From 8ddf795590acd75990cca9e149dd0d851b5582a4 Mon Sep 17 00:00:00 2001 From: benjas <909336740@qq.com> Date: Sat, 24 Apr 2021 16:15:18 +0800 Subject: [PATCH] =?UTF-8?q?Add.=20=E5=8D=87=E7=BB=B4=E5=8F=AF=E5=88=86?= =?UTF-8?q?=E9=97=AE=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../7.支持向量机.md | 39 +++++++++++++++++- .../assets/1619232957172.png | Bin 0 -> 4698 bytes .../assets/1619234003387.png | Bin 0 -> 10133 bytes .../assets/1619234073290.png | Bin 0 -> 10795 bytes 4 files changed, 38 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/1619232957172.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1619234003387.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1619234073290.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.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.md index 887dbbc..ef43f88 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.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.md @@ -64,5 +64,42 @@ Knowledge tree -### 多维 +### 升维可分问题 +1. 当有人拿着棍子指着你时,你只能看到棍子的横截面,是一个点,它是一维的。我们无法将两个点区分开来。因为她们重叠了。 + + ![1619232957172](assets/1619232957172.png) + + > 右边红色线表示看的方向 + +2. 当有人拿着棍子指着其它地方,我们能看到整个棍子,这时候是二维的。我们可以一把刀劈开,把红豆和绿豆区分开。所以,红豆和绿豆虽然在一维的时候不能分开,但在二维时线性可分了。 + + ![1619234003387](assets/1619234003387.png) + +3. 也可能二维不可分, 如下图 + + ![1619234073290](assets/1619234073290.png) + +4. 这时候我们可以把棍子看作三维中的棍子,有体积的。如果把棍子立在地上,很有可能红豆靠南侧,绿豆靠北侧,我们像劈柴一样从上至下即可劈开(分开),也一样是线性可分。 + +5. 如果三维还不能线性可分,那就升到思维 + +**总会从某一个维度开始,它变成线性可分了,即只要不断的增加维度(特征)总能区分开来** + +同时,我们发现高维中的超平面,映射到低维空间中时,可能会变成曲线或其它的划分形式。 + +这也就是为什么,在SVM中我们同样使用超平面来划分,SVM可以划分非线性的数据集。 + +它本质上仍然是线性超平面,不过是高维中的线性超平面。 + + + +**那么升维一定会线性可分吗?** + +**会不会升到无穷维了仍然线性不可分?** + +答案是不会的,首先要明白,我们的数据集一定是基于真实的某种分布,分为A类的样本和B类的一定在本质上有区别。只要有区别,就一定可以区分开来,一定在某个高维度上线性可分。 + +**另外,总能上升到有个维度空间中线性可分,无限上升的同时有没有可能在N+1维度又不可分了?** + +不会,随着维度的上升,我们获得的信息越来越多。当第N维的数据已经足够划分时,更多的信息量并不会出现又不可分的情况。 \ 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/1619232957172.png b/机器学习算法理论及应用/李航——统计学习方法/assets/1619232957172.png new file mode 100644 index 0000000000000000000000000000000000000000..1e2b1aa65c598a46e11d705deb579d507ece855b GIT binary patch literal 4698 zcmV-g5~b~lP) z+m9T_b;f_Es(WVd7cQ5ixYSY}9_7JaqQsF!+r*DVN-8K(qC|uSHs`u4akx8W?&mv)4k^pM~P_E2Am{LosF98JGmL2~NnekJ>;W$39v zvLLAlf}%J?iUg#9d6>F)MyGo3$GjNO70h0$CFu#0T5~~A0i)f&t2Cvc{txp3YxIFb zKYK_35BRhec3XY6_g?WG>0J9>cX^+haKA4rg?4L7xk~2hX&dKC{`ua}erD7x1Q3I& zZ@wdv>qo6!9=y@L;{iv*gSKwbMb1oC(RCgKq;<&+Z5K2Rc{nh%HcO}P4vwwszv($x z^uL8446P%mb%wY1+1~C^Q$~=EWgH;(vkUrYM0WRkAI>vwr@yG>qnzipAS+Y`Ww!H5)ECkzAi;JgFzsr^lDyaMWJ zpK5uZ6nglu($e9OnnXD3GV1d(xKnXM%(}g$1fJq14z1^3NAVlGQ2v37Oa2fBi#L zLX9M?tq|Hb@idYIrygSrMk*MI!@b5nZEvA@r?s>#ELj(-B!D(gEpY^q$^k0uD91{Z z<1)vo9wrag7!;2~(R<6>Te`!&r6r<`b%uwAu;bGVO-xZ4ogf)G20*NiSQ8LKO%6Z? 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