One Hot Encoding

Multi-classification problem

tf.keras.datasets provides some data sets:

boston_housing module: Public API for tf.keras.datasets.boston_housing namespace.
cifar10 module: Public API for tf.keras.datasets.cifar10 namespace.
cifar100 module: Public API for tf.keras.datasets.cifar100 namespace.
fashion_mnist module: Public API for tf.keras.datasets.fashion_mnist namespace.
imdb module: Public API for tf.keras.datasets.imdb namespace.
mnist module: Public API for tf.keras.datasets.mnist namespace.
reuters module: Public API for tf.keras.datasets.reuters namespace.

Today we use the cifar10 data set to explain:

Basic data analysis process

When we are prepare to use a new data set, the first thing is to download the data set.

The cifar10 data set is in tensorflow, so the first thing is to install tensorflow.

pip install tensorflow-cpu

Enter the above command in the CMD command prompt (search in win10)

tensorflow will be installed on your computer. Please note that tensorflow is a deep learning library, the library has two versions of CPU and GPU, because the GPU version is extremely troublesome to install, so I recommend installing the CPU version here.

I will tell you about the GPU version installation in the anaconda and deeplearning tutorial.

Deep learning requires a huge amount of calculation. Generally, the CPU has only 4-16 cores, and even the most powerful CPU today will generally not exceed 100 cores. That is to say, if I want to train a deep learning model, a CPU can only train 16 data at a time, and deep learning generally contains tens of thousands of data and extremely complex networks. So using CPU to train deep learning often takes a very long time.

However, GPUs often have hundreds of thousands of cores, so when we use GPUs for calculations, they are dozens of times faster than CPUs, which compresses the calculations that would otherwise take several days to dozens of minutes to dozens of minutes.

New GPUs often have TPU cores (computing cores that only support integer numbers, and deep learning often does not require such high precision), and these tensor cores often have faster computing speeds.

Designing GPU computing programs is a very complicated thing. Fortunately, libraries like tensorflow have helped us design programs. The same program can run on both the CPU and the GPU.

Then we can load the cifar data set and visualize it:

from tensorflow.keras.datasets import cifar10

(x_train, y_train), (x_test, y_test) = cifar10.load_data()

print('x_train.shape =', x_train.shape)
print('y_train.shape =', y_train.shape)

print()

print('x_train[:5] =', x_train[:5])
print('y_train[:5] =', y_train[:5])

import matplotlib.pyplot as plt

for i in range(1, 31):
    plt.subplot(5, 6, i)
    plt.imshow(x_train[i])
    plt.title('label={}'.format(y_train[i]))
    plt.axis('off')

plt.tight_layout()
plt.show()

The output is as follows:

x_train.shape = (50000, 32, 32, 3)
y_train.shape = (50000, 1)

x_train[:5] = [[[[ 59  62  63]
   [ 43  46  45]
   [ 50  48  43]
   ...
   [158 132 108]
   [152 125 102]
   [148 124 103]]

  [[ 16  20  20]
   [  0   0   0]
   [ 18   8   0]
   ...
   [123  88  55]
   [119  83  50]
   [122  87  57]]

  [[ 25  24  21]
   [ 16   7   0]
   [ 49  27   8]
   ...
   [118  84  50]
   [120  84  50]
   [109  73  42]]

  ...

  [[208 170  96]
   [201 153  34]
   [198 161  26]
   ...
   [160 133  70]
   [ 56  31   7]
   [ 53  34  20]]

  [[180 139  96]
   [173 123  42]
   [186 144  30]
   ...
   [184 148  94]
   [ 97  62  34]
   [ 83  53  34]]

  [[177 144 116]
   [168 129  94]
   [179 142  87]
   ...
   [216 184 140]
   [151 118  84]
   [123  92  72]]]


 [[[154 177 187]
   [126 137 136]
   [105 104  95]
   ...
   [ 91  95  71]
   [ 87  90  71]
   [ 79  81  70]]

  [[140 160 169]
   [145 153 154]
   [125 125 118]
   ...
   [ 96  99  78]
   [ 77  80  62]
   [ 71  73  61]]

  [[140 155 164]
   [139 146 149]
   [115 115 112]
   ...
   [ 79  82  64]
   [ 68  70  55]
   [ 67  69  55]]

  ...

  [[175 167 166]
   [156 154 160]
   [154 160 170]
   ...
   [ 42  34  36]
   [ 61  53  57]
   [ 93  83  91]]

  [[165 154 128]
   [156 152 130]
   [159 161 142]
   ...
   [103  93  96]
   [123 114 120]
   [131 121 131]]

  [[163 148 120]
   [158 148 122]
   [163 156 133]
   ...
   [143 133 139]
   [143 134 142]
   [143 133 144]]]


 [[[255 255 255]
   [253 253 253]
   [253 253 253]
   ...
   [253 253 253]
   [253 253 253]
   [253 253 253]]

  [[255 255 255]
   [255 255 255]
   [255 255 255]
   ...
   [255 255 255]
   [255 255 255]
   [255 255 255]]

  [[255 255 255]
   [254 254 254]
   [254 254 254]
   ...
   [254 254 254]
   [254 254 254]
   [254 254 254]]

  ...

  [[113 120 112]
   [111 118 111]
   [105 112 106]
   ...
   [ 72  81  80]
   [ 72  80  79]
   [ 72  80  79]]

  [[111 118 110]
   [104 111 104]
   [ 99 106  98]
   ...
   [ 68  75  73]
   [ 70  76  75]
   [ 78  84  82]]

  [[106 113 105]
   [ 99 106  98]
   [ 95 102  94]
   ...
   [ 78  85  83]
   [ 79  85  83]
   [ 80  86  84]]]


 [[[ 28  25  10]
   [ 37  34  19]
   [ 38  35  20]
   ...
   [ 76  67  39]
   [ 81  72  43]
   [ 85  76  47]]

  [[ 33  28  13]
   [ 34  30  14]
   [ 32  27  12]
   ...
   [ 95  82  55]
   [ 96  82  56]
   [ 85  72  45]]

  [[ 39  32  15]
   [ 40  33  17]
   [ 57  50  33]
   ...
   [ 93  76  52]
   [107  89  66]
   [ 95  77  54]]

  ...

  [[ 83  73  52]
   [ 87  77  56]
   [ 84  74  52]
   ...
   [ 99  93  70]
   [ 90  84  61]
   [ 81  75  52]]

  [[ 88  72  51]
   [ 90  74  52]
   [ 93  77  56]
   ...
   [ 80  74  53]
   [ 76  70  49]
   [ 82  76  55]]

  [[ 97  78  56]
   [ 94  75  53]
   [ 93  75  53]
   ...
   [ 54  47  28]
   [ 63  56  37]
   [ 72  65  46]]]


 [[[170 180 198]
   [168 178 196]
   [177 185 203]
   ...
   [162 179 215]
   [158 178 214]
   [157 177 212]]

  [[168 181 198]
   [172 185 201]
   [171 183 200]
   ...
   [159 177 212]
   [156 176 211]
   [154 174 209]]

  [[154 170 186]
   [149 165 181]
   [129 144 162]
   ...
   [161 178 214]
   [157 177 212]
   [154 174 209]]

  ...

  [[ 74  84  80]
   [ 76  85  81]
   [ 78  85  82]
   ...
   [ 71  75  78]
   [ 68  72  75]
   [ 61  65  68]]

  [[ 68  76  77]
   [ 69  77  78]
   [ 72  79  78]
   ...
   [ 76  80  83]
   [ 71  75  78]
   [ 71  75  78]]

  [[ 67  75  78]
   [ 68  76  79]
   [ 69  75  76]
   ...
   [ 75  79  82]
   [ 71  75  78]
   [ 73  77  80]]]]
y_train[:5] = [[6]
 [9]
 [9]
 [4]
 [1]]

cifar10 contains a total of ten different types.

Each type is represented by a number. They are from 0-9.

Maximum likelihood analysis

Maximum likelihood analysis is our most commonly used analysis method.

For example, there is a baby who just came into this world. He doesn't know anything.

You tell him what a panda is, and he learned what a panda is.

You tell him what a horse is, and he learned what a horse is.

At this time you showed him a picture of a zebra. He has never seen a zebra, but he has seen horses and pandas. He thinks that zebras look more like pandas, so zebras are pandas.

This is the maximum likelihood analysis. For another example, in the morning there are dense clouds and the weather forecast says it might rain in the afternoon, so you bring an umbrella before you go out. This is also a maximum likelihood analysis, because you believe it is likely to rain in the afternoon, so in order not to get wet, you Bring an umbrella. If you don't think it will rain in the afternoon, then you will not bring an umbrella because it is a troublesome thing.

Maximum likelihood analysis is to find the probability of each event, then compare these probabilities, and consider that the highest probability event will occur.

For example, if I throw a dice, but this dice has been manipulated, the probability of 5 face up is 80%, and the probability of the other faces up is only 4%. Then after maximum likelihood analysis, I Think 5 is up.

One Hot Encoding

We return to the cifar10 classification problem.

The code of the airplane is 0, the code of the bird is 2, and the code of the car is 1.

There is a thing that looks like both a bird and an airplane. The definition of airplane is 0 and the definition of bird is 2. Then the weight of the probability of this thing should be around 1, right? So if we analyze according to the maximum likelihood, this thing is likely to be a car.

This is obviously wrong, if we directly weight according to the number, then there will be confusion between things.

So we use one-hot encoding to solve this problem.

airplane =  [ 1, 0, 0 ]
car =       [ 0, 1, 0 ]
bird =      [ 0, 0, 1 ]

One-hot encoding is to turn the original label into a sparse matrix. Each different type is represented on a different column, and the remaining columns are all 0.

Then when the probability distribution of an object is [0.6, 0, 0.4], this object is an airplane according to the maximum likelihood analysis, instead of being defined as a car.

Code and implementation

from tensorflow.keras.datasets import cifar10

(x_train, y_train), (x_test, y_test) = cifar10.load_data()

print('y_train.shape =', y_train.shape)
print('y_train[:10] =\n', y_train[:10])
print()



from tensorflow.keras.utils import to_categorical

y_train_onehot = to_categorical(y_train)

print('y_train_onehot.shape =', y_train_onehot.shape)
print('y_train_onehot[:10] =\n', y_train_onehot[:10])

There are many ways to implement one-hot encoding, and to_categorical is one of the easiest ways.

We can observe whether the position of 1 in the figure below is the same as the label above. (Hint: start from 0)

y_train.shape = (50000, 1)
y_train[:10] =
 [[6]
 [9]
 [9]
 [4]
 [1]
 [1]
 [2]
 [7]
 [8]
 [3]]

y_train_onehot.shape = (50000, 10)
y_train_onehot[:10] =
 [[0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]
 [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]]
>>>

The above is the way to realize one-hot encoding, let's talk about how to restore one-hot encoding:

y_train_onehot = [
    [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
    [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
    [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
    [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
    [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
    [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
    [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
    [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
    [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
    [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ]
    ]

import numpy as np

for i in y_train_onehot:
    print( np.argmax(i) )

argmax is a function specially used to solve maximum likelihood analysis and one-hot encoding fallback. Its meaning is to find out where the maximum value appears in a set of data.

We use the same set of data to test and you will find that the backed one-hot encoding is exactly the same as the label before encoding.

One-hot coding is very commonly used in deep learning and machine learning.

This section introduces the cafir10 data set and some keras commonly used data sets, as well as what is maximum likelihood analysis and one-hot coding.

Need to pay attention to

from tensorflow.keras.utils import to_categorical

y_train = [ 1, 2, 3 ]
print(to_categorical(y_train))

The result of the above code is:

[[0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]
>>>

There are three types of our input, but to_categorical gives four types of results, indicating that to_categorical starts from 0.

from tensorflow.keras.utils import to_categorical

y_train = [ 1, 9, 14 ]
print(to_categorical(y_train))

The above code is as follows:

[[0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]
>>>

to_categorical will faithfully encode the numbers into one-hot codes in the order from 0-1-2-3, which means that even if I only have three categories 1, 9, 14, it will still be encoded into a huge matrix. When your categories are not continuous, you need to make the categories continuous or use other methods to encode one-hot encoding.

from tensorflow.keras.utils import to_categorical

y_train = [ 'cat', 'dog', 'monkey' ]
print(to_categorical(y_train))

The output of the above program is as follows:

Traceback (most recent call last):
  File "xxxxx.py", line 4, in <module>
    print(to_categorical(y_train))
  File "...\np_utils.py", line 69, in to_categorical
    y = np.array(y, dtype='int')
ValueError: invalid literal for int() with base 10: 'cat'

You will find that to_categorical can only be numbered according to numbers, and this number has to be an integer number.

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Start time of this page: December 25, 2021

Completion time of this page: December 28, 2021

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