AI Feature Engineeering (Gemini)
Adding dimensions to a feature space is a core part of feature engineering, a process where developers use domain knowledge and data transformations to create new features that improve a machine learning model's performance.
Here are several ways to add more dimensions to a feature space:
1. Creating Interaction Features
This involves combining two or more existing features to create a new, more informative feature. This can help a model capture relationships that a simple linear model might miss.
Multiplication: Multiplying two features to capture their combined effect. For example, in a housing price dataset, you might create a new feature for Area by multiplying Length and Width. A new dimension could be price_per_sq_ft.
Ratios: Dividing one feature by another. For example, Price per Square Foot could be a new feature.
Polynomial Features: Raising existing features to a power (e.g., Age², Weight³). This is a powerful technique for capturing non-linear relationships. A model might not learn that Age has a non-linear relationship with a target variable, but providing Age² as a new dimension can help it discover this.
2. Using Domain Knowledge
A developer's understanding of the data's subject matter can be a powerful source for creating new, useful features.
Time-based Features: For time-series data, you can create new dimensions like Day of the Week, Month, Is it a Holiday?, or Time of Day. You could also create lag features, where the value of a variable at a previous time step becomes a new dimension.
Aggregation: If you have multiple records for a single entity (e.g., a customer's purchase history), you can aggregate them to create new dimensions like Average Monthly Spend or Total Number of Transactions.
3. Feature Encoding
This is often used to convert non-numerical data into a numerical format, which can dramatically increase the number of dimensions.
One-Hot Encoding: A common technique for categorical features. If a feature like "City" has 50 unique values, you can create 50 new binary dimensions (columns), one for each city.
For each data point, the corresponding city's column will have a 1, and all others will have a 0. This is a classic way to increase dimensionality for a model that can only handle numerical inputs.
Word Embeddings: In natural language processing, you can transform words in a text document into dense vectors. These vectors can have hundreds of dimensions, and they represent the semantic meaning of the words.
4. Kernel Methods
This is a more abstract way to increase dimensionality, often used implicitly by algorithms like Support Vector Machines (SVMs).
The Kernel Trick: Kernel functions map data from a low-dimensional space to a much higher (sometimes infinite-dimensional) feature space. This is done to make the data linearly separable in the new space, even if it wasn't in the original space.
You do not explicitly create the new features; the kernel function handles the transformation, allowing the algorithm to work with the data as if it were in a higher dimension.
In all these cases, a developer is intentionally increasing the number of features (and thus the dimensionality of the feature space) to give a model more information or to represent the existing information in a way that is easier for the model to learn.