由於 Michael Nielsen 先生已經將那個長七十四行之派生程式講解的十分清楚的了，此處也就不再贅述。直接跳接執行段文本︰
How well does the program recognize handwritten digits? Well, let’s start by loading in the MNIST data. I’ll do this using a little helper program, mnist_loader.py, to be described below. We execute the following commands in a Python shell,
>>> import mnist_loader >>> training_data, validation_data, test_data = \ ... mnist_loader.load_data_wrapper()
Of course, this could also be done in a separate Python program, but if you’re following along it’s probably easiest to do in a Python shell.
After loading the MNIST data, we’ll set up a Network with 30 hidden neurons. We do this after importing the Python program listed above, which is named network,
>>> import network >>> net = network.Network([784, 30, 10])
Finally, we’ll use stochastic gradient descent to learn from the MNIST training_data over 30 epochs, with a mini-batch size of 10, and a learning rate of 
,
>>> net.SGD(training_data, 30, 10, 3.0, test_data=test_data)
Note that if you’re running the code as you read along, it will take some time to execute – for a typical machine (as of 2015) it will likely take a few minutes to run. I suggest you set things running, continue to read, and periodically check the output from the code. If you’re in a rush you can speed things up by decreasing the number of epochs, by decreasing the number of hidden neurons, or by using only part of the training data. Note that production code would be much, much faster: these Python scripts are intended to help you understand how neural nets work, not to be high-performance code! And, of course, once we’ve trained a network it can be run very quickly indeed, on almost any computing platform. For example, once we’ve learned a good set of weights and biases for a network, it can easily be ported to run in Javascript in a web browser, or as a native app on a mobile device. In any case, here is a partial transcript of the output of one training run of the neural network. The transcript shows the number of test images correctly recognized by the neural network after each epoch of training. As you can see, after just a single epoch this has reached 9,129 out of 10,000, and the number continues to grow,
Epoch 0: 9129 / 10000
Epoch 1: 9295 / 10000
Epoch 2: 9348 / 10000
...
Epoch 27: 9528 / 10000
Epoch 28: 9542 / 10000
Epoch 29: 9534 / 10000
That is, the trained network gives us a classification rate of about 95 percent – 95.42 percent at its peak (“Epoch 28”)! That’s quite encouraging as a first attempt. I should warn you, however, that if you run the code then your results are not necessarily going to be quite the same as mine, since we’ll be initializing our network using (different) random weights and biases. To generate results in this chapter I’ve taken best-of-three runs.
…… ※學習會退化耶 ？
然而此刻我們並不談這些執行結果。為求能更深入理解那個程式之『學習過程』，我們需要安裝一些 Python 『工具』程式庫。就像 Michael Nielsen 先生不只打包了 MNIST 之『資料庫』︰
neural-networks-and-deep-learning/data/
mnist.pkl.gz
。還寫了一個方便的『導入』程式︰
neural-networks-and-deep-learning/src/mnist_loader.py
。但當改天需要使用 MNIST 原始資料庫時，
THE MNIST DATABASE
of handwritten digits
Yann LeCun, Courant Institute, NYU
Corinna Cortes, Google Labs, New York
Christopher J.C. Burges, Microsoft Research, Redmond
………
自己還是得了解它的檔案格式
FILE FORMATS FOR THE MNIST DATABASE
The data is stored in a very simple file format designed for storing vectors and multidimensional matrices. General info on this format is given at the end of this page, but you don’t need to read that to use the data files.
All the integers in the files are stored in the MSB first (high endian) format used by most non-Intel processors. Users of Intel processors and other low-endian machines must flip the bytes of the header.
There are 4 files:
train-images-idx3-ubyte: training set images
train-labels-idx1-ubyte: training set labels
t10k-images-idx3-ubyte: test set images
t10k-labels-idx1-ubyte: test set labels
The training set contains 60000 examples, and the test set 10000 examples.
The first 5000 examples of the test set are taken from the original NIST training set. The last 5000 are taken from the original NIST test set. The first 5000 are cleaner and easier than the last 5000.
TRAINING SET LABEL FILE (train-labels-idx1-ubyte):
[offset] [type] [value] [description]
0000 32 bit integer 0x00000801(2049) magic number (MSB first)
0004 32 bit integer 60000 number of items
0008 unsigned byte ?? label
0009 unsigned byte ?? label
........
xxxx unsigned byte ?? label
The labels values are 0 to 9.
TRAINING SET IMAGE FILE (train-images-idx3-ubyte):
[offset] [type] [value] [description]
0000 32 bit integer 0x00000803(2051) magic number
0004 32 bit integer 60000 number of images
0008 32 bit integer 28 number of rows
0012 32 bit integer 28 number of columns
0016 unsigned byte ?? pixel
0017 unsigned byte ?? pixel
........
xxxx unsigned byte ?? pixel
Pixels are organized row-wise. Pixel values are 0 to 255. 0 means background (white), 255 means foreground (black).
TEST SET LABEL FILE (t10k-labels-idx1-ubyte):
[offset] [type] [value] [description]
0000 32 bit integer 0x00000801(2049) magic number (MSB first)
0004 32 bit integer 10000 number of items
0008 unsigned byte ?? label
0009 unsigned byte ?? label
........
xxxx unsigned byte ?? label
The labels values are 0 to 9.
TEST SET IMAGE FILE (t10k-images-idx3-ubyte):
[offset] [type] [value] [description]
0000 32 bit integer 0x00000803(2051) magic number
0004 32 bit integer 10000 number of images
0008 32 bit integer 28 number of rows
0012 32 bit integer 28 number of columns
0016 unsigned byte ?? pixel
0017 unsigned byte ?? pixel
........
xxxx unsigned byte ?? pixel
Pixels are organized row-wise. Pixel values are 0 to 255. 0 means background (white), 255 means foreground (black).
───
。故而於此介紹兩套派生程式庫︰
Introduction
matplotlib is a python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. matplotlib can be used in python scripts, the python and ipython shell (ala MATLAB®* or Mathematica®†), web application servers, and six graphical user interface toolkits.
matplotlib tries to make easy things easy and hard things possible. You can generate plots, histograms, power spectra, bar charts, errorcharts, scatterplots, etc, with just a few lines of code. For a sampling, see the screenshots, thumbnail gallery, and examples directory
For simple plotting the pyplot interface provides a MATLAB-like interface, particularly when combined with IPython. For the power user, you have full control of line styles, font properties, axes properties, etc, via an object oriented interface or via a set of functions familiar to MATLAB users.
───
以及
Python Imaging Library (PIL)
The Python Imaging Library (PIL) adds image processing capabilities to your Python interpreter. This library supports many file formats, and provides powerful image processing and graphics capabilities.
Status
The current free version is PIL 1.1.7. This release supports Python 1.5.2 and newer, including 2.5 and 2.6. A version for 3.X will be released later.
……
或應改為
About
Goals
The fork author’s goal is to foster and support active development of PIL through:
- Continuous integration testing via Travis CI
- Publicized development activity on GitHub
- Regular releases to the Python Package Index
License
Like PIL, Pillow is licensed under the MIT-like open source PIL Software License:
Software License
The Python Imaging Library (PIL) is
Copyright © 1997-2011 by Secret Labs AB
Copyright © 1995-2011 by Fredrik Lundh
By obtaining, using, and/or copying this software and/or its associated documentation, you agree that you have read, understood, and will comply with the following terms and conditions:
Permission to use, copy, modify, and distribute this software and its associated documentation for any purpose and without fee is hereby granted, provided that the above copyright notice appears in all copies, and that both that copyright notice and this permission notice appear in supporting documentation, and that the name of Secret Labs AB or the author not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission.
SECRET LABS AB AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL SECRET LABS AB OR THE AUTHOR BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
Why a fork?
PIL is not setuptools compatible. Please see this Image-SIG post for a more detailed explanation. Also, PIL’s current bi-yearly (or greater) release schedule is too infrequent to accommodate the large number and frequency of issues reported.
What about PIL?
Note
Prior to Pillow 2.0.0, very few image code changes were made. Pillow 2.0.0 added Python 3 support and includes many bug fixes from many contributors.
As more time passes since the last PIL release, the likelihood of a new PIL release decreases. However, we’ve yet to hear an official “PIL is dead” announcement. So if you still want to support PIL, please report issues here first, then open corresponding Pillow tickets here.
Please provide a link to the first ticket so we can track the issue(s) upstream.
───
以方便 MNIST 手寫阿拉伯數字之『圖像顯示』和『圖形處理』，或將更可以『驗證』它之『辨識』能力乎？？！！