For any vector
a
a
a and
b
b
b, we have
∥
a
∥
2
−
∥
a
∥
2
2
2
∥
b
∥
2
≤
∥
b
∥
2
−
∥
b
∥
2
2
2
∥
b
∥
2
\|a\|_{2} - \frac{\|a\|_{2}^{2}}{2\|b\|_{2}} \leq \|b\|_{2} - \frac{\|b\|_{2}^{2}}{2\|b\|_{2}}
∥a∥2−2∥b∥2∥a∥22≤∥b∥2−2∥b∥2∥b∥22
参考文献：Feiping Nie, Heng Huang, Xiao Cai, and Chris Ding. Efficient and robust feature selection via joint l 2 , 1 l_{2,1} l2,1 -norms minimization. In NIPS, 2010.