|
方法：<span class="MathJax" id="MathJax-Element-722-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk近邻法
适用问题：多类分类，回归
模型特点：特征空间，样本点
模型类型：判别模型 一、介绍<span class="MathJax" id="MathJax-Element-808-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk近邻法是一种基本分类与回归方法。思想是给定一个训练数据集，其中样本类别给定，分类时，对新的样本，根据其<span class="MathJax" id="MathJax-Element-809-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk个最近邻的训练实例的类别，通过多数表决等方式进行预测。 引用百度来的一张图，直观理解下k近邻算法： ![]()
目标是判断中心绿色点的类别，当<span class="MathJax" id="MathJax-Element-810-Frame" tabindex="0" data-mathml="k=3" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">k=3k=3时，所形成的圆内红色三角形数量最多，则目标为红色类，当<span class="MathJax" id="MathJax-Element-811-Frame" tabindex="0" data-mathml="k=5" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">k=5k=5时，所形成的圆内蓝色正方形最多，则目标为蓝色类，这就是<span class="MathJax" id="MathJax-Element-812-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk近邻算法。 <span class="MathJax" id="MathJax-Element-813-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk近邻的三要素是：<span class="MathJax" id="MathJax-Element-814-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk值得选择、距离度量及分类决策规则。 本文介绍<span class="MathJax" id="MathJax-Element-815-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk近邻算法，三要素及代码实现，kd树和搜索kd树的算法将在另一片博文中介绍。 二、k近邻算法算法：输入：训练数据集
T=(x1,y1),(x2,y2),⋯,(xN,yN)T=(x1,y1),(x2,y2),⋯,(xN,yN)
其中，xixi为实例的特征向量，yiyi为实例的类别，i=1,2,⋯,N.i=1,2,⋯,N.
输出：实例<span class="MathJax" id="MathJax-Element-1186-Frame" tabindex="0" data-mathml="x" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">xx所属的类<span class="MathJax" id="MathJax-Element-1187-Frame" tabindex="0" data-mathml="y." role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">y.y. 算法步骤：- 根据给定的距离度量，在训练集TT中找出与xx最邻近的kk个点，涵盖着kk个点的xx的邻域记作Nk(x)Nk(x);
在<span class="MathJax" id="MathJax-Element-4186-Frame" tabindex="0" data-mathml="Nk(x)" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">Nk(x)Nk(x)中根据分类规则（如多数表决）决定<span class="MathJax" id="MathJax-Element-4187-Frame" tabindex="0" data-mathml="x" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">xx的类别<span class="MathJax" id="MathJax-Element-4188-Frame" tabindex="0" data-mathml="y" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">yy：
y=argmaxci∑xi∈Nk(x)I(yi=cj),i=1,2,⋯,N;j=1,2,⋯,k.y=argmaxci∑xi∈Nk(x)I(yi=cj),i=1,2,⋯,N;j=1,2,⋯,k.
<span class="MathJax" id="MathJax-Element-4190-Frame" tabindex="0" data-mathml="I" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">II为指示函数，即当<span class="MathJax" id="MathJax-Element-4191-Frame" tabindex="0" data-mathml="Yi=ci" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">Yi=ciYi=ci时，<span class="MathJax" id="MathJax-Element-4192-Frame" tabindex="0" data-mathml="I=1" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">I=1I=1，否则为0. 当<span class="MathJax" id="MathJax-Element-4193-Frame" tabindex="0" data-mathml="k=1" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">k=1k=1时，称为最近邻算法。
三、k近邻的三要素下面我们介绍k近邻法的三个基本要素：距离度量、k值的选择和分类决策规则的确定。 3.1 距离度量特征空间中两个实例点的距离是两个实例点相似程度的反映，一般使用的是欧氏距离，也可以使其他距离，如<span class="MathJax" id="MathJax-Element-4851-Frame" tabindex="0" data-mathml="LP" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">LPLP距离和Minkowski距离。
下面是每个距离的定义： 设特征空间<span class="MathJax" id="MathJax-Element-4852-Frame" tabindex="0" data-mathml="X" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">XX是<span class="MathJax" id="MathJax-Element-4853-Frame" tabindex="0" data-mathml="n" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">nn维实数向量空间<span class="MathJax" id="MathJax-Element-4854-Frame" tabindex="0" data-mathml="Rn," role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">Rn,Rn, <span class="MathJax" id="MathJax-Element-4855-Frame" tabindex="0" data-mathml="xi" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">xixi,<span class="MathJax" id="MathJax-Element-4856-Frame" tabindex="0" data-mathml="xj∈X," role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">xj∈X,xj∈X, <span class="MathJax" id="MathJax-Element-4857-Frame" tabindex="0" data-mathml="xi=(xi(1),xi(2),⋯,xi(n))T" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">xi=(xi(1),xi(2),⋯,xi(n))Txi=(xi(1),xi(2),⋯,xi(n))T,<span class="MathJax" id="MathJax-Element-4858-Frame" tabindex="0" data-mathml="xj=(xj(1),xj(2),⋯,xj(n))T," role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">xj=(xj(1),xj(2),⋯,xj(n))T,xj=(xj(1),xj(2),⋯,xj(n))T, <span class="MathJax" id="MathJax-Element-4859-Frame" tabindex="0" data-mathml="xi,xj" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">xi,xjxi,xj的<span class="MathJax" id="MathJax-Element-4860-Frame" tabindex="0" data-mathml="Lp" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">LpLp距离为：
Lp(xi,xj)=(∑i=1n|xi(l)−xj(l)|p)1pLp(xi,xj)=(∑i=1n|xi(l)−xj(l)|p)1p
这里<span class="MathJax" id="MathJax-Element-4862-Frame" tabindex="0" data-mathml="p≥1" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">p≥1p≥1.当<span class="MathJax" id="MathJax-Element-4863-Frame" tabindex="0" data-mathml="p=2" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">p=2p=2时，称为欧氏距离，即
L2(xi,xj)=(∑i=1n|xi(l)−xj(l)|2)12L2(xi,xj)=(∑i=1n|xi(l)−xj(l)|2)12
当<span class="MathJax" id="MathJax-Element-4865-Frame" tabindex="0" data-mathml="p=1" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">p=1p=1时 ，称为曼哈顿距离，即
L1(xi,xj)=∑i=1n|xi(l)−xj(l)|L1(xi,xj)=∑i=1n|xi(l)−xj(l)|
当<span class="MathJax" id="MathJax-Element-4867-Frame" tabindex="0" data-mathml="p=∞" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">p=∞p=∞时，取各个坐标距离的最大值，即
L∞(xi,xj)=maxl|xi(l)−xj(l)|L∞(xi,xj)=maxl|xi(l)−xj(l)|
3.2 kk值的选择k值的选择会对结果产生直接的影响。 如果选择较小的k值，就相当于用较小的邻域中的训练实例进行预测，近似误差会减小，只有输入实例较近的训练实例才会对预测结果起作用，但确定是估计误差会增大，因为预测结果会对邻近的实例点非常敏感，如果邻近的实例点恰巧是噪声，预测结果就会出错。<span class="MathJax" id="MathJax-Element-5360-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk值的减小意味着模型变得复杂，容易产生过拟合（这句话可以理解为<span class="MathJax" id="MathJax-Element-5361-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk增大，邻域边界相对更平滑，<span class="MathJax" id="MathJax-Element-5362-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk减小，邻域边界更弯曲，更参差不平，更复杂，可以画图帮助理解）。 如果选择较大的k值，就相当于用较大邻域中的训练实例进行预测，其优点是可以减少学习的估计误差，缺点是学习的近似误差会增大，这时与输入实例较远的训练实例也会起预测作用，使预测发生错误，<span class="MathJax" id="MathJax-Element-5363-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk值的增大就意味着整体的模型变得简单。 当<span class="MathJax" id="MathJax-Element-5364-Frame" tabindex="0" data-mathml="k=N" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">k=Nk=N是，无论输入什么，都将简单预测为最多实例点的类，是不可取得。 在应用中，<span class="MathJax" id="MathJax-Element-5365-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk值一般去一个比较小的数值，采用交叉验证选取最优<span class="MathJax" id="MathJax-Element-5366-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk值。 3.3 分类决策规则<span class="MathJax" id="MathJax-Element-6302-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk近邻法中的分类决策规则一般采用多数表决，即由输入实例的<span class="MathJax" id="MathJax-Element-6303-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk个邻近的训练实例中的多数类决定。 多数表决规则等价于经验风险最小化，解释如下：如果分类的损失函数为0-1损失函数，分类函数为
f:Rn→{c1,c2,⋯,cK}f:Rn→{c1,c2,⋯,cK}
那么误分类的概率是
P(Y≠f(X))=1−P(Y=f(X))P(Y≠f(X))=1−P(Y=f(X))
对于给定实例xx，其最近邻的kk个训练实例点构成的集合Nk(x)Nk(x).如果涵盖Nk(x)Nk(x)的区域的类别是cjcj,那么误分类率是
1k∑xi∈Nk(x)I(yi≠cj)=1−1k∑xi∈Nk(x)I(yi=cj)1k∑xi∈Nk(x)I(yi≠cj)=1−1k∑xi∈Nk(x)I(yi=cj)
要使误分类率最小即经验风险最小，就要使∑xi∈Nk(x)I(yi=cj)∑xi∈Nk(x)I(yi=cj)最大，所以多数表决规则等价于经验风险最小化。
四、模型的优缺点KNN算法不仅可以用于分类，还可以用于回归。通过找出一个样本的k个最近邻居，将这些邻居的属性的平均值赋给该样本，就可以得到该样本的属性。更有用的方法是将不同距离的邻居对该样本产生的影响给予不同的权值，如权值与距离成反比。 优点：1.简单，易于理解，易于实现，无需估计参数，无需训练；
2. 适合对稀有事件进行分类；
3.特别适合于多分类问题(multi-modal,对象具有多个类别标签)， kNN比SVM的表现要好。 缺点：1.该算法在分类时有个主要的不足是，当样本不平衡时，如一个类的样本容量很大，而其他类样本容量很小时，有可能导致当输入一个新样本时，该样本的<span class="MathJax" id="MathJax-Element-6319-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk个邻居中大容量类的样本占多数。 该算法只计算“最近的”邻居样本，某一类的样本数量很大，那么或者这类样本并不接近目标样本，或者这类样本很靠近目标样本。无论怎样，数量并不能影响运行结果。 2.该方法的另一个不足之处是计算量较大，因为对每一个待分类的文本都要计算它到全体已知样本的距离，才能求得它的<span class="MathJax" id="MathJax-Element-6320-Frame" tabindex="0" data-mathml="k" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; font-size: 16px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; word-break: break-all; position: relative;">kk个最近邻点。 3.可理解性差，无法给出像决策树那样的规。 五、代码实现sklearn有现有的包可以调用，具体如下： >>> X = [[0], [1], [2], [3]]>>> y = [0, 0, 1, 1]>>> from sklearn.neighbors import KNeighborsClassifier>>> neigh = KNeighborsClassifier(n_neighbors=3)>>> neigh.fit(X, y) KNeighborsClassifier(...)>>> print(neigh.predict([[1.1]]))[0]>>> print(neigh.predict_proba([[0.9]]))[[ 0.66666667 0.33333333]]kd树和kd树的最近邻搜索将单独作为一篇文章介绍。
| 
收藏
淘帖
踩
