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1013. Battle Over Cities (25) It is vitally important to have all the cities connected by highways in a war. If a city is occupied by the enemy, all the highways from/toward that city are closed. We must know immediately if we need to repair any other highways to keep the rest of ... 阅读全文
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Kernels 我们首先来回顾kernel函数的定义：一个函数$K(x,y)$为kernel函数当且仅当对$\forall g, \int K(x,y)g(x)g(y)dxdy\geq 0$成立。另外，根据Mercer's theorem，存在一个映射$\Phi$使$K(x,y)=\langle \Phi(x),\Phi(y)\rangle$，并且对任意有限的点，kernel矩阵是半正定的。一、核函数的封闭性 Hadamard product：$$\mathbf{A}\circ\mathbf{B}=\left[\begin{array}&a_{11}b_{11}&a_{ 阅读全文
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Linear & Ridge Regression 对于$n$个数据$\{(x_1,y_1),(x_2,y_2),\cdots,(x_n,y_n)\},x_i\in\mathbb{R}^d,y_i\in\mathbb{R}$。我们采用以下矩阵来记上述数据：\begin{equation}\math... 阅读全文
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