1 Pattern Recognition: Statistical and Neural Lonnie C. Ludeman Lecture 3 Sept 16, 2005 Nanjing University of Science & Technology

2 Review 1 Basic Pattern Classification Approaches Statistical Syntactical Neural Networks Fuzzy System Ad Hoc Procedures

3 Review 2 Pattern Recognition Approaches K-Means Clustering Hierarical Clustering Fuzzy Clustering Adaptive Clustering

4 Review 3 DO NOT force the same Solution on all problems

5 Lecture 3 Topics 1. Classification Examples 2. Basic Pattern Classification Structure 3. Statistical Pattern Classification

6 Example 1 : Character Classification Consider the classification of Binary Images of letters a and b of different fonts Given a black and white letter Classify it as coming from Class “A” or Class “B”

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8 Example 2 : String Classification Class 1: { ab n c : n=0, 1, 2, ……….} = { ac, abc, abbc, abbbc, ………} Class 2: { a n bc : n=0, 1, 2, ……….} = { bc, abc, aabc, aaabc, ………} Given a string of symbols from the set S={a,b,c} determine whether the string comes from class 1 or class 2 or neither class abbbbbbc -> Class 1 aaaabc -> Class 2 aabbcc -> neither class Use Syntactical Approach

9 Grammar A grammar G is a four tuple G: (S,T, N, P ) S a start symbol T a set of terminals N a set of nonterminals P a set of production rules For our example: {ab n c : n=0, 1, 2, ……. } S={s} T = {c} N = {a,b} P ={ s->a, a->ab, b->bb, b ->bc }

10 Use Neural Networks

11 Example 4: Statistical Method

12 Basic Pattern Classification Structure

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17 Decision Rule for Deciding a “0” or a “1” If y 1 > T decide “0” y 1 < T decide “1” y 1 = T flip an honest coin decide “0”if it comes up heads decide “1” if it comes up tails

18 Lecture 3 Summary 1. Classification Examples 2. Basic Pattern Classification Structure 3. Statistical Pattern Classification