From 3f8595aa35f490b0d2215e5bcd242ea356bd486f Mon Sep 17 00:00:00 2001 From: benjas <909336740@qq.com> Date: Wed, 28 Apr 2021 14:09:13 +0800 Subject: [PATCH] =?UTF-8?q?Ddd.=20=E5=87=A0=E4=BD=95=E5=87=BD=E6=95=B0?= =?UTF-8?q?=E9=97=B4=E9=9A=94=E6=8E=A8=E5=AF=BC?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../7.支持向量机——升维打击.md | 55 +++++++++++++++++- .../assets/1619585510005.png | Bin 0 -> 21960 bytes .../assets/1619585515305.png | Bin 0 -> 11525 bytes .../assets/1619585608306.png | Bin 0 -> 66185 bytes .../assets/1619585628157.png | Bin 0 -> 41217 bytes .../assets/1619585642761.png | Bin 0 -> 36387 bytes 6 files changed, 54 insertions(+), 1 deletion(-) create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1619585510005.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1619585515305.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1619585608306.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1619585628157.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1619585642761.png diff --git a/机器学习算法理论及应用/李航——统计学习方法/7.支持向量机——升维打击.md b/机器学习算法理论及应用/李航——统计学习方法/7.支持向量机——升维打击.md index 7c028ed..21b8183 100644 --- a/机器学习算法理论及应用/李航——统计学习方法/7.支持向量机——升维打击.md +++ b/机器学习算法理论及应用/李航——统计学习方法/7.支持向量机——升维打击.md @@ -114,4 +114,57 @@ Summarization 2. 构造出来的超平面使得其与最近的点的距离最大。 3. SVM也可划分非线性数据集。 4. 它通过高维中的线性超平面再低维中的投影来完成非线性的划分。因此从直观上来讲,我们的模型必定有一个升维的操作。 -5. 这是总体的概念。 \ No newline at end of file +5. 这是总体的概念。 + + + +### 支持向量机 + +Support vector machines + +函数间隔:![1619585515305](assets/1619585515305.png) + +几何间隔:![1619585510005](assets/1619585510005.png) + +这里使用的是几何间隔,前面讲到这里就不重复了 + + + +**最大间隔分离超平面:** + +目前讲的是线性超平面 + +![1619585608306](assets/1619585608306.png) + +> 图中心,虚线到实线的距离我们称之为γ,我们要做的是最大化γ,使得这个超平面调整为γ的一个最大值,等价于找到了最优的超平面 + +![1619585628157](assets/1619585628157.png) + +> γ:表示几何间隔 +> +> s.t. 表示约束 +> +> yi:正负1。保证算出来的数始终是大于0的,如上图中“圈”表示+1的样本“×”表示负一的样本,那么某个“圈”是正数,乘以上方的yi(正数),正正得正,某个点“×”是负数,乘以下方的yi(负数),负负得正。 + +**简化上方的式子:** + +我们知道max的γ是几何间隔,那么我们变换一下 +$$ +\frac{\hat{γ}}{||w||} 其中,\hat{γ}表示函数间隔,除以w二范数就是几何间隔了。 +$$ + +$$ +既然我们最终是\frac{\hat{γ}}{||w||} ,那么式子我们可以简化成 +$$ + +$$ +y_i(wx_i+b)≥\hat{γ},其中\hat{γ}是函数间隔 +$$ + + + + + + + +![1619585642761](assets/1619585642761.png) \ No newline at end of file diff --git a/机器学习算法理论及应用/李航——统计学习方法/assets/1619585510005.png 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