Example:
x = np.array([0, 1, 2, 1, 0])
output = to_categorical(x)
print(output)
# Output:
# [[1. 0. 0.]
# [0. 1. 0.]
# [0. 0. 1.]
# [0. 1. 0.]
# [1. 0. 0.]]
Reasoning:
Each element in the input array is transformed into a one-hot encoded vector,
where the index corresponding to the value in the input array is set to 1,
and all other indices are set to 0.
One-hot encoding is a method used to represent categorical variables as binary vectors. This technique is useful in machine learning when dealing with categorical data that has no ordinal relationship.
In one-hot encoding, each category is represented by a binary vector with a length equal to the number of categories. The vector has a value of 1 at the index corresponding to the category and 0 at all other indices.
For example, if you have three categories: 0, 1, and 2, the one-hot encoded vectors would be:
This method ensures that the model does not assume any ordinal relationship between categories, which is crucial for many machine learning algorithms. The one-hot encoding process can be mathematically represented as follows:
Given a category \( x_i \) from a set of categories \( \{0, 1, \ldots, n-1\} \), the one-hot encoded vector \( \mathbf{v} \) is:
\[ \mathbf{v}_i = \begin{cases} 1 & \text{if } i = x_i \\ 0 & \text{otherwise} \end{cases} \]This vector \( \mathbf{v} \) will have a length equal to the number of unique categories.
import numpy as np
def to_categorical(x, n_col=None):
# One-hot encoding of nominal values
# If n_col is not provided, determine the number of columns from the input array
if not n_col:
n_col = np.amax(x) + 1
# Initialize a matrix of zeros with shape (number of samples, n_col)
one_hot = np.zeros((x.shape[0], n_col))
# Set the appropriate elements to 1
one_hot[np.arange(x.shape[0]), x] = 1
return one_hot