Mixing
Is this the correct iterative version of the multiplicative update rule for matrix factorization?
$begingroup$
So we have $A_{mtimes n}approx P_{mtimes k}Q_{ktimes n}.$ Using the multiplicative update rule due to Lee we, in general, write that:
$$Pleftarrow P circ frac{AQ^T}{PQQ^T}$$
and
$$Qleftarrow Q circ frac{P^TA}{P^TPQ}.$$
Since I am working with very large matrices, I don't have access to the whole matrix in memory. Give $(i,j,A[i][j])$, I can fetch $P[i][:]$ and $Q[:][j],$ where $P[i][:]$ is the $i'$th row vector of the matrix $P$ and $Q[:][j]$ is the $j$'th column vector of the matrix $Q.$ I therefore intend to write a method which does the following:
def update(i, j, matrix_value_at_ij):
// Goal is to update the vector P[i][:] and Q[:][j]
p_vect = get_vector_from_memory(i) // returns P[i][:] as a column vector
q_vect = get_vector_from_memory(j) // return Q[:][j] as a column vector
for c in range(k):
p_vect[k] = p_vect[k]* (coeff_AQ_t)/(coeff_PQQ_t)
q_vect[k] = q_vect[k]* (coeff_P_tA)/(coeff_P_tPQ)
I don't know how to compute (coeff_AQ_t)/(coeff_PQQ_t) and (coeff_P_tA)/(coeff_P_tPQ) under this constraint. Any ideas would be much appreciated.
matrix-decomposition
asked Jan 16 at 20:49
Hello_WorldHello_World
4,14121831
$endgroup$
migrated from stats.stackexchange.com Jan 18 at 11:37
This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
add a comment |
$begingroup$
So we have $A_{mtimes n}approx P_{mtimes k}Q_{ktimes n}.$ Using the multiplicative update rule due to Lee we, in general, write that:
$$Pleftarrow P circ frac{AQ^T}{PQQ^T}$$
and
$$Qleftarrow Q circ frac{P^TA}{P^TPQ}.$$
Since I am working with very large matrices, I don't have access to the whole matrix in memory. Give $(i,j,A[i][j])$, I can fetch $P[i][:]$ and $Q[:][j],$ where $P[i][:]$ is the $i'$th row vector of the matrix $P$ and $Q[:][j]$ is the $j$'th column vector of the matrix $Q.$ I therefore intend to write a method which does the following:
def update(i, j, matrix_value_at_ij):
// Goal is to update the vector P[i][:] and Q[:][j]
p_vect = get_vector_from_memory(i) // returns P[i][:] as a column vector
q_vect = get_vector_from_memory(j) // return Q[:][j] as a column vector
for c in range(k):
p_vect[k] = p_vect[k]* (coeff_AQ_t)/(coeff_PQQ_t)
q_vect[k] = q_vect[k]* (coeff_P_tA)/(coeff_P_tPQ)
I don't know how to compute (coeff_AQ_t)/(coeff_PQQ_t) and (coeff_P_tA)/(coeff_P_tPQ) under this constraint. Any ideas would be much appreciated.
matrix-decomposition
asked Jan 16 at 20:49
Hello_WorldHello_World
4,14121831
$endgroup$
migrated from stats.stackexchange.com Jan 18 at 11:37
This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
$begingroup$
I would strongly suggest to instead peruse existing packages and frameworks that support the kind of large multiplications you need, as surely this is a widespread use case. For example TensorFlow should be able to do such updates as it has built-in logic for lazy-loading of weights. Even if your code is correct, it will likely be orders of magnitude slower than existing implementations of such multiplications.
$endgroup$
– Alex R.
Jan 16 at 20:57
$begingroup$
@AlexR. You are right. But I intend to implement this algorithm from scratch.
$endgroup$
– Hello_World
Jan 18 at 13:12
add a comment |
$begingroup$
So we have $A_{mtimes n}approx P_{mtimes k}Q_{ktimes n}.$ Using the multiplicative update rule due to Lee we, in general, write that:
$$Pleftarrow P circ frac{AQ^T}{PQQ^T}$$
and
$$Qleftarrow Q circ frac{P^TA}{P^TPQ}.$$
Since I am working with very large matrices, I don't have access to the whole matrix in memory. Give $(i,j,A[i][j])$, I can fetch $P[i][:]$ and $Q[:][j],$ where $P[i][:]$ is the $i'$th row vector of the matrix $P$ and $Q[:][j]$ is the $j$'th column vector of the matrix $Q.$ I therefore intend to write a method which does the following:
def update(i, j, matrix_value_at_ij):
// Goal is to update the vector P[i][:] and Q[:][j]
p_vect = get_vector_from_memory(i) // returns P[i][:] as a column vector
q_vect = get_vector_from_memory(j) // return Q[:][j] as a column vector
for c in range(k):
p_vect[k] = p_vect[k]* (coeff_AQ_t)/(coeff_PQQ_t)
q_vect[k] = q_vect[k]* (coeff_P_tA)/(coeff_P_tPQ)
I don't know how to compute (coeff_AQ_t)/(coeff_PQQ_t) and (coeff_P_tA)/(coeff_P_tPQ) under this constraint. Any ideas would be much appreciated.
matrix-decomposition
asked Jan 16 at 20:49
Hello_WorldHello_World
4,14121831
$endgroup$
So we have $A_{mtimes n}approx P_{mtimes k}Q_{ktimes n}.$ Using the multiplicative update rule due to Lee we, in general, write that:
$$Pleftarrow P circ frac{AQ^T}{PQQ^T}$$
and
$$Qleftarrow Q circ frac{P^TA}{P^TPQ}.$$
Since I am working with very large matrices, I don't have access to the whole matrix in memory. Give $(i,j,A[i][j])$, I can fetch $P[i][:]$ and $Q[:][j],$ where $P[i][:]$ is the $i'$th row vector of the matrix $P$ and $Q[:][j]$ is the $j$'th column vector of the matrix $Q.$ I therefore intend to write a method which does the following:
def update(i, j, matrix_value_at_ij):
// Goal is to update the vector P[i][:] and Q[:][j]
p_vect = get_vector_from_memory(i) // returns P[i][:] as a column vector
q_vect = get_vector_from_memory(j) // return Q[:][j] as a column vector
for c in range(k):
p_vect[k] = p_vect[k]* (coeff_AQ_t)/(coeff_PQQ_t)
q_vect[k] = q_vect[k]* (coeff_P_tA)/(coeff_P_tPQ)
I don't know how to compute (coeff_AQ_t)/(coeff_PQQ_t) and (coeff_P_tA)/(coeff_P_tPQ) under this constraint. Any ideas would be much appreciated.
matrix-decomposition
matrix-decomposition
asked Jan 16 at 20:49
Hello_WorldHello_World
4,14121831
asked Jan 16 at 20:49
Hello_WorldHello_World
4,14121831
asked Jan 16 at 20:49
Hello_WorldHello_World
4,14121831
asked Jan 16 at 20:49
Hello_WorldHello_World
4,14121831
asked Jan 16 at 20:49
Hello_WorldHello_World
4,14121831
4,14121831
migrated from stats.stackexchange.com Jan 18 at 11:37
This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
migrated from stats.stackexchange.com Jan 18 at 11:37
This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
$begingroup$
I would strongly suggest to instead peruse existing packages and frameworks that support the kind of large multiplications you need, as surely this is a widespread use case. For example TensorFlow should be able to do such updates as it has built-in logic for lazy-loading of weights. Even if your code is correct, it will likely be orders of magnitude slower than existing implementations of such multiplications.
$endgroup$
– Alex R.
Jan 16 at 20:57
$begingroup$
@AlexR. You are right. But I intend to implement this algorithm from scratch.
$endgroup$
– Hello_World
Jan 18 at 13:12
add a comment |
$begingroup$
I would strongly suggest to instead peruse existing packages and frameworks that support the kind of large multiplications you need, as surely this is a widespread use case. For example TensorFlow should be able to do such updates as it has built-in logic for lazy-loading of weights. Even if your code is correct, it will likely be orders of magnitude slower than existing implementations of such multiplications.
$endgroup$
– Alex R.
Jan 16 at 20:57
$begingroup$
@AlexR. You are right. But I intend to implement this algorithm from scratch.
$endgroup$
– Hello_World
Jan 18 at 13:12
$begingroup$
I would strongly suggest to instead peruse existing packages and frameworks that support the kind of large multiplications you need, as surely this is a widespread use case. For example TensorFlow should be able to do such updates as it has built-in logic for lazy-loading of weights. Even if your code is correct, it will likely be orders of magnitude slower than existing implementations of such multiplications.
$endgroup$
– Alex R.
Jan 16 at 20:57
$begingroup$
I would strongly suggest to instead peruse existing packages and frameworks that support the kind of large multiplications you need, as surely this is a widespread use case. For example TensorFlow should be able to do such updates as it has built-in logic for lazy-loading of weights. Even if your code is correct, it will likely be orders of magnitude slower than existing implementations of such multiplications.
$endgroup$
– Alex R.
Jan 16 at 20:57
$begingroup$
@AlexR. You are right. But I intend to implement this algorithm from scratch.
$endgroup$
– Hello_World
Jan 18 at 13:12
$begingroup$
@AlexR. You are right. But I intend to implement this algorithm from scratch.
$endgroup$
– Hello_World
Jan 18 at 13:12
add a comment |
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$begingroup$
I would strongly suggest to instead peruse existing packages and frameworks that support the kind of large multiplications you need, as surely this is a widespread use case. For example TensorFlow should be able to do such updates as it has built-in logic for lazy-loading of weights. Even if your code is correct, it will likely be orders of magnitude slower than existing implementations of such multiplications.
$endgroup$
– Alex R.
Jan 16 at 20:57
$begingroup$
@AlexR. You are right. But I intend to implement this algorithm from scratch.
$endgroup$
– Hello_World
Jan 18 at 13:12