Non-negative probabilistic Poisson-gamma matrix factorization and tensor CP decomposition with sparse input and internal components. This is a (more) memory efficient version of Poisson Factorization in pure python that takes advantage of the fact that inference updates for Poisson Factorization needs to be performed only on the non-zero entries of the input matrix/tensor. Both models consist on a hierarchical probabilistic model with a Poisson likelihood for the matrix entries, and Gamma distributed latent factors vectors for rows and columns (in the matrix case) or each mode (in the tensor case, effectively meaning that we are performing a non-negative CP decomposition).
For the matrix case the expected value of latent factor can be accessed via the attributes Eb and Et of the poisson factorization object, while for the tensor CP decomposition the expected value of latent factors can be acessed via the attribute Eb indexed by the mode.
- numpy_indexed
- scipy
- numpy
- scikit-learn
The input for the train method on the matrix factorization should be a numpy array representing a sparse matrix. An array with shape (N,3), where N is the number of non-zero entries and for each non-zero entry an array with [row, column, value] ).
A dense array equivalent for each entry would be Matrix[row,colum]=value.
Example:
[ [row_1, col_1, matrix_entry_row_1_col_1],
[row_2, col_2, matrix_entry_row_2_col_2],
[row_3, col_3, matrix_entry_row_3_col_3],
... ]
The input for the train method on the tensor factorization should be a numpy array representing a sparse vector. An array of shape (N,N_modes+1), where N is the number of non-zero entries, N_mode is the number of modes in the tensor, and for each non-zero entry an array of size N_modes+1 with [mode1, mode2, ... , mode_N,value].
A dense tensor array equivalent for each entry would be Tensor[mode1, mode2, ... , mode_N]=value.
Example:
[ [mode1_1, mode2_1, ... , mode_N_1, value_1],
[mode1_2, mode2_2, ... , mode_N_2, value_2],
... ]
To use sparse poisson matrix factorization add the following import:
import sparse_poisson as sp
poisson = sp.PoissonMF(n_components=15,max_iter=1000,smoothness=0.1,verbose=True,tol=0.0001,a=0.1,b=0.1)
poisson.fit(X)`
To use sparse poisson tensor factorization add the following import:
import sparse_tensor as st
poisson = st.PoissonTF(n_components=15,max_iter=1000,smoothness=0.1,verbose=True,tol=0.0001,a=0.1,b=0.1)
poisson.fit(X)`
This implementation is modification of the code found in PMF by Dawen Liang dliang@ee.columbia.edu
To understand the models implemented look at the Following bibliography: