79 lines
3.3 KiB
Python
79 lines
3.3 KiB
Python
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# %load mnist_loader.py
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"""
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mnist_loader
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~~~~~~~~~~~~
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A library to load the MNIST image data. For details of the data
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structures that are returned, see the doc strings for ``load_data``
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and ``load_data_wrapper``. In practice, ``load_data_wrapper`` is the
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function usually called by our neural network code.
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"""
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#### Libraries
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# Standard library
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import pickle
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import gzip
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# Third-party libraries
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import numpy as np
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def load_data():
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"""Return the MNIST data as a tuple containing the training data,
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the validation data, and the test data.
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The ``training_data`` is returned as a tuple with two entries.
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The first entry contains the actual training images. This is a
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numpy ndarray with 50,000 entries. Each entry is, in turn, a
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numpy ndarray with 784 values, representing the 28 * 28 = 784
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pixels in a single MNIST image.
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The second entry in the ``training_data`` tuple is a numpy ndarray
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containing 50,000 entries. Those entries are just the digit
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values (0...9) for the corresponding images contained in the first
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entry of the tuple.
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The ``validation_data`` and ``test_data`` are similar, except
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each contains only 10,000 images.
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This is a nice data format, but for use in neural networks it's
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helpful to modify the format of the ``training_data`` a little.
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That's done in the wrapper function ``load_data_wrapper()``, see
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below.
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"""
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f = gzip.open('mnist.pkl.gz', 'rb')
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training_data, validation_data, test_data = pickle.load(f, encoding="latin1")
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f.close()
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return (training_data, validation_data, test_data)
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def load_data_wrapper():
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"""Return a tuple containing ``(training_data, validation_data,
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test_data)``. Based on ``load_data``, but the format is more
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convenient for use in our implementation of neural networks.
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In particular, ``training_data`` is a list containing 50,000
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2-tuples ``(x, y)``. ``x`` is a 784-dimensional numpy.ndarray
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containing the input image. ``y`` is a 10-dimensional
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numpy.ndarray representing the unit vector corresponding to the
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correct digit for ``x``.
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``validation_data`` and ``test_data`` are lists containing 10,000
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2-tuples ``(x, y)``. In each case, ``x`` is a 784-dimensional
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numpy.ndarry containing the input image, and ``y`` is the
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corresponding classification, i.e., the digit values (integers)
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corresponding to ``x``.
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Obviously, this means we're using slightly different formats for
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the training data and the validation / test data. These formats
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turn out to be the most convenient for use in our neural network
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code."""
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tr_d, va_d, te_d = load_data()
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training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]
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training_results = [vectorized_result(y) for y in tr_d[1]]
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training_data = zip(training_inputs, training_results)
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validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]
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validation_data = zip(validation_inputs, va_d[1])
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test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]
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test_data = zip(test_inputs, te_d[1])
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return (training_data, validation_data, test_data)
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def vectorized_result(j):
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"""Return a 10-dimensional unit vector with a 1.0 in the jth
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position and zeroes elsewhere. This is used to convert a digit
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(0...9) into a corresponding desired output from the neural
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network."""
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e = np.zeros((10, 1))
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e[j] = 1.0
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return e
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