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学习笔记426—keras中to_categorical函数解析

keras中to_categorical函数解析

1.to_categorical的功能

简单来说，to_categorical就是将类别向量转换为二进制（只有0和1）的矩阵类型表示。其表现为将原有的类别向量转换为独热编码的形式。先上代码看一下效果：

from keras.utils.np_utils import *
#类别向量定义
b = [0,1,2,3,4,5,6,7,8]
#调用to_categorical将b按照9个类别来进行转换
b = to_categorical(b, 9)
print(b)
  
执行结果如下：
[[1. 0. 0. 0. 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. 1. 0. 0. 0. 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. 1. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 1. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 1.]]

to_categorical最为keras中提供的一个工具方法，从以上代码运行可以看出，将原来类别向量中的每个值都转换为矩阵里的一个行向量，从左到右依次是0,1,2，...8个类别。2表示为[0. 0. 1. 0. 0. 0. 0. 0. 0.]，只有第3个为1，作为有效位，其余全部为0。
2.one_hot encoding(独热编码)介绍

独热编码又称为一位有效位编码，上边代码例子中其实就是将类别向量转换为独热编码的类别矩阵。也就是如下转换：

     0  1  2  3  4  5  6  7  8
0=> [1. 0. 0. 0. 0. 0. 0. 0. 0.]
1=> [0. 1. 0. 0. 0. 0. 0. 0. 0.]
2=> [0. 0. 1. 0. 0. 0. 0. 0. 0.]
3=> [0. 0. 0. 1. 0. 0. 0. 0. 0.]
4=> [0. 0. 0. 0. 1. 0. 0. 0. 0.]
5=> [0. 0. 0. 0. 0. 1. 0. 0. 0.]
6=> [0. 0. 0. 0. 0. 0. 1. 0. 0.]
7=> [0. 0. 0. 0. 0. 0. 0. 1. 0.]
8=> [0. 0. 0. 0. 0. 0. 0. 0. 1.]

那么一道思考题来了，让你自己编码实现类别向量向独热编码的转换，该怎样实现呢？

以下是我自己粗浅写的一个小例子，仅供参考：

def convert_to_one_hot(labels, num_classes):
    #计算向量有多少行
    num_labels = len(labels)
    #生成值全为0的独热编码的矩阵
    labels_one_hot = np.zeros((num_labels, num_classes))
    #计算向量中每个类别值在最终生成的矩阵“压扁”后的向量里的位置
    index_offset = np.arange(num_labels) * num_classes
    #遍历矩阵，为每个类别的位置填充1
    labels_one_hot.flat[index_offset + labels] = 1
    return labels_one_hot
#进行测试
b = [2, 4, 6, 8, 6, 2, 3, 7]
print(convert_to_one_hot(b,9))
  
测试结果：
[[0. 0. 1. 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. 0. 0. 0. 0. 0. 0. 1.]
 [0. 0. 0. 0. 0. 0. 1. 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. 0. 0. 1. 0.]]

3.源码解析

to_categorical在keras的utils/np_utils.py中，源码如下：

def to_categorical(y, num_classes=None, dtype='float32'):
    """Converts a class vector (integers) to binary class matrix.
    E.g. for use with categorical_crossentropy.
    # Arguments
        y: class vector to be converted into a matrix
            (integers from 0 to num_classes).
        num_classes: total number of classes.
        dtype: The data type expected by the input, as a string
            (`float32`, `float64`, `int32`...)
    # Returns
        A binary matrix representation of the input. The classes axis
        is placed last.
    # Example
    ```python
    # Consider an array of 5 labels out of a set of 3 classes {0, 1, 2}:
    > labels
    array([0, 2, 1, 2, 0])
    # `to_categorical` converts this into a matrix with as many
    # columns as there are classes. The number of rows
    # stays the same.
    > to_categorical(labels)
    array([[ 1.,  0.,  0.],
           [ 0.,  0.,  1.],
           [ 0.,  1.,  0.],
           [ 0.,  0.,  1.],
           [ 1.,  0.,  0.]], dtype=float32)
    ```
    """
    #将输入y向量转换为数组
    y = np.array(y, dtype='int')
    #获取数组的行列大小
    input_shape = y.shape
    if input_shape and input_shape[-1] == 1 and len(input_shape) > 1:
        input_shape = tuple(input_shape[:-1])
    #y变为1维数组
    y = y.ravel()
    #如果用户没有输入分类个数，则自行计算分类个数
    if not num_classes:
        num_classes = np.max(y) + 1
    n = y.shape[0]
    #生成全为0的n行num_classes列的值全为0的矩阵
    categorical = np.zeros((n, num_classes), dtype=dtype)
    #np.arange(n)得到每个行的位置值，y里边则是每个列的位置值
    categorical[np.arange(n), y] = 1
    #进行reshape矫正
    output_shape = input_shape + (num_classes,)
    categorical = np.reshape(categorical, output_shape)
    return categorical