NMF-Torch

A PyTorch implementation on Non-negative Matrix Factorization.

Installation

This package is published on PyPI:

pip install nmf-torch

Usage

NMF

Given a non-negative numeric matrix X of shape M-by-N (M is number of samples, N number of features) in either numpy array or torch tensor structure, run the following code:

from nmf import run_nmf
H, W, err = run_nmf(X, n_components=20)

will decompose X into two new non-negative matrices:

• H of shape (M, 20), representing the transformed coordinates of samples regarding the 20 components;
• W of shape (20, N), representing the composition of each component in terms of features;

along with the loss between X and its approximation H*W.

Advanced Settings

By default, run_nmf function uses the batch HALS solver for NMF decomposition. In total, there are other solvers available in NMF-torch:

• HALS: Hierarchical Alternative Least Squares ([Kimura et al., 2015]). The default.
• MU: Multiplicative Update. Set algo='mu' in run_nmf function.
• BPP: Alternative non-negative least squares with Block Principal Pivoting method ([Kim & Park, 2011]). Set algo='bpp' in run_nmf function.

Besides, each solver has two modes: batch and online. The online mode is a modified version which is scalable for input matrix of a large number of samples. You can set mode='online' in run_nmf function to switch to use the online mode.

The default beta loss is Frobenius (L2) distance, which is the most commonly used. By changing beta_loss parameter in run_nmf function, users can specify other beta loss metrics:

• KL divergence: beta_loss='kullback-leibler' or beta_loss=1.0;
• Itakura-Saito divergence: beta_loss='itakura-saito' or beta_loss=0;
• Or any non-negative float number.

Notice that since online mode only works for L2 loss, if you specify other beta loss, run_nmf will automatically switch back to batch mode.

For the other parameters in run_nmf function, please type help(run_nmf) in your Python interpreter to view.

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Data Integration using Integrative NMF (iNMF)

In this case, we have a list of k batches, with their corresponding non-negative numeric matrices to be integrated. Let X be such a list, and all matrices in X have the same number of features, i.e. each X_i in X has shape (M_i, N), where M_i is number of samples in batch i, and N is number of features.

The following code:

from nmf import integrative_nmf
H, W, V, err = integrative_nmf(X, n_components=20)

will perform iNMF, which results in the following non-negative matrices:

• H: List of matrices of shape (M_i, 20), each of which represents the transformed coordinates of samples regarding components of the corresponding batch;
• W of shape (20, N), representing the common composition (shared information) across the given batches in terms of features;
• V: List of matrices of the same shape (20, N), each of which represents the batch-specific composition in terms of features of the corresponding batch,

along with the overall L2 loss between X_i and its approximation H_i * (W + V_i) for each batch i.

Advanced Settings

Similarly as in run_nmf function above, integrative_nmf provides 2 modes (batch and online) and 3 solvers: HALS, MU, and BPP. By default, batch HALS is used. You can switch to other solvers and modes by specifying algo and mode parameters.

There is another important parameter lam for the coefficient for regularization terms, with default value 5.0. If set to 0, then no regularization will be applied.

Notice that only L2 loss is accepted in iNMF.

For the other parameters in integrative_nmf function, please type help(integrative_nmf) in your Python interpreter to view.