Spoken Dialog Systems and Voice XML : Intro to Pattern Recognition. Esther Levin Dept of Computer Science CCNY. Some materials used in this course were taken from the textbook “Pattern Classification” by Duda et al., John Wiley & Sons, 2001
Dept of Computer Science
Some materials used in this course were taken from the textbook “Pattern Classification” by Duda et al., John Wiley & Sons, 2001
with the permission of the authors and the publisher
Genome Sequence MatchingMore Pattern Recognition Applications
“A pattern is the opposite of a chaos; it is an entity vaguely defined, that could be given a name.”
A v t u I h D U w K
Ç ş ğ İ ü Ü Ö Ğ
This is the set of all suggested features to explore for use in our classifier!
Select the length of the fish as a possible feature for discrimination
The length is a poor feature alone!
Select the lightness as a possible feature.
Task of decision theory
Fish x = [x1, x2]
2 ones we already have. A precaution should be taken not to reduce the performance by adding such
Issue of generalization!
2 aim of designing a classifier is to correctly classify novel input
Observe: Can do much better with two features
Entities are not to be multiplied without necessity
William of Occam
3 aim of designing a classifier is to correctly classify novel input
4 aim of designing a classifier is to correctly classify novel input
How do we know when we have collected an adequately large and representative set of examples for training and testing the system?
Depends on the characteristics of the problem domain. Simple to extract, invariant to irrelevant transformation insensitive to noise.
Unsatisfied with the performance of our linear fish classifier and want to jump to another class of model
Use data to determine the classifier. Many different procedures for training classifiers and choosing models
Measure the error rate (or performance) and switch from one set of features & models to another one.
What is the trade off between computational ease and performance?
(How an algorithm scales as a function of the number of features, number or training examples, number patterns or categories?)
Do all these images represent an `A'?
How do we know what features to select, and how do we select them…?
What type of classifier shall we use. Is there best classifier…?
How do we train…?
How do we combine prior knowledge with
How do we evaluate our performance
Validate the results. Confidence in decision?
is not singular
n-th order polynomial, with n roots.
The principles of probability theory, describing the behavior of systems with random characteristics, are of fundamental importance to pattern recognition.
Tables of occurrences and relative frequencies
It is often helpful when calculating conditional probabilities to create a simple table containing the number of occurrences of each outcome, or the relative frequencies of each outcome, for each of the independent variables. The tables below illustrate the use of this method for the cookies.
The table on the right is derived from the table on the left by dividing each entry by the total number of cookies under consideration, or 80 cookies.
2. 0.07+0.04 +0.03 +0.18 =0.32Cars are assembled in four possible locations. Plant I supplies 20% of the cars; plant II, 24%; plant III, 25%; and plant IV, 31%. There is 1 year warrantee on every car.
The company collected data that shows
P(claim| plant I) = 0.05; P(claim|Plant II)=0.11;
P(claim|plant III) = 0.03; P(claim|Plant IV)=0.18;
Cars are sold at random.
An owned just submitted a claim for her car. What are the posterior probabilities that this car was made in plant I, II, III and IV?
P(claim|plant II)P(plant II) +
P(claim|plant III)P(plant III) +
P(claim|plant IV)P(plant IV) =0.0687
= P(claim|plant I) * P(plant I)/P(claim) = 0.146
= P(claim|plant II) * P(plant II)/P(claim) = 0.384
= P(claim|plant III) * P(plant III)/P(claim) = 0.109
= P(claim|plant IV) * P(plant IV)/P(claim) = 0.361
3. It is known that 1% of population suffers from a particular disease. A blood test has a 97% chance to identify the disease for a diseased individual, by also has a 6% chance of falsely indicating that a healthy person has a disease.
a. What is the probability that a random person has a positive blood test.
b. If a blood test is positive, what’s the probability that the person has the disease?
c. If a blood test is negative, what’s the probability that the person does not have the disease?Example 3
Examples: uniform distribution, dirac distribution; particular disease. A blood test has a 97% chance to identify the disease for a diseased individual, by also has a 6% chance of falsely indicating that a healthy person has a disease.
Mutual information: reduction in uncertainty about one variable due to knowledge of other variable.