Mixing
How can I measure the difference/similarity between two vectors?
0
$begingroup$
How can I measure the difference/similarity of two vectors?
That is...Let us suppose that I have two vectors in R^3: v1 = {1,8,3} v2 = {2,5,10} Let us consider that v1 and v2 are representing directions.
I would like to measure how much v1 and v2 are pointing to the same direction.
vector-spaces
asked Feb 1 at 15:04
ZaratrutaZaratruta
1112
$endgroup$
migrated from mathoverflow.net Feb 1 at 16:01
This question came from our site for professional mathematicians.
|
show 1 more comment
0
$begingroup$
How can I measure the difference/similarity of two vectors?
That is...Let us suppose that I have two vectors in R^3: v1 = {1,8,3} v2 = {2,5,10} Let us consider that v1 and v2 are representing directions.
I would like to measure how much v1 and v2 are pointing to the same direction.
vector-spaces
asked Feb 1 at 15:04
ZaratrutaZaratruta
1112
$endgroup$
migrated from mathoverflow.net Feb 1 at 16:01
This question came from our site for professional mathematicians.
2
$begingroup$
Look up the dot product.
$endgroup$
– Wojowu
Feb 1 at 15:09
1
$begingroup$
In the sapiens vector space, one can use the Myers-Brigg personality test.
$endgroup$
– usul
Feb 1 at 15:15
1
$begingroup$
If the main concern is the similarity of the direction of the vectors I would normalise before taking the inner-product, so take $frac{langle v_{1},v_{2}rangle}{|v_{1}||v_{2}|}=cos(theta)$ where $theta$ is the angle between the two vectors.
$endgroup$
– Floris Claassens
Feb 1 at 16:22
1
$begingroup$
Thank you for your suggestions. I forgot to mention that I would like to find a measure tht is able to capture the fact that an angle of 180 degrees would produce the maximum difference. I have found the cosine similarity, but it seems that this measure assumes that maximaly different vectors have 90 degress between them.
$endgroup$
– Zaratruta
Feb 1 at 16:33
$begingroup$
$langle v_1,v_2rangle |v_1times v_2|$ will be proportional to $sin2theta$. Normalize first, as @FlorisClaassens suggests.
$endgroup$
– amd
Feb 1 at 18:23
|
show 1 more comment
0
0
0
$begingroup$
How can I measure the difference/similarity of two vectors?
That is...Let us suppose that I have two vectors in R^3: v1 = {1,8,3} v2 = {2,5,10} Let us consider that v1 and v2 are representing directions.
I would like to measure how much v1 and v2 are pointing to the same direction.
vector-spaces
asked Feb 1 at 15:04
ZaratrutaZaratruta
1112
$endgroup$
How can I measure the difference/similarity of two vectors?
That is...Let us suppose that I have two vectors in R^3: v1 = {1,8,3} v2 = {2,5,10} Let us consider that v1 and v2 are representing directions.
I would like to measure how much v1 and v2 are pointing to the same direction.
vector-spaces
vector-spaces
asked Feb 1 at 15:04
ZaratrutaZaratruta
1112
asked Feb 1 at 15:04
ZaratrutaZaratruta
1112
asked Feb 1 at 15:04
ZaratrutaZaratruta
1112
asked Feb 1 at 15:04
ZaratrutaZaratruta
1112
asked Feb 1 at 15:04
ZaratrutaZaratruta
1112
1112
migrated from mathoverflow.net Feb 1 at 16:01
This question came from our site for professional mathematicians.
migrated from mathoverflow.net Feb 1 at 16:01
This question came from our site for professional mathematicians.
2
$begingroup$
Look up the dot product.
$endgroup$
– Wojowu
Feb 1 at 15:09
1
$begingroup$
In the sapiens vector space, one can use the Myers-Brigg personality test.
$endgroup$
– usul
Feb 1 at 15:15
1
$begingroup$
If the main concern is the similarity of the direction of the vectors I would normalise before taking the inner-product, so take $frac{langle v_{1},v_{2}rangle}{|v_{1}||v_{2}|}=cos(theta)$ where $theta$ is the angle between the two vectors.
$endgroup$
– Floris Claassens
Feb 1 at 16:22
1
$begingroup$
Thank you for your suggestions. I forgot to mention that I would like to find a measure tht is able to capture the fact that an angle of 180 degrees would produce the maximum difference. I have found the cosine similarity, but it seems that this measure assumes that maximaly different vectors have 90 degress between them.
$endgroup$
– Zaratruta
Feb 1 at 16:33
$begingroup$
$langle v_1,v_2rangle |v_1times v_2|$ will be proportional to $sin2theta$. Normalize first, as @FlorisClaassens suggests.
$endgroup$
– amd
Feb 1 at 18:23
|
show 1 more comment
2
$begingroup$
Look up the dot product.
$endgroup$
– Wojowu
Feb 1 at 15:09
1
$begingroup$
In the sapiens vector space, one can use the Myers-Brigg personality test.
$endgroup$
– usul
Feb 1 at 15:15
1
$begingroup$
If the main concern is the similarity of the direction of the vectors I would normalise before taking the inner-product, so take $frac{langle v_{1},v_{2}rangle}{|v_{1}||v_{2}|}=cos(theta)$ where $theta$ is the angle between the two vectors.
$endgroup$
– Floris Claassens
Feb 1 at 16:22
1
$begingroup$
Thank you for your suggestions. I forgot to mention that I would like to find a measure tht is able to capture the fact that an angle of 180 degrees would produce the maximum difference. I have found the cosine similarity, but it seems that this measure assumes that maximaly different vectors have 90 degress between them.
$endgroup$
– Zaratruta
Feb 1 at 16:33
$begingroup$
$langle v_1,v_2rangle |v_1times v_2|$ will be proportional to $sin2theta$. Normalize first, as @FlorisClaassens suggests.
$endgroup$
– amd
Feb 1 at 18:23
2
2
$begingroup$
Look up the dot product.
$endgroup$
– Wojowu
Feb 1 at 15:09
$begingroup$
Look up the dot product.
$endgroup$
– Wojowu
Feb 1 at 15:09
1
1
$begingroup$
In the sapiens vector space, one can use the Myers-Brigg personality test.
$endgroup$
– usul
Feb 1 at 15:15
$begingroup$
In the sapiens vector space, one can use the Myers-Brigg personality test.
$endgroup$
– usul
Feb 1 at 15:15
1
1
$begingroup$
If the main concern is the similarity of the direction of the vectors I would normalise before taking the inner-product, so take $frac{langle v_{1},v_{2}rangle}{|v_{1}||v_{2}|}=cos(theta)$ where $theta$ is the angle between the two vectors.
$endgroup$
– Floris Claassens
Feb 1 at 16:22
$begingroup$
If the main concern is the similarity of the direction of the vectors I would normalise before taking the inner-product, so take $frac{langle v_{1},v_{2}rangle}{|v_{1}||v_{2}|}=cos(theta)$ where $theta$ is the angle between the two vectors.
$endgroup$
– Floris Claassens
Feb 1 at 16:22
1
1
$begingroup$
Thank you for your suggestions. I forgot to mention that I would like to find a measure tht is able to capture the fact that an angle of 180 degrees would produce the maximum difference. I have found the cosine similarity, but it seems that this measure assumes that maximaly different vectors have 90 degress between them.
$endgroup$
– Zaratruta
Feb 1 at 16:33
$begingroup$
Thank you for your suggestions. I forgot to mention that I would like to find a measure tht is able to capture the fact that an angle of 180 degrees would produce the maximum difference. I have found the cosine similarity, but it seems that this measure assumes that maximaly different vectors have 90 degress between them.
$endgroup$
– Zaratruta
Feb 1 at 16:33
$begingroup$
$langle v_1,v_2rangle |v_1times v_2|$ will be proportional to $sin2theta$. Normalize first, as @FlorisClaassens suggests.
$endgroup$
– amd
Feb 1 at 18:23
$begingroup$
$langle v_1,v_2rangle |v_1times v_2|$ will be proportional to $sin2theta$. Normalize first, as @FlorisClaassens suggests.
$endgroup$
– amd
Feb 1 at 18:23
|
show 1 more comment
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2
$begingroup$
Look up the dot product.
$endgroup$
– Wojowu
Feb 1 at 15:09
1
$begingroup$
In the sapiens vector space, one can use the Myers-Brigg personality test.
$endgroup$
– usul
Feb 1 at 15:15
1
$begingroup$
If the main concern is the similarity of the direction of the vectors I would normalise before taking the inner-product, so take $frac{langle v_{1},v_{2}rangle}{|v_{1}||v_{2}|}=cos(theta)$ where $theta$ is the angle between the two vectors.
$endgroup$
– Floris Claassens
Feb 1 at 16:22
1
$begingroup$
Thank you for your suggestions. I forgot to mention that I would like to find a measure tht is able to capture the fact that an angle of 180 degrees would produce the maximum difference. I have found the cosine similarity, but it seems that this measure assumes that maximaly different vectors have 90 degress between them.
$endgroup$
– Zaratruta
Feb 1 at 16:33
$begingroup$
$langle v_1,v_2rangle |v_1times v_2|$ will be proportional to $sin2theta$. Normalize first, as @FlorisClaassens suggests.
$endgroup$
– amd
Feb 1 at 18:23