Relaxation of weighted norm distance?
I measure the weighted distance between two vector $a$ and $b$ with dimensions weighted by vector $w$ in $mathbb{R}^n$, by the weighted 1-norm:
$$N_1 = sum_i^n |w_i(a-b)_i| = sum_i^n |w_i||(a-b)_i|$$
A relaxation (by relaxing $w_i$) of this norm, that works well for me as input for my classifier, is:
$$N_{1,R} = sum_i^n w_i|(a-b)_i|$$
Could someone point me to a reference of this $N_{1,R}$?
Thank you very much for your help and suggestions.
linear-algebra reference-request vector-spaces norm
asked Dec 7 '18 at 5:27
THNTHN
1138
add a comment |
I measure the weighted distance between two vector $a$ and $b$ with dimensions weighted by vector $w$ in $mathbb{R}^n$, by the weighted 1-norm:
$$N_1 = sum_i^n |w_i(a-b)_i| = sum_i^n |w_i||(a-b)_i|$$
A relaxation (by relaxing $w_i$) of this norm, that works well for me as input for my classifier, is:
$$N_{1,R} = sum_i^n w_i|(a-b)_i|$$
Could someone point me to a reference of this $N_{1,R}$?
Thank you very much for your help and suggestions.
linear-algebra reference-request vector-spaces norm
asked Dec 7 '18 at 5:27
THNTHN
1138
add a comment |
I measure the weighted distance between two vector $a$ and $b$ with dimensions weighted by vector $w$ in $mathbb{R}^n$, by the weighted 1-norm:
$$N_1 = sum_i^n |w_i(a-b)_i| = sum_i^n |w_i||(a-b)_i|$$
A relaxation (by relaxing $w_i$) of this norm, that works well for me as input for my classifier, is:
$$N_{1,R} = sum_i^n w_i|(a-b)_i|$$
Could someone point me to a reference of this $N_{1,R}$?
Thank you very much for your help and suggestions.
linear-algebra reference-request vector-spaces norm
asked Dec 7 '18 at 5:27
THNTHN
1138
I measure the weighted distance between two vector $a$ and $b$ with dimensions weighted by vector $w$ in $mathbb{R}^n$, by the weighted 1-norm:
$$N_1 = sum_i^n |w_i(a-b)_i| = sum_i^n |w_i||(a-b)_i|$$
A relaxation (by relaxing $w_i$) of this norm, that works well for me as input for my classifier, is:
$$N_{1,R} = sum_i^n w_i|(a-b)_i|$$
Could someone point me to a reference of this $N_{1,R}$?
Thank you very much for your help and suggestions.
linear-algebra reference-request vector-spaces norm
linear-algebra reference-request vector-spaces norm
asked Dec 7 '18 at 5:27
THNTHN
1138
asked Dec 7 '18 at 5:27
THNTHN
1138
edited Dec 12 '18 at 7:28
THN
asked Dec 7 '18 at 5:27
THNTHN
1138
asked Dec 7 '18 at 5:27
THNTHN
1138
asked Dec 7 '18 at 5:27
THNTHN
1138
1138
add a comment |
add a comment |
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