CSE 473: Pattern Recognition
Recall the Pattern Recognition Approaches
So Far
Determine feature vector x
Train a system
Classify the unknown pattern
Recall the Pattern Recognition Approaches
So Far
Determine feature vector x
Train a system
Classify
CSE 473: Pattern Recognition
Unsupervised Learning:
Clustering
What is Cluster Analysis?
Finding groups of objects such that the objects in a group will
be similar (or related) to one another and different from (or
unrelated to) the objects in other grou
CSE 473: Pattern Recognition
Template Matching
Template Matching
Typical Applications
Speech Recognition
Motion Estimation in Video Coding
Data Base Image Retrieval
Written Word Recognition
Bioinformatics
Template Matching
The Goal:
Given a set of refe
Nonlinear Classifier
Review of Perceptrons Capability
Recall the AND or OR functions
x1
x2 AND
0
0
1
1
0
1
0
1
0
0
0
1
OR
0
1
1
1
Review of Perceptrons Capability
Recall the AND or OR functions
x1
x2 AND Class OR Class
0
0
1
1
0
1
0
1
0
0
0
1
B
B
B
A
0
1
Two-Class case again
Let, we have N
training samples
Find a linear hyperplane (decision boundary) that will separate the data
Two-Class case again
B1
One Possible Solution
Two-Class case again
B2
Another possible solution
Two-Class case again
B
2
Other po
CSE 473: Pattern Recognition
Syntactic Pattern Recognition
using
Graph Theory
Graphical Approaches to SyntPR
Graphical alternatives for structural representations
Natural extensions of higher dimensional grammars
Graphs are valuable tools for represent
CSE 473: Pattern Recognition
Template Matching
Template Matching
Typical Applications
Speech Recognition
Motion Estimation in Video Coding
Data Base Image Retrieval
Written Word Recognition
Bioinformatics
Template Matching
The Goal:
Given a set of
CSE 473
Pattern Recognition
Bayesian Classifier
and its Variants
2
Classification Example 1
Given:
A doctor knows that meningitis causes stiff neck 50% of the time
one of every 50,000 persons has meningitis
one of every 20 persons has stiff neck
3
Cla
CSE 473
Pattern Recognition
Bayesian Belief Networks
Let we have l random variables
The joint probability is given by,
p( x1, x2 ,., x) p( x | x 1,., x1 ) p( x 1 | x 2 ,., x1 ) .
.p( x2 | x1 ) p( x1 )
Bayesian Belief Networks
The formula
p( x1, x2 ,., x
Context Dependent Classification
Context Dependent Classification
Recall context free classification
No relation exist among classes
No relation exists among objects (feature vectors)
A new object is classified to any class independent of the
previous
CSE 473: Pattern Recognition
1
Linear Classifier: Introduction
Classifies linearly separable patterns
Assume proper forms for the discriminant
functions
may not be optimal
very simple to use
2
Linear discriminant functions and decisions
surfaces
Defi
CSE 473
Pattern Recognition
Non-Linear Classifiers
Some Non-linear Classifiers
Neural Network
Decision Tree
Non-linear SVM
Non-linear SVM
Transform data into higher dimensional space
Non-linear SVM
Another Example
Non-linear SVM
Another Example
Non-
CSE 473
Pattern Recognition
Lecturer:
Dr. Md. Monirul Islam
Course Outline
Introduction to Pattern Recognition
Bayesian Classification and its variants
Linear Classifiers: Perceptron Algorithms and its Variants,
Linear SVM
Non-Linear Classifiers: Multilay
Theory of Computation
Regular Expressions
1
Introduction
Regular languages are defined and described by
use of finite automata.
In this lecture, we introduce Regular
Expressions as an equivalent way, yet more
elegant, to describe regular languages.
2
From
CSE 211
Theory of Computation
Example 1.21
A language consists of all binary strings that
contain 001 as a substring
Again, it can have a string from earth to moon!
Which information is crucial here?
Let us think
Example of accepted strings
0010, 10
CSE 211: Theory of Computation
Non Deterministic Finite
Automata
1
The Regular Operations (Recap)
Let A and B be 2 regular languages above the
same alphabet, . We define the 3 Regular
Operations:
Union: A B x | x A or x B .
Concatenation: A B xy | x A a
Theory of Computation
Context Free Languages
1
Introduction and Motivation
In this lecture, we turn to Context Free
Grammars (CFG) and Context Free
Languages (CFL).
CFG is a more powerful method of describing
languages
CFG can describe certain features
CSE 211
Theory of Computation
Finite Automata
A Finite Automaton
Figure 1.4 is called the state diagram of M1.
It has three states, labeled q1, q2, and q3.
The start state, q1, is indicated by the arrow pointing at it
The accept state, q2, is the one with
Theory of Computation
Regular Expressions
1
Lemma <If a language L is regular then L can be
described by regular expression.
2
Proof Stages
The proof follows the following stages:
1. Define Generalized Nondeterministic Finite
Automaton (GNFA in short).
2.
Theory of Computation
Non Regular Languages
1
Introduction and Motivation
In this lecture we ask: Are all languages regular?
The answer is negative.
The simplest example is the language
B a b | n 0
Try to think about this language.
n
2
n
Introduction and
CSE 211
Definition of (FAs) Computation
We already know this informally and gone
through the following slides about it
Definition of (FAs) Computation
What happens when this automaton receives an input string,
say, 1101?
1101
Definition of (FAs) Computa
CSE 211: Theory of Computation
Non Deterministic Finite
Automata
1
NFA Example
An automaton over unary alphabet accepting
words whose length is divided either by 2 or
by 3.
2
NFA Example
An automaton over unary alphabet accepting
words whose length is d
CSE 211
Theory of Computation
Introduction
Book
Introduction to the
Theory of
Computation
Third Edition
-Michael Sipser
Further Information
2 Credit Course
2 classes per week
2+1 = 3 Class Tests
Best 2 will be selected
Syllabus
Language theory; Finit
Code Coverage
Code coverage is a measure used to describe the degree to
which the source code of a program is tested by a particular
test suite.
High code coverage means
more thoroughly tested
has a lower chance of containing software bugs
1
Coverage
Software quality control
techniques
Fault avoidance: prevents errors before the
system is released.
reviews, inspections, walkthroughs, development
methodologies, testing, verification
Fault tolerance: enables the system to recover
from (some classes o
What is a UML class diagram?
A UML class diagram is a picture of the classes in an OO
system
their fields and methods
connections between the classes that interact or inherit from each
other
Not represented in a UML class diagram:
details of how the
Equivalence partitioning
Divides the input data of a software unit into partitions of equivalent
data assuming that all the conditions in one partition will be treated
in the same way by the software.
We need to test only one condition from each partiti
Requirement Discovery
RequirementDiscovery
SoftwareEngineering&Information
SystemDesign
CSE307
CSE307Presnetation5
1
Outline
Define system
y
requirements
q
Understand the concept of requirements
management.
Identify
Id if seven fact-finding
f
fi di tec
Systems Analysis
CSE 307
Presentation 4
1
Topic Overview
Define systems analysis
Describe a number of systems analysis approaches for
solving business system problems
Describe the scope definition, problem analysis,
requirements analysis, logical desig
Requirements Discovery Methods
Requirements discovery the process, used by
systems analysts for identifying or extracting system
problems and solution requirements from the user
community.
Approaches include:
Fact Finding
Joint Requirements Planning
C