子空间 $V = L(x_1, \,x_2,\,\cdots,\,x_m))$ 上定义一个泛函 $f$
$\begin{aligned} f: V \rightarrow {\mathbb R^C}, && \text{$C$ 是类别个数} \end{aligned}$
则可以定义 $f$ 的能量函数为
$\begin{aligned} E(f) &= \frac{1}{2} {\displaystyle\sum_{i=1}^{m}\sum_{j=1}^m (W)_{ij} ||f(x_i) - f(x_j)||^2}\\ &= \frac{1}{2}{\displaystyle\sum_{i=1}^{m}\sum_{j=1}^m (W)_{ij}( ||f(x_i)||^2 - 2 f(x_i)^Tf(x_j) + ||f(x_j)||^2)}\\ &= {\displaystyle\sum_{i=1}^{m}\sum_{j=1}^m}(W)_{ij}||f(x_i)||^2 - {\displaystyle\sum_{i=1}^{m}\sum_{j=1}^m}f(x_i)^Tf(x_j)(W)_{ij} & \text{$i$, $j$ 的对称性} \end{aligned}$