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

network layers, deep learning optimizers, data loading utilities, and multi-gpu, and multi-node support. Functions are executed immediately instead of enqueued in a static graph, improving ease of use begin Before you can run an NGC deep learning framework container, your Docker ® environment must support NVIDIA GPUs. To run a container, issue the appropriate command as explained in Running A Container Container and specify the registry, repository, and tags. About this task On a system with GPU support for NGC containers, when you run a container, the following occurs: ‣ The Docker engine loads the image

Experimental support Experimental support Experimental support Supported planned post 2.0 Supported Custom training loop Experimental support Experimental support Support planned post post 2.0 Support planned post 2.0 No support yet Supported Estimator API Limited Support Not supported Limited Support Limited Support Limited Support Limited Support SavedModel：生产级 TensorFlow 模型格式

支持向量机概述 01 支持向量机概述 02 线性可分支持向量机 03 线性支持向量机 04 线性不可分支持向量机 4 1.支持向量机概述 支 持 向 量 机 （ Support Vector Machine, SVM ） 是 一 类 按 监 督 学 习 （ supervised learning）方式对数据进行二元分类的广义线性 分类器（generalized linear 误的情 况。软间隔，就是允许一定量的样本分类错误。 软间隔 硬间隔 线性可分 线性不可分 6 支持向量 1.支持向量机概述 算法思想 找到集合边缘上的若干数据（称为 支持向量（Support Vector）） ，用这些点找出一个平面（称为决 策面），使得支持向量到该平面的 距离最大。 距离 7 1.支持向量机概述 背景知识 任意超平面可以用下面这个线性方程来描述： 大于50000，则使用支 持向量机会非常慢，解决方案是创造、增加更多的特征，然后使用逻辑回归 或不带核函数的支持向量机。 28 参考文献 [1] CORTES C, VAPNIK V. Support-vector networks[J]. Machine learning, 1995, 20(3): 273–297. [2] Andrew Ng. Machine Learning[EB/OL]

state that in this book, we have chosen to work with Tensorflow 2.0 (TF) because it has exhaustive support for building and deploying efficient models on devices ranging from TPUs to edge devices at the time would lead to a 32 / 8 = 4x reduction in space. This fits in well since there is near-universal support for unsigned and signed 8-bit integer data types. 4. The quantized weights are persisted with the addition and subtraction, these gains need to be evaluated in practical settings because they require support from the underlying hardware. Moreover, multiplications and divisions are cheaper at lower precisions

and the TFLite model. Unfortunately we do not (as of the time of writing this chapter) have the support to natively realize the size and latency gains from the clustering. However, we can use gzip to exploit sparse, the matrix multiplication can be performed in half the time. With the advent of hardware support for sparsity and many industrial and academic use cases reporting significant improvements, we feel consecutive values of (the number of bits allocated per value). With that being said, first-class support for clustering in machine learning frameworks like Tensorflow and PyTorch is pending as of the time

later (no GPU support) • Raspbian 9.0 or later �� pip �� TensorFlow tensorflow —Current release for CPU-only (recommended for beginners) tensorflow-gpu —Current release with GPU support (Ubuntu and Windows) Windows) tf-nightly —Nightly build for CPU-only (unstable) tf-nightly-gpu —Nightly build with GPU support (unstable, Ubuntu and Windows) “Hello TensorFlow” Try it “Hello TensorFlow” “Hello TensorFlow”

with the existing resource constraints. Similarly, having models directly on-device would also support new offline applications of these models. As an example, the Google Translate application supports example, to get size and latency improvements with quantized models, we need the inference platform to support common neural net layers in quantized mode. TFLite supports quantized models, by allowing export with libraries like GEMMLOWP and XNNPACK for fast inference. Similarly, PyTorch uses QNNPACK to support quantized operations. Refer to Figure 1-17 for an illustration of how infrastructure fits in training

branches to identical channel dimensions to support addition combination operation. Next, we project the branches to identical feature space as well to support concatenation combination operation. The two augmentation saw extensive growth. Popular deep learning frameworks such as PyTorch and Tensorflow added support for data cleaning and augmentation but they left the responsibilities of choosing appropriate parameters