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

session with Spark applications. • externals – engines: contains all kinds of SQL engines that we support, e.g. Apache Spark, Apache Flink(coming soon). – spark-3.0.1-bin-hadoop2.7: a pre-downloaded official -version java version "11.0.5" 2019-10-15 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.5+10-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.5+10-LTS, mixed mode) The recommended place to /usr/share/hue/desktop/conf/hue.ini > hue.ini 1. Modify the hue.ini [beeswax] # Kyuubi 1.1.x support thrift version from 1 to 10 thrift_version=7 # change to your username to avoid permissions issue

session with Spark applications. • externals – engines: contains all kinds of SQL engines that we support, e.g. Apache Spark, Apache Flink(coming soon). – spark-3.0.1-bin-hadoop2.7: a pre-downloaded official -version java version "11.0.5" 2019-10-15 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.5+10-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.5+10-LTS, mixed mode) The recommended place to /usr/share/hue/desktop/conf/hue.ini > hue.ini 1. Modify the hue.ini [beeswax] # Kyuubi 1.1.x support thrift version from 1 to 10 thrift_version=7 # change to your username to avoid permissions issue

a session with Spark applications. externals engines: contains all kinds of SQL engines that we support, e.g. Apache Spark, Apache Flink(coming soon). spark-3.0.1-bin-hadoop2.7: a pre-downloaded official -version java version "11.0.5" 2019-10-15 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.5+10-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.5+10-LTS, mixed mode) The recommended place to /usr/share/hue/desktop/conf/hue.ini > hue.ini 1. Modify the hue.ini [beeswax] # Kyuubi 1.1.x support thrift version from 1 to 10 thrift_version=7 # change to your username to avoid permissions issue

a session with Spark applications. externals engines: contains all kinds of SQL engines that we support, e.g. Apache Spark, Apache Flink(coming soon). spark-3.0.1-bin-hadoop2.7: a pre-downloaded official -version java version "11.0.5" 2019-10-15 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.5+10-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.5+10-LTS, mixed mode) The recommended place to /usr/share/hue/desktop/conf/hue.ini > hue.ini 1. Modify the hue.ini [beeswax] # Kyuubi 1.1.x support thrift version from 1 to 10 thrift_version=7 # change to your username to avoid permissions issue

Availability Kyuubi, Release 1.4.1-incubating – engines: contains all kinds of SQL engines that we support, e.g. Apache Spark, Apache Flink(coming soon). • licenses: a bunch of licenses included. • jars: -version java version "11.0.5" 2019-10-15 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.5+10-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.5+10-LTS, mixed mode) The recommended place to /usr/share/hue/desktop/conf/hue.ini > hue.ini 1. Modify the hue.ini [beeswax] # Kyuubi 1.1.x support thrift version from 1 to 10 thrift_version=7 # change to your username to avoid permissions issue

High Availability Kyuubi, Release 1.3.0 – engines: contains all kinds of SQL engines that we support, e.g. Apache Spark, Apache Flink(coming soon). • licenses: a bunch of licenses included. • jars: -version java version "11.0.5" 2019-10-15 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.5+10-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.5+10-LTS, mixed mode) The recommended place to /usr/share/hue/desktop/conf/hue.ini > hue.ini 1. Modify the hue.ini [beeswax] # Kyuubi 1.1.x support thrift version from 1 to 10 thrift_version=7 # change to your username to avoid permissions issue

a session with Spark applications. externals engines: contains all kinds of SQL engines that we support, e.g. Apache Spark, Apache Flink(coming soon). licenses: a bunch of licenses included. jars: packages -version java version "11.0.5" 2019-10-15 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.5+10-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.5+10-LTS, mixed mode) The recommended place to /usr/share/hue/desktop/conf/hue.ini > hue.ini 1. Modify the hue.ini [beeswax] # Kyuubi 1.1.x support thrift version from 1 to 10 thrift_version=7 # change to your username to avoid permissions issue

a session with Spark applications. externals engines: contains all kinds of SQL engines that we support, e.g. Apache Spark, Apache Flink(coming soon). licenses: a bunch of licenses included. jars: packages -version java version "11.0.5" 2019-10-15 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.5+10-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.5+10-LTS, mixed mode) The recommended place to /usr/share/hue/desktop/conf/hue.ini > hue.ini 1. Modify the hue.ini [beeswax] # Kyuubi 1.1.x support thrift version from 1 to 10 thrift_version=7 # change to your username to avoid permissions issue