wNMF: weighted Non-Negative matrix Factorization

# wNMF: Weighted Non-Negative Matrix Factorization

`wNMF` implements a simple version of Non-Negative Matrix Factorization (NMF) that utilizes a weight matrix to weight the importance of each feature in each sample of the data matrix to be factorized.

`wNMF` is easy to use, because it behaves like an `sklearn.decomposition` model, but also allows for multiple fitting attempts.

More information about the modified multiplicative update algorithim utilized can be found here: Blondel, Vincent & Ho, Ngoc-Diep & Van Dooren, Paul. (2007). Weighted Nonnegative Matrix Factorization and Face Feature Extraction

`wNMF` specifically implements solutions for determining the decomposed matrices U and V when minimizing the Frobenius Norm or the Kullback-Leibler Divergence:

## Installation

This package is available on PyPI and can be installed with `pip`:

```\$ pip install wNMF
```

```\$ git clone https://github.com/asn32/weighted-nmf.git
\$ cd weighted-nmf
\$ python3 setup.py install --user
```

## Usage

`wNMF` is a python library that can be imported.

```import wNMF
```

And it can be used like an `sklearn.decomposition` model.

First create an instance of the `wNMF` model by setting the number of components.

Other parameters can be set too, such as the loss function, maximum number of iterations, and whether or not to track the decreasing error over every single run.

```## Mock data, a 100x100 data matrix, reduce to 25 dimensions
n=100
features = 100
components=25
X = 100*np.random.uniform(size=n*features).reshape(features,n)
W = np.ones_like(X)

## Define the model / fit
model = wNMF(n_components=25,
beta_loss='kullback-leibler',
max_iter=1000,
track_error=True)
```

Then, fit the model to the data using the instance methods `wNMF().fit` or `wNMF().fit_transform`.

```fit = model.fit(X=X,W=W,n_run=5)
```

After the fit is complete, explore the fit quality by examining the decomposed matrices and / or overall error.

```## Get the best solutions
lowest_error = fit.err)
best_V = fit.V
best_U = fit.U

## Or look at all the solutions from the 5 runs in this example
all_Vs = fit.V_all
```

## Disclaimer

`wnmf` is provided with no guarantees