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What is Pattern Recognition Recognizing the fish! 1
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WHAT İS PATTERN Structures regulated by rules Goal:Represent empirical knowledge in mathematical forms the Mathematics of Perception Need: Algebra, probability theory, graph theory
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All flows! Heraclitos It is only the invariance, the permanent facts, that enable us to find the meaning in a world of flux. We can only perceive variances Our aim is to find the invariant laws of our varying obserbvations Pattern Recognition
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Learning vs Recognition Learning: Find the Mathematical Model of a class, using data Recognition: Use that model to recognize the unknown object 4
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Two Schools of Thought 5 Statistical Pattern Recognition: Express the image class by a random variable corresponding to class features and model the class by finding the probability density fonction Structural Pattern Recognition Express the image class by a set of picture primitives. Model the class by finding the relationship among the primitives using grammars or a graphs
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1. STATISTICAL PR: ASSUMPTION SOURCE: Hypothesis Classes Obljects CHANNEL: Noisy OBSERVATION: Multiple sensor Variations
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Probability Theory Apples and Oranges
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Probability Theory Marginal Probability Conditional Probability Joint Probability Red Urn:x1 C1 samples Blue urn:x2 c2 samples Oranges: y161 Apples: y221
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Probability Theory Sum Rule Product Rule
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The Rules of Probability Sum Rule Product Rule
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Bayes’ Theorem posterior likelihood × prior
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Probability Densities
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Expectations Conditional Expectation (discrete) Approximate Expectation (discrete and continuous)
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Variances and Covariances
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1. BASİC CONCEPTS 15 A class is a set of objects having some important properties in common A feature extractor is a program that inputs the data (image) and extracts features that can be used in classification. A classifier is a program that inputs the feature vector and assigns it to one of a set of designated classes or to the “reject” class. With what kinds of classes do you work?
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Feature Vector Representation X=[x1, x2, …, xn], each xj a real number xj may be an object measurement xj may be count of object parts Example: object rep. [#holes, #strokes, moments, …] 16
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Possible Features for char rec. 17
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Modeling the source Functions f(x, K) perform some computation on feature vector x Knowledge K from training or programming is used Final stage determines class 18
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Two Schools of Thought 19 Statistical Pattern Recognition: Express the image class by a random variable corresponding to class features and model the class by finding the probability density fonction Structural Pattern Recognition Express the image class by a set of picture primitives. Model the class by finding the relationship among the primitives using grammars or a graphs
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Classifiers often used in CV 20 Nearest Mean Classifier Nearest neighbor classifier Bayesian Classifiers ---------------------------------- Decision Tree Classifiers Artificial Neural Net Classifiers Support Vector Machines
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1. Classification using nearest class mean Compute the Euclidean distance between feature vector X and the mean of each class. Choose closest class, if close enough (reject otherwise) 21
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Nearest mean might yield poor results with complex structure Class 2 has two modes; where is its mean? But if modes are detected, two subclass mean vectors can be used 22
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Scaling coordinates by Covariance Matrix Define Mahalanobis Distance between two vectors x-x c = [ x-x c ] T C -1 [x-x c ] Where covariance matrix C = 1/N { (x i – x c ) T (x i – x c )} 23
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2. Nearest Neighbor Classification –The k – nearest-neighbor rule Goal: Classify x by assigning it the label most frequently represented among the k nearest samples and use a voting scheme
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Pattern Classification, Chapter 4 (Part 2)25
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Pattern Classification, Chapter 4 (Part 2) 26
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Bayes Decision Making Thomas Bayes 1701--1761 27 Goal: Given the training data compute max P(wi/x) i
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Bayesian decision-making 28
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Bayes 29
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Normal distribution 0 mean and unit std deviation Table enables us to fit histograms and represent them simply New observation of variable x can then be translated into probability Stockman CSE803 Fall 200830
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Parametric Models can be used Stockman CSE803 Fall 200831
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Cherry with bruise Intensities at about 750 nanometers wavelength Some overlap caused by cherry surface turning away Stockman CSE803 Fall 200832
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Information Theory:Claude Shannon 1916- 2001 Goal: Find the amount of information carried by a specific value of a r.v. Need something intuitive.
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Information Theory: C. Shannon Information: giving form or shape to the mind Assumptions: Source Receiver Information is the quality of a messagemessage it may be a truth or a lie, if the amount of information in the received message increases, the message is more accurate. Need a common alphabet to communucate message
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Quantification of information.information Given r.v. X and p(x), what is the amount of information when we receive an outcome of x? Self Information h(x)= -log p (x) Low probability Surprise High info Base e: nats Base 2: bits
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Entropy: Average of self information needed to specify the state of a random variable. 36 Given a set of training vectors S, if there are c classes, Entropy(S) = -pi log (pi) Where pi is the proportion of category i examples in S. i=1 c 2 If all examples belong to the same category, the entropy is 0. If the examples are equally mixed (1/c examples of each class), the entropy is a maximum at 1.0. e.g. for c=2, -.5 log.5 -.5 log.5 = -.5(-1) -.5(-1) = 1 22
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Entropy: Why does entropy measures information? İt makes sense intuitively “Nobody knows what entropy really is, so in any discussion you will always have an advan tage". Von Neumann
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Entropy
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2. Structural Techniques: Goal: Represent the classes by graphs 40
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Training the system: Given the training data Step 1: Process the image –Remove noise –binarize –Find skeleton –Normalize the size Step 2: Extract features –Side, lake, bay Step 3: Represent the character by a graph 41
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3. Represent the character by a graph: G(N, A) 42
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Training: represent each class by a graph Recognition: Use graph similarities to assign a label 43
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Decision Trees: 44 #holes L-W ratio #strokes best axis direction #strokes - / 1 x w 0 A 8 B 0 1 2 < t t 2 4 01 0 60 90 0 1
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Binary decision tree 45
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Entropy-Based Automatic Decision Tree Construction 46 Node 1 What feature should be used? What values? Training Set S x1=(f11,f12,…f1m) x2=(f21,f22, f2m). xn=(fn1,f22, f2m) Quinlan suggested information gain in his ID3 system and later the gain ratio, both based on entropy.
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Information Gain 47 The information gain of an attribute A is the expected reduction in entropy caused by partitioning on this attribute. Gain(S,A) = Entropy(S) - ----- Entropy(Sv) v Values(A) |Sv| |S| where Sv is the subset of S for which attribute A has value v. Choose the attribute A that gives the maximum information gain.
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Information Gain (cont) 48 Attribute A v1vk v2 Set S repeat recursively Information gain has the disadvantage that it prefers attributes with large number of values that split the data into small, pure subsets. S={s S | value(A)=v1}
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Gain Ratio 49 Gain ratio is an alternative metric from Quinlan’s 1986 paper and used in the popular C4.5 package (free!). GainRatio(S,A) = ------------------ Gain(S,a) SplitInfo(S,A) SplitInfo(S,A) = - ----- log ------ |Si| |S| |Si| |S| where Si is the subset of S in which attribute A has its ith value. 2 i=1 ni SplitInfo measures the amount of information provided by an attribute that is not specific to the category.
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Information Content 50 Note: A related method of decision tree construction using a measure called Information Content is given in the text, with full numeric example of its use.
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Artificial Neural Nets 51 Artificial Neural Nets (ANNs) are networks of artificial neuron nodes, each of which computes a simple function. An ANN has an input layer, an output layer, and “hidden” layers of nodes............. Inputs Outputs
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Node Functions 52 x1x2xjxnx1x2xjxn output output = g ( xj * w(j,i) ) Function g is commonly a step function, sign function, or sigmoid function (see text). neuron i w(1,i) w(j,i)
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Neural Net Learning 55 That’s beyond the scope of this text; only simple feed-forward learning is covered. The most common method is called back propagation. There are software packages available. What do you use?
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How to Measure PERFORMANCE Classification rate: Count the number of correctly classified sample in wi, ci, find the frequencey classification rate=ci/N 56
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2-Class problem Estimated Class 1 (var)Estimated Class 1 (yok) True Class 1 (var)True hit, Correct Detection False dismissal, false negative True Class 2 (yok)False positive False alarm, True dismissal 57
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Receiver Operating Curve ROC Plots correct detection rate versus false alarm rate Generally, false alarms go up with attempts to detect higher percentages of known objects 58
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Presicion- Recall in CBIR or DR 59
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Confusion matrix shows empirical performance 60
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