Is there a specific mathematical terminology for matrix/tensor with holes(missing elements)?
$begingroup$
Consider a matrix-with-hole like below:
$$
begin{bmatrix}
None & x \
y & 0
end{bmatrix}
$$
We can define two variants of means for the above object:
one is to calculate means by row first (None values do not count) then calculate the mean of means:
M1 = 1/2 * (x + 1/2 * (y + 0)) = x/2 + y/4
the other is to calculate means by columns first (None values do not count) then calculate the mean of mean:
M2 = 1/2 * (y + 1/2 * (x + 0)) = x/4 + y/2
If we generalize this kind of matrix-with-holes to an n-dim-tensor-with-holes, then there would be n! different orders of calculating the means.
My question is, is this kind of mathematical object well studied? Is there a name for these matrix/tensor with holes(missing elements)?
I explored https://en.wikipedia.org/wiki/List_of_matrices and it seems this kind of weird object is not qualified to be categorized as "matrix" and as a result it is really difficult to find the right keyword for it.
Thank you!
matrices terminology tensors
edited Nov 30 '18 at 5:17
Omnomnomnom
127k790178
asked Nov 30 '18 at 5:04
Qian HongQian Hong
163
$endgroup$
add a comment |
$begingroup$
Consider a matrix-with-hole like below:
$$
begin{bmatrix}
None & x \
y & 0
end{bmatrix}
$$
We can define two variants of means for the above object:
one is to calculate means by row first (None values do not count) then calculate the mean of means:
M1 = 1/2 * (x + 1/2 * (y + 0)) = x/2 + y/4
the other is to calculate means by columns first (None values do not count) then calculate the mean of mean:
M2 = 1/2 * (y + 1/2 * (x + 0)) = x/4 + y/2
If we generalize this kind of matrix-with-holes to an n-dim-tensor-with-holes, then there would be n! different orders of calculating the means.
My question is, is this kind of mathematical object well studied? Is there a name for these matrix/tensor with holes(missing elements)?
I explored https://en.wikipedia.org/wiki/List_of_matrices and it seems this kind of weird object is not qualified to be categorized as "matrix" and as a result it is really difficult to find the right keyword for it.
Thank you!
matrices terminology tensors
edited Nov 30 '18 at 5:17
Omnomnomnom
127k790178
asked Nov 30 '18 at 5:04
Qian HongQian Hong
163
$endgroup$
2
$begingroup$
This isn't exactly what you seem to be looking for, but matrices with missing entries are sometimes called "partially observed matrices" or "partial matrices".
$endgroup$
– Omnomnomnom
Nov 30 '18 at 5:16
$begingroup$
@Omnomnomnom Thank you! And I agree with you that "matrices with none entries" is different with "matrices with missing entries". In term of functional programming language, matrices with none entries is type of "Matrix (Maybe (Constant|Variable))" while matrices with missing entries is type of "Matrix (Constant|Variable)"
$endgroup$
– Qian Hong
Nov 30 '18 at 5:27
add a comment |
$begingroup$
Consider a matrix-with-hole like below:
$$
begin{bmatrix}
None & x \
y & 0
end{bmatrix}
$$
We can define two variants of means for the above object:
one is to calculate means by row first (None values do not count) then calculate the mean of means:
M1 = 1/2 * (x + 1/2 * (y + 0)) = x/2 + y/4
the other is to calculate means by columns first (None values do not count) then calculate the mean of mean:
M2 = 1/2 * (y + 1/2 * (x + 0)) = x/4 + y/2
If we generalize this kind of matrix-with-holes to an n-dim-tensor-with-holes, then there would be n! different orders of calculating the means.
My question is, is this kind of mathematical object well studied? Is there a name for these matrix/tensor with holes(missing elements)?
I explored https://en.wikipedia.org/wiki/List_of_matrices and it seems this kind of weird object is not qualified to be categorized as "matrix" and as a result it is really difficult to find the right keyword for it.
Thank you!
matrices terminology tensors
edited Nov 30 '18 at 5:17
Omnomnomnom
127k790178
asked Nov 30 '18 at 5:04
Qian HongQian Hong
163
$endgroup$
Consider a matrix-with-hole like below:
$$
begin{bmatrix}
None & x \
y & 0
end{bmatrix}
$$
We can define two variants of means for the above object:
one is to calculate means by row first (None values do not count) then calculate the mean of means:
M1 = 1/2 * (x + 1/2 * (y + 0)) = x/2 + y/4
the other is to calculate means by columns first (None values do not count) then calculate the mean of mean:
M2 = 1/2 * (y + 1/2 * (x + 0)) = x/4 + y/2
If we generalize this kind of matrix-with-holes to an n-dim-tensor-with-holes, then there would be n! different orders of calculating the means.
My question is, is this kind of mathematical object well studied? Is there a name for these matrix/tensor with holes(missing elements)?
I explored https://en.wikipedia.org/wiki/List_of_matrices and it seems this kind of weird object is not qualified to be categorized as "matrix" and as a result it is really difficult to find the right keyword for it.
Thank you!
matrices terminology tensors
matrices terminology tensors
edited Nov 30 '18 at 5:17
Omnomnomnom
127k790178
asked Nov 30 '18 at 5:04
Qian HongQian Hong
163
edited Nov 30 '18 at 5:17
Omnomnomnom
127k790178
asked Nov 30 '18 at 5:04
Qian HongQian Hong
163
edited Nov 30 '18 at 5:17
Omnomnomnom
127k790178
edited Nov 30 '18 at 5:17
Omnomnomnom
127k790178
edited Nov 30 '18 at 5:17
Omnomnomnom
127k790178
127k790178
asked Nov 30 '18 at 5:04
Qian HongQian Hong
163
asked Nov 30 '18 at 5:04
Qian HongQian Hong
163
asked Nov 30 '18 at 5:04
Qian HongQian Hong
163
163
2
$begingroup$
This isn't exactly what you seem to be looking for, but matrices with missing entries are sometimes called "partially observed matrices" or "partial matrices".
$endgroup$
– Omnomnomnom
Nov 30 '18 at 5:16
$begingroup$
@Omnomnomnom Thank you! And I agree with you that "matrices with none entries" is different with "matrices with missing entries". In term of functional programming language, matrices with none entries is type of "Matrix (Maybe (Constant|Variable))" while matrices with missing entries is type of "Matrix (Constant|Variable)"
$endgroup$
– Qian Hong
Nov 30 '18 at 5:27
add a comment |
2
$begingroup$
This isn't exactly what you seem to be looking for, but matrices with missing entries are sometimes called "partially observed matrices" or "partial matrices".
$endgroup$
– Omnomnomnom
Nov 30 '18 at 5:16
$begingroup$
@Omnomnomnom Thank you! And I agree with you that "matrices with none entries" is different with "matrices with missing entries". In term of functional programming language, matrices with none entries is type of "Matrix (Maybe (Constant|Variable))" while matrices with missing entries is type of "Matrix (Constant|Variable)"
$endgroup$
– Qian Hong
Nov 30 '18 at 5:27
2
2
$begingroup$
This isn't exactly what you seem to be looking for, but matrices with missing entries are sometimes called "partially observed matrices" or "partial matrices".
$endgroup$
– Omnomnomnom
Nov 30 '18 at 5:16
$begingroup$
This isn't exactly what you seem to be looking for, but matrices with missing entries are sometimes called "partially observed matrices" or "partial matrices".
$endgroup$
– Omnomnomnom
Nov 30 '18 at 5:16
$begingroup$
@Omnomnomnom Thank you! And I agree with you that "matrices with none entries" is different with "matrices with missing entries". In term of functional programming language, matrices with none entries is type of "Matrix (Maybe (Constant|Variable))" while matrices with missing entries is type of "Matrix (Constant|Variable)"
$endgroup$
– Qian Hong
Nov 30 '18 at 5:27
$begingroup$
@Omnomnomnom Thank you! And I agree with you that "matrices with none entries" is different with "matrices with missing entries". In term of functional programming language, matrices with none entries is type of "Matrix (Maybe (Constant|Variable))" while matrices with missing entries is type of "Matrix (Constant|Variable)"
$endgroup$
– Qian Hong
Nov 30 '18 at 5:27
add a comment |
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$begingroup$
This isn't exactly what you seem to be looking for, but matrices with missing entries are sometimes called "partially observed matrices" or "partial matrices".
$endgroup$
– Omnomnomnom
Nov 30 '18 at 5:16
$begingroup$
@Omnomnomnom Thank you! And I agree with you that "matrices with none entries" is different with "matrices with missing entries". In term of functional programming language, matrices with none entries is type of "Matrix (Maybe (Constant|Variable))" while matrices with missing entries is type of "Matrix (Constant|Variable)"
$endgroup$
– Qian Hong
Nov 30 '18 at 5:27