在soft-margin SVM中C表示衡量要分离面间隔最胖还是要犯错最少。 当C大的时候，我们希望犯错尽量少，当C小的时候，我们希望分离面要胖胖的。 soft-margin SVM仍然是QP问题，这时候有 \tilde{d}+1+N 个变量，和2N个限制条件。

2024年2月29日 · Two approaches to margins in SVMs are Hard Margin and Soft Margin. In a hard margin SVM, the objective is to identify a hyperplane that completely separates data points belonging to different classes, ensuring a clear demarcation …

2018年8月3日 · Soft Margin SVM 去除异常样本的方法： 扩大该限定条件，设定容错空间 ，允许个别极端的或者错误的样本点，分布在支撑向量所在直线与决策边界之间的区域；

• SVM became famous when, using images as input, it gave accuracy comparable to neural-network with hand-designed features in a handwriting recognition task

即使svm试图做到最大间隔，但仍然可能过拟合。 原因之一是使用了如rbf核函数的强大的特征转换，另一个原因是—— 坚持将所有资料分开(separable) 。 如下图所示：

In machine learning, support vector machines (SVMs, also support vector networks[1]) are supervised max-margin models with associated learning algorithms that analyze data for classification and regression analysis.

为了解决这一问题，软间隔SVM（Soft Margin SVM）应运而生，通过引入 松弛变量 允许部分样本点违反间隔要求，同时引入 正则化参数 控制违反间隔的程度。 本文将详细推导软间隔SVM的数学模型，并从对偶问题的角度深入探讨 拉格朗日乘子 α的取值与样本点是否为支持向量之间的关系，特别是分析当α_i* = C时松弛变量ξ_i的取值及其对分类结果的影响。 1. 原始（Primal）优化问题. 软间隔SVM的目标是在最大化分类间隔的同时，允许部分样本点违反间隔要求。 其优化问题 …

2025年2月13日 · The difference between a hard margin and a soft margin in SVMs lies in the separability of the data. If our data is linearly separable, we go for a hard margin. However, if this is not the case, it won’t be feasible to do that.

soft margin classifier does exactly this. Rather than seeking the largest possible margin so that every observation is not only on the correct side of the hyperplane but also on the correct side of the margin, we instead allow some observations to be on the incorrect side of the margin, or even the incorrect side of the hyperplane.

2019年4月30日 · The goal of this post is to explain the concepts of Soft Margin Formulation and Kernel Trick that SVMs employ to classify linearly inseparable data. If you want to get a refresher on the basics of SVM first, I’d recommend going through the following posts.