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

runs independently and isolated. Developers can choose modules to deploy based on their own needs. Support multiple platforms: Baetyl supports multiple hardware and software platforms, such as X86 and ARM official module baetyl-hub provides message subscription and publishing functions based on the MQTT protocol [http://docs.oasis-open.org/mqtt/mqtt/v3.1.1/os/mqtt- v3.1.1-os.html], and supports four access and the engine is responsible for starting and stopping the process. NOTE: Process mode does not support resource restrictions, no need to expose ports, map devices. At present, the above two modes basically

. . . . . . . . . . . . . . . . . . . . . . . . . . 111 16 Customize Runtime Module 115 16.1 Protocol Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . independently and isolated. Developers can choose modules to deploy based on their own needs. • Support multiple platforms: Baetyl supports multiple hardware and software platforms, such as X86 and ARM official module baetyl-hub provides message subscription and publishing functions based on the MQTT protocol, and supports four access methods: TCP, SSL, WS, and WSS; • The official module baetyl-remote-mqtt

third-party libraries for Node runtime Import Lodash third-party libraries Customize Runtime Module Protocol Convention Configuration Convention Start/Stop Convention Customize Module Directory Convention runs independently and isolated. Developers can choose modules to deploy based on their own needs. Support multiple platforms: Baetyl supports multiple hardware and software platforms, such as X86 and ARM official module baetyl-hub provides message subscription and publishing functions based on the MQTT protocol [http://docs.oasis-open.org/mqtt/mqtt/v3.1.1/os/mqtt- v3.1.1-os.html], and supports four access

. . . . . . . . . . . . . . . . . . . . . . . . . . 101 15 Customize Runtime Module 105 15.1 Protocol Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . independently and isolated. Developers can choose modules to deploy based on their own needs. • Support multiple platforms: Baetyl supports multiple hardware and software platforms, such as X86 and ARM official module baetyl-hub provides message subscription and publishing functions based on the MQTT protocol, and supports four access methods: TCP, SSL, WS, and WSS; • The official module baetyl-remote-mqtt

The current implementations are: Hive Thrift Protocol A HiveServer2-compatible interface that allows end users to use a thrift client(cross-language support, both tcp and http), a Java Database Connectivity(JDBC) easy submission of self-contained applications for batch processing, such as Spark jobs. MySQL Protocol A MySQL-compatible interface that allows end users to use MySQL Connectors, such as Connector/J creating a session with engines. externals - engines: contains all kinds of SQL engines that we support licenses: a bunch of licenses included. jars: packages needed by the Kyuubi server. logs: where

The current implementations are: Hive Thrift Protocol A HiveServer2-compatible interface that allows end users to use a thrift client(cross-language support, both tcp and http), a Java Database Connectivity(JDBC) easy submission of self-contained applications for batch processing, such as Spark jobs. MySQL Protocol A MySQL-compatible interface that allows end users to use MySQL Connectors, such as Connector/J creating a session with engines. externals - engines: contains all kinds of SQL engines that we support licenses: a bunch of licenses included. jars: packages needed by the Kyuubi server. logs: where the

The current implementations are: Hive Thrift Protocol A HiveServer2-compatible interface that allows end users to use a thrift client(cross-language support, both tcp and http), a Java Database Connectivity(JDBC) easy submission of self-contained applications for batch processing, such as Spark jobs. MySQL Protocol A MySQL-compatible interface that allows end users to use MySQL Connectors, such as Connector/J creating a session with engines. externals - engines: contains all kinds of SQL engines that we support licenses: a bunch of licenses included. jars: packages needed by the Kyuubi server. logs: where the

The current implementations are: Hive Thrift Protocol A HiveServer2-compatible interface that allows end users to use a thrift client(cross-language support, both tcp and http), a Java Database Connectivity(JDBC) easy submission of self-contained applications for batch processing, such as Spark jobs. MySQL Protocol A MySQL-compatible interface that allows end users to use MySQL Connectors, such as Connector/J creating a session with engines. externals - engines: contains all kinds of SQL engines that we support licenses: a bunch of licenses included. jars: packages needed by the Kyuubi server. logs: where the