow for (y
1width) newRow(1,y) getBit(lastRow,y)
end totalPattern totalPattern newRow end
image(totalPattern63) colormap(gray) axis
off
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Workshop Overview

• You will be provided with 2 booklets
• A Matlab Manual
• A Matlab Workbook
• The aim is work at your own pace, reading through
  the manual, and to use Matlab to answer the
  corresponding questions in the Workbook
• Feel free to ask questions at any time

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Workbook Overview

• The Matlab Interface
• How to enter Matrices
• Matrix Manipulation
• How to reference elements
• Graphics Functions
• Programming with Matlab
• Implementing Cellular Automata
• Implementing Genetic Algorithms
• Implementing Backpropagation
• Using the Neural Network Toolbox

Introduction to Matlab
Implementing Cognitive Models
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Section 7 Implementing Simple Cellular Automata

• Cellular Automata are a very simple form of
  artificial life
• Demonstrates that highly complex behaviour can
  emerge from very simple mechanisms
• Much of the complexity in nature can be
  understood in such terms

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Section 7 Implementing Simple Cellular Automata

• The tutorial focuses on 1d Cellular Automata

Given a initial row of cells, new rows are
generated following a set of defined rules
Rules the rules specify what the colour of a
cell in the new row should be, given the colour
of it and its neighbours in the previous row.
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Section 7 Implementing Simple Cellular Automata

• The resulting pattern can be fairly simple

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Section 7 Implementing Simple Cellular Automata

• The resulting pattern can contain nested patterns

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Section 7 Implementing Simple Cellular Automata

• The resulting pattern can be completely random
  (non-repeating if you look down a single column)

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Section 7 Implementing Simple Cellular Automata

• Such patterns are ubiquitous in nature

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Section 8 Implementing a GA Toolbox

• Evolution is, in effect, a method of searching
  among an enormous number of possibilities for
  solutions. In biology the enormous set of
  possibilities is the set of possible genetic
  sequences, and the desired solutions are highly
  fit organisms organisms well able to survive
  and reproduce in their environment. Evolution
  can also be seen as a method for designing
  innovative solutions to complex problems.

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Section 8 Implementing a GA Toolbox
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Section 8 Implementing a GA Toolbox

• In this section of the Workbook, you will be
  implementing a general Genetic Algorithm toolbox
• Includes roulette wheel and tournament selection,
  mutation and crossover.
• Although a simple fitness function is tested,
  this can be readily modified to handle more
  complex tasks (e.g. evolution of neural networks)
• I will be taking a small introductory tutorial on
  Genetic Algorithms at 11

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Section 9-10 Neural Networks

• If you have a background in neural networks,
  these sections teach you how to implement
  backpropagation from scratch, and how to use
  Matlabs Neural Network Toolbox
• Tasks explored include
• Autoencoders emulating the self-organising
  nature of the primate visual cortex
• Detecting mines using sonar

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Timetable

• 9 1030 Programming
• 1030-1100 Morning Tea
• 1100 Intro to Genetic Algorithms
• 1100-1230 Programming
• 1230-130 Lunch
• 130-300 Programming
• 300-330 Afternoon Tea
• 300-500 Programming