关于多示例学习
m a x H ( A , B ) = max ⁡ { max ⁡ a ∈ A min ⁡ b ∈ B ∥ a − b ∥ 2 , max ⁡ b ∈ B min ⁡ a ∈ A ∥ b − a ∥ 2 } \mathrm{maxH}(\mathbf{A}, \mathbf{B}) = \max \{\max_{a \in \mathbf{A}} \min_{b \in \mathbf{B}} \|a - b\|_2, \max_{b \in \mathbf{B}} \min_{a \in \mathbf{A}} \|b - a\|_2\} maxH(A,B)=max{a∈Amax​b∈Bmin​∥a−b∥2​,b∈Bmax​a∈Amin​∥b−a∥2​}
JAVA 代码：

double maxABDis=1;
double maxBADis=1;
for(int i=0;i<m;i++){
	double minBuffer=10000;
	for(int j=0;j<n;j++){
		if(minBuffer>dis(a[i],b(i))){
			minBuffer=dis(a[i],b(i));
		}//of if
	}//of for j
	if(maxABDis<minBuffer){
		maxABDis=minBuffer;
	}//of if
}//of for i
for(int i=0;i<n;i++){
	double minBuffer=10000;
	for(int j=0;j<m;j++){
		if(minBuffer>dis(b[i],a(i))){
			minBuffer=dis(b[i],a(i));
		}//of if
	}//of for j
	if(maxBADis<minBuffer){
		maxBADis=minBuffer;
	}//of if
}//of for i
if(maxABDis>maxBADis){
	return maxABDis;
}
else{
	return maxBADis;
}//of if

作业:

1.定义一个标签分布系统, 即各标签的值不是 0/1, 而是 [ 0 , 1 ] [0, 1] [0,1]区间的实数, 且同一对象的标签和为1.

答：Definition : A multi-label decision system is a tuple S = ( X , Y ) S = (\mathbf{X}, \mathbf{Y}) S=(X,Y) where X = [ x i j ] n × m ∈ R n × m \mathbf{X} = [x_{ij}]_{n \times m} \in \mathbb{R}^{n \times m} X=[xij​]n×m​∈Rn×m is the data matrix, Y = [ y i k ] n × l ∈ [ 0 , 1 ] n × l \mathbf{Y} = [y_{ik}]_{n \times l} \in[0, 1]^{n \times l} Y=[yik​]n×l​∈[0,1]n×l is the label matrix, n n n is the number of instances, m m m is the number of features, and l l l is the number of labels and ∑ k = 1 l y i k = 1 , i ∈ { 1 , 2 , … , n } \sum \limits_{k=1}^{l}y_{ik}=1,i \in \{1,2,\dots,n\} k=1∑l​yik​=1,i∈{1,2,…,n}.

2.找一篇小组的论文来详细分析数学表达式, 包括其涵义, 规范, 优点和缺点.

答：后续完善.