Contents 1 Introduction 5 2 Basic Discriminants 2.1 Linear Discriminant Analysis for Two Populations 2.1.1 Classification of Normal Populations when1=∑2=∑...·........ 9 2.2 Fisher's Discriminant Analysis·.....·...·.·.················ 12 2.3 Further Concerns....··· 14 3 Support Vector Machines 17 3.1 Lagrange Multipliers。·.······························· 17 3.2 Hard Margin Support Vector Machines.····.·.·.····.··. 19 3.3 L1 Soft Margin Support Vector Machines..:··.···..·········.·· 25 3.4 Kernel Methods.·············· 28 3.5 Further Concerns .. 33 4 Applications in R 35 4.1 LDA in R...·..·. 。。 36Contents 1 Introduction 5 2 Basic Discriminants 7 2.1 Linear Discriminant Analysis for Two Populations . . . . . . . . . . . . . . . . . . . 7 2.1.1 Classification of Normal Populations when Σ1 = Σ2 = Σ . . . . . . . . . . . . 9 2.2 Fisher’s Discriminant Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Further Concerns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Support Vector Machines 17 3.1 Lagrange Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Hard Margin Support Vector Machines . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 L1 Soft Margin Support Vector Machines . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Kernel Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.5 Further Concerns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Applications in R 35 4.1 LDA in R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3