We often deal with numerical values that are sparse and scattered all over the place. We don't really need to store these values. This is where one-hot encoding comes into the picture. We can think of one-hot encoding as a tool that tightens feature vectors. It looks at each feature and identifies the total number of distinct values. It uses a one-of-k scheme to encode values. Each feature in the feature vector is encoded based on this scheme. This helps us to be more efficient in terms of space.

Let's say we are dealing with four-dimensional feature vectors. To encode the nth feature in a feature vector, the encoder will go through the nth feature in each feature vector and count the number of distinct values. If the number of distinct values is k, it will transform the feature into a k-dimensional vector where only one value is 1 and all other values are 0. Let's take a simple example to understand how this works.

Let's see how to encode data in Python:

1. Let's take an array with four rows (vectors) and three columns (features):

>> data = np.array([[1, 1, 2], [0, 2, 3], [1, 0, 1], [0, 1, 0]])
>> print(data)

The following result is printed:

[[1 1 2]
 [0 2 3]
 [1 0 1]
 [0 1 0]]

Let's analyze the values present in each column (feature):

• The first feature has two possible values: 0, 1
• The second feature has three possible values: 0, 1, 2
• The third feature has four possible values: 0, 1, 2, 3

So, overall, the sum of the possible values present in each feature is given by 2 + 3 + 4 = 9. This means that 9 entries are required to uniquely represent any vector. The three features will be represented as follows:

• Feature 1 starts at index 0
• Feature 2 starts at index 2
• Feature 3 starts at index 5

2. To encode categorical integer features as a one-hot numeric array, the preprocessing.OneHotEncoder() function can be used as follows:

>> encoder = preprocessing.OneHotEncoder()
>> encoder.fit(data)

The first row of code sets the encoder, then the fit() function fits the OneHotEncoder object to a data array.

3. Now we can transform the data array using one-hot encoding. To do this, the transform() function will be used as follows:

>> encoded_vector = encoder.transform([[1, 2, 3]]).toarray()

If you were to print encoded_vector, the expected output would be:

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

The result is clear: the first feature (1) has an index of 1, the second feature (3) has an index of 4, and the third feature (3) has an index of 8. As we can verify, only these positions are occupied by a 1; all the other positions have a 0. Remember that Python indexes the positions starting from 0, so the 9 entries will have indexes from 0 to 8.

The preprocessing.OneHotEncoder() function encodes categorical integer features as a one-hot numeric array. Starting from an array of integers or strings that denotes the values assumed by categorical characteristics (discrete), this function encodes the characteristics using a one-hot coding scheme, returning dummy variables. This creates a binary column for each category and returns a sparse array or a dense array.

It often happens that you have to convert categorical data. This is due to the fact that many machine learning algorithms can't work directly with categorical data. To use these methods, it is necessary to first transform categorical data into numerical data. This is required for both input and output variables.

• Scikit-learn's official documentation of the sklearn.preprocessing.OneHotEncoder() function: https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.OneHotEncoder.html.