Search

L_q Norm

Properties
tmp
Author
Empty
Date
Empty
Link
Empty
Created
8/11/2021, 2:17:00 PM
Tags
Empty

Norm의 종류

L_q norm에 대해 확 와닿는 표현이 있어서 기록용으로 남깁니다.
Do you count how many non-zero elements it has ? L0L_0
Do you add up all the elements ? L1L_1
Do you measure how "long" the "arrow" is ? L2L_2
Do you use the size of the biggest element ? LL_\infty
Do you measure the total length of ellipsoid's axes by a matrix ? X\| X \|_* (Nuclear norm)

Nuclear norm : X\| X \|_*

Definition
A=trace(ATA)=i=1min(m,n)σi(A)\| A \| = \text{trace}(\sqrt{A^TA}) = \sum_{i=1}^{\min (m, n)} \sigma_i (A)
where σi(A)\sigma_i (A) is the ii-th largest singular value of AA.

Hilbert norm : AH\| A \|_\mathcal{H}

참고한 자료

Follow me on Facebook and Github. Thank you
TOP