Lecture Notes on Support Vector Machine Feng Li fli@sdu.edu.cn Shandong University, China 1 Hyperplane and Margin In a n-dimensional space, a hyper plane is defined by ωT x + b = 0 (1) where ω ∈ Rn the margin is defined as γ = min i γ(i) (6) 1 ? ? ! ? ! Figure 1: Margin and hyperplane. 2 Support Vector Machine 2.1 Formulation The hyperplane actually serves as a decision boundary to differentiating samples are so-called support vector, i.e., the vectors “supporting” the margin boundaries. We can redefine ω by w = � s∈S αsy(s)x(s) where S denotes the set of the indices of the support vectors 4 Kernel

Lecture 6: Support Vector Machine Feng Li Shandong University fli@sdu.edu.cn December 28, 2021 Feng Li (SDU) SVM December 28, 2021 1 / 82 Outline 1 SVM: A Primal Form 2 Convex Optimization Review parallely along ω (b < 0 means in opposite direction) Feng Li (SDU) SVM December 28, 2021 3 / 82 Support Vector Machine A hyperplane based linear classifier defined by ω and b Prediction rule: y = sign(ωTx Scaling ! and " such that min& ' & !() & + " = 1 Feng Li (SDU) SVM December 28, 2021 14 / 82 Support Vector Machine (Primal Form) Maximizing 1/∥ω∥ is equivalent to minimizing ∥ω∥2 = ωTω min ω,b ωTω

pandas: powerful Python data analysis toolkit Release 0.19.0 Wes McKinney & PyData Development Team Oct 02, 2016 CONTENTS 1 What’s New 3 1.1 v0.19.0 (October 2, 2016) . . . . . . . . . . . . . . time-series aware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 read_csv has improved support for duplicate column names . . . . . . . . . . . . . . . . . 9 read_csv supports parsing Categorical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Series.tolist() will now return Python types . . . . . . . . . . . . . . . . . . . . . . 18 Series operators for different indexes . .

pandas: powerful Python data analysis toolkit Release 0.19.1 Wes McKinney & PyData Development Team Nov 03, 2016 CONTENTS 1 What’s New 3 1.1 v0.19.1 (November 3, 2016) . . . . . . . . . . . . . time-series aware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 read_csv has improved support for duplicate column names . . . . . . . . . . . . . . . . . 10 read_csv supports parsing Categorical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Series.tolist() will now return Python types . . . . . . . . . . . . . . . . . . . . . . 19 Series operators for different indexes . .

pandas: powerful Python data analysis toolkit Release 0.20.3 Wes McKinney & PyData Development Team Jul 07, 2017 CONTENTS 1 What’s New 3 1.1 v0.20.3 (July 7, 2017) . . . . . . . . . . . . . . . Enhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.1.5 Better support for compressed URLs in read_csv . . . . . . . . . . . . . . . . . 13 1.3.1.6 Pickle file I/O now now supports compression . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1.7 UInt64 Support Improved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.1.8 GroupBy on Categoricals

pandas: powerful Python data analysis toolkit Release 1.4.2 Wes McKinney and the Pandas Development Team Apr 02, 2022 CONTENTS 1 Getting started 3 1.1 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933 2.22.4 Setting startup options in Python/IPython environment . . . . . . . . . . . . . . . . . . . . 934 2.22.5 Frequently used options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2849 4.12.2 Python support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2849 4.13

pandas: powerful Python data analysis toolkit Release 0.13.1 Wes McKinney & PyData Development Team February 03, 2014 CONTENTS 1 What’s New 3 1.1 v0.13.1 (February 3, 2014) . . . . . . . . . . . October 9, 2011) . . . . . . . . . . . . . . . . . . . . . . . . 95 2 Installation 97 2.1 Python version support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 i 4.3 Getting Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4

pandas: powerful Python data analysis toolkit Release 0.15.2 Wes McKinney & PyData Development Team December 11, 2014 CONTENTS 1 What’s New 3 1.1 v0.15.2 (December 12, 2014) . . . . . . . . . . October 9, 2011) . . . . . . . . . . . . . . . . . . . . . . . . 166 2 Installation 169 2.1 Python version support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4.3 Getting Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4

pandas: powerful Python data analysis toolkit Release 1.0.5 Wes McKinney and the Pandas Development Team Jun 17, 2020 CONTENTS 1 Getting started 3 1.1 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807 2.17.3 Setting startup options in Python/IPython environment . . . . . . . . . . . . . . . . . . . . 808 2.17.4 Frequently Used Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2384 4.7.2 Python Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2385 4.8 Roadmap

pandas: powerful Python data analysis toolkit Release 0.25.3 Wes McKinney& PyData Development Team Nov 02, 2019 CONTENTS i ii pandas: powerful Python data analysis toolkit, Release 0.25.3 Date: Issues & Ideas | Q&A Support | Mailing List pandas is an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language language. See the overview for more detail about whats in the library. CONTENTS 1 pandas: powerful Python data analysis toolkit, Release 0.25.3 2 CONTENTS CHAPTER ONE WHATS NEW IN 0.25.2 (OCTOBER 15