Categorical features are those that represent data in categorical or textual form. Handling categorical features can be a challenging task in machine learning because most algorithms require numerical input data. In this regard, several advanced techniques have been developed to handle such data, including target encoding and entity embeddings.
**Target Encoding**
Target encoding is a method of converting categorical features into numerical values based on the mean value of the target variable. It is also known as mean encoding, likelihood encoding, and impact encoding. The idea behind target encoding is that it uses information from the target variable to create new features for the model.
The target mean is calculated for each category and then used as a numerical value for that category. The target mean is calculated as:
$\large{ \displaystyle\textrm{Target Mean} = \frac{\sum y_i}{n_i}}$
Where yi is the target variable value for the ith instance in the category and ni is the number of instances in the category.
Target encoding can be useful in cases where the cardinality of the categorical feature is high or when there is a strong relationship between the categorical feature and the target variable.
Example:
Suppose we have a dataset of customers with their respective purchase amounts, where the feature Product is categorical and has the following values: "A", "B", "C", "D". We can perform target encoding to convert the categorical values into numerical values based on their occurrence in the dataset, in the following way:
| Product | Target |
| --------| ------ |
| A | 10 |
| B | 20 |
| C | 40 |
| D | 5 |The target encoding for each category can be calculated as:
$$\large{ \displaystyle\mathrm{TargetEncoding}(A) = \frac{10}{1}=10}$$
$$\large{ \displaystyle\mathrm{TargetEncoding}(B) = \frac{20}{1}=20}$$
$$\large{ \displaystyle\mathrm{TargetEncoding}(C) = \frac{40}{1}=40}$$
$$\large{ \displaystyle\mathrm{TargetEncoding}(D) = \frac{5}{1}=5}$$
Thus, the categorical variable Product can be converted to numerical values using target encoding as follows:
| Product | Target Encoding |
| --------| ---------------|
| A | 10 |
| B | 20 |
| C | 40 |
| D | 5 |**Entity Embeddings**
Entity embedding is a technique used to represent categorical variables in a continuous low-dimensional space. The idea behind entity embedding is to map each level of a categorical variable to a unique vector in the continuous space. This mapping is learned during the training of the machine learning model, allowing it to capture the relationship between the categorical variable and the target variable.
Entity embeddings have been shown to be effective in several machine learning applications, including natural language processing, recommendation systems, and image recognition.
The process of generating entity embeddings involves creating an embedding matrix containing a vector representation of each level of the categorical variable. The embedding matrix is then used as an additional input to the machine learning model. The embedding matrix can be learned using a neural network by minimizing a loss function that measures the difference between the predicted and actual values.
Example:
Suppose we have a dataset of customers with their respective demographic data, where the categorical feature Gender has the following values: "Male", "Female", and "Other". We can perform entity embedding to convert the categorical values into continuous vector representation, as follows:
| Gender | Embedding Vector |
| --------| ---------------|
| Male | [0.1, 0.3, 0.2] |
| Female | [0.2, 0.4, 0.5] |
| Other | [0.5, 0.1, 0.4] |Thus, the categorical variable Gender can be converted to continuous vector representation using entity embedding as follows:
| Gender | Embedding Vector |
| --------| ---------------|
| Male | [0.1, 0.3, 0.2] |
| Female | [0.2, 0.4, 0.5] |
| Other | [0.5, 0.1, 0.4] |In conclusion, target encoding and entity embedding are advanced techniques for handling categorical features in machine learning. Both techniques have proven to be useful in real-world applications, and their effectiveness depends on the particular dataset and the problem at hand.