Matrix Factorization (MF) Example

Demonstrates matrix factorization with MXNet on the MovieLens 100k dataset.

You need to have python package pandas and bokeh installed (pip install pandas bokeh).



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import mxnet as mx
from movielens_data import get_data_iter, max_id
from matrix_fact import train



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# If MXNet is not compiled with GPU support (e.g. on OSX), set to [mx.cpu(0)]
# Can be changed to [mx.gpu(0), mx.gpu(1), ..., mx.gpu(N-1)] if there are N GPUs
ctx = [mx.gpu(0)]



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train_test_data = get_data_iter(batch_size=50)
max_user, max_item = max_id('./ml-100k/u.data')
(max_user, max_item)

Linear MF



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def plain_net(k):
    # input
    user = mx.symbol.Variable('user')
    item = mx.symbol.Variable('item')
    score = mx.symbol.Variable('score')
    # user feature lookup
    user = mx.symbol.Embedding(data = user, input_dim = max_user, output_dim = k) 
    # item feature lookup
    item = mx.symbol.Embedding(data = item, input_dim = max_item, output_dim = k)
    # predict by the inner product, which is elementwise product and then sum
    pred = user * item
    pred = mx.symbol.sum(data = pred, axis = 1)
    pred = mx.symbol.Flatten(data = pred)
    # loss layer
    pred = mx.symbol.LinearRegressionOutput(data = pred, label = score)
    return pred

net1 = plain_net(64)
mx.viz.plot_network(net1)



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results1 = train(net1, train_test_data, num_epoch=15, learning_rate=0.02, ctx=ctx)

Neural Network (non-linear) MF



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def get_one_layer_mlp(hidden, k):
    # input
    user = mx.symbol.Variable('user')
    item = mx.symbol.Variable('item')
    score = mx.symbol.Variable('score')
    # user latent features
    user = mx.symbol.Embedding(data = user, input_dim = max_user, output_dim = k)
    user = mx.symbol.Activation(data = user, act_type='relu')
    user = mx.symbol.FullyConnected(data = user, num_hidden = hidden)
    # item latent features
    item = mx.symbol.Embedding(data = item, input_dim = max_item, output_dim = k)
    item = mx.symbol.Activation(data = item, act_type='relu')
    item = mx.symbol.FullyConnected(data = item, num_hidden = hidden)
    # predict by the inner product
    pred = user * item
    pred = mx.symbol.sum(data = pred, axis = 1)
    pred = mx.symbol.Flatten(data = pred)
    # loss layer
    pred = mx.symbol.LinearRegressionOutput(data = pred, label = score)
    return pred

net2 = get_one_layer_mlp(64, 64)
mx.viz.plot_network(net2)



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results2 = train(net2, train_test_data, num_epoch=15, learning_rate=0.02, ctx=ctx)

Visualizing results

Now let's draw a single chart that compares the learning curves of the three different models. We'll use the bokeh library since it gives nice interactive charting.



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import bokeh
import bokeh.io
import bokeh.plotting
bokeh.io.output_notebook()
import pandas as pd

def viz_lines(fig, results, legend, color):
    df = pd.DataFrame(results._data['eval'])
    fig.line(df.elapsed,df.RMSE, color=color, legend=legend, line_width=2)
    df = pd.DataFrame(results._data['train'])
    fig.line(df.elapsed,df.RMSE, color=color, line_dash='dotted', alpha=0.1)

fig = bokeh.plotting.Figure(x_axis_type='datetime', x_axis_label='Training time', y_axis_label='RMSE')
viz_lines(fig, results1, "Linear MF", "orange")
viz_lines(fig, results2, "MLP", "blue")

bokeh.io.show(fig)

Acknowledgement

This tutorial is based on examples from xlvector/github.



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# What if we let the linear model train for a longer time?
results1 = train(net1, train_test_data, num_epoch=30, learning_rate=0.02, ctx=ctx)

Next steps

See this notebook to try using fancier network structures and optimizers on this same problem.



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