MopheusFI is a Python implementation of factorized learning described in paper: Enabling and Optimizing Non-linear Feature Interactions in Factorized Linear Algebra
- Python 2.7
- NumPy 1.13
- SciPy 1.0.0
- SciKit Learn
- Python developer kit (C++ rewrite is used)
- PyTorch 1.0
- To install, simply run
python setup.py install. - To build C++ module, run
python setup.py build_ext --inplace.
Simply import NormalizedMatrix like a NumPy matrix. Then apply linear algebra operations on it.
E.g
s = np.matrix([[1.0, 2.0], [4.0, 3.0], [5.0, 6.0], [8.0, 7.0], [9.0, 1.0]])
k = [np.array([0, 1, 1, 0, 1])]
r = [np.matrix([[1.1, 2.2], [3.3, 4.4]])]
x = np.matrix([[1.0], [2.0], [3.0], [4.0], [5.0], [6.0], [7.0], [8.0], [9.0], [10.0], [11.0], [12.0], [13.0], [14.0]])
# materialized matrix with feature interaction
m = np.matrix([[ 1. , 2. , 1. , 2. , 4. , 1.1 , 2.2 , 1.21, 2.42, 4.84, 1.1 , 2.2 , 2.2 , 4.4 ],
[ 4. , 3. , 16. , 12. , 9. , 3.3 , 4.4 , 10.89, 14.52, 19.36, 13.2 , 17.6 , 9.9 , 13.2 ],
[ 5. , 6. , 25. , 30. , 36. , 3.3 , 4.4 , 10.89, 14.52, 19.36, 16.5 , 22. , 19.8 , 26.4 ],
[ 8. , 7. , 64. , 56. , 49. , 1.1 , 2.2 , 1.21, 2.42, 4.84, 8.8 , 17.6 , 7.7 , 15.4 ],
[ 9. , 1. , 81. , 9. , 1. , 3.3 , 4.4 , 10.89, 14.52, 19.36, 29.7 , 39.6 , 3.3 , 4.4 ]])
# normalized matrix
n_matrix = nm.NormalizedMatrix(s, r, k, second_order=true)
# result:
n_matrix.dot(x):
array([[ 266.56],
[1282.9 ],
[1926.5 ],
[1408.56],
[1663.4 ]])
m_matrix.dot(x):
array([[ 266.56],
[1282.9 ],
[1926.5 ],
[1408.56],
[1663.4 ]])
add, substract, divide, multiply, dot product, cross product, inverse
This library is implemented as a high-level wrapper. It might conflict with existing machine learning libraries if the libraries skip high-level implementation to optimize linear algebra in C kernel.