机器学习中范数的梯度推导

推导过程如下

∥R−UVT∥2F=(R−UVT)T(R−UVT)=(RT−VUT)(R−UVT)=RTR−RTUVT−VUTR+VUTUVT

∂(∥R−UVT∥2F)∂V=−RTU−RTU+(VUTU+VUTU)=−2(RT−VUT)U=−2(R−UVT)TU

∂(∥R−UVT∥2F)∂VT=−UTR−UTR+(UTUVT+UTUVT)=−2UT(R−UVT)

∂(∥R−UVT∥2F)∂U=−RV−RV+(UVTV+UVTV)=−2(R−UVT)V

参考资料：
1. The Matrix Cookbook(Page 10-11): http://www.cs.cornell.edu/courses/cs6780/2010fa/materials/matrix_cookbook.pdf
2. https://www.zhihu.com/question/31845977