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smooth-convex-kl-nmf

About

Repository holding implementations for Non-negative matrix factorization (NMF) based on Kullback-Leibler divergence and additional smoothness and sparsity constraints.

As a starting point the code provided implements an inefficient version of the NMF approach described in

Essid, S. and Févotte, C.,
Smooth nonnegative matrix factorization for unsupervised audiovisual document structuring. 
IEEE Transactions on Multimedia, 15(2), 2013, pp.415-425.

The paper describes a method for unsupervised NMF on datasets of Bag-of-Words features learned from video and audio data. The method is used for the speaker diarization (who spoke when) problem. The optimization process includes regularization for smoothness and sparsity for the activation matrix.

Note: The code will be improved over time and implemented in a GPU accelerated framework (i.e. minpy) with MiniBatch support. While there are two versions of NMF currently (a smoothed KL-NMF and a smoothed convex KL-NMF), only the later is currently optimized. Next step is to support graphics card acceleration (possibly through mxnet).

There are currently three functions in scnmf.py. smoothNMF, smoothConvexNMF, and miniBatchSmoothConvexNMF which is a version that supports large datasets. Currently only the smoothConvexNMF and its minibatched versions are optimized.

How to run

  1. Clone the directory
 $ git clone https://github.com/mmxgn/smooth-convex-kl-nmf
  1. Install the requirements using pip
$ cd smooth-convex-kl-nmf
$ pip install --user -r requirements.txt
  1. Install the package
$ python setup.py install --user

Then you can create a new file runnmf.py at the same directory as scnmf.py and add the following:

%matplotlib inline

from scnmf import *
X = np.abs(np.random.randn(10, 3))
Y = np.array([
    [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1],
    [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]
]).astype(np.float32)
Y += np.abs(np.random.randn(Y.shape[0], Y.shape[1]) * 0.00001)
V = np.matmul(X, Y)

L, H, cost = smoothConvexNMF(V, 3, beta=0.01, max_iter=1000)

# or

L, H, cost = miniBatchSmoothConvexNMF(V, 3, beta=0.01, batch_size=2, epochs=1000)

# Originally V = WH, but here we constrained W to be a linear combination of the rows of V.

W = np.matmul(V, L)

print(cost[-1])

# Plot the cost (requires matplotlib)
import matplotlib.pyplot as plt
plt.figure()
plt.plot(cost)
plt.title('cost')
plt.xlabel('iteration #')

# Plot dictionary matrix W
plt.figure()
plt.imshow(W, aspect='auto')
plt.title('W')

You can run it then with python runnmf.py which will print the cost at the last iteration. Of course you could do better things with it like plotting the cost curve, showing V, W, and H as images, and the like.