Dimensionality Reduction
Dimensionality reduction techniques transform high-dimensional data into a lower-dimensional space while preserving important information and structure.
What is Dimensionality Reduction?
Dimensionality reduction is the process of reducing the number of random variables under consideration by obtaining a set of principal variables. It can be divided into feature selection and feature extraction approaches.
These techniques are essential when dealing with high-dimensional data, which can suffer from the "curse of dimensionality" - as the number of features increases, the amount of data needed to generalize accurately grows exponentially.
Key Characteristics
- Reduces computational complexity and storage requirements
- Helps mitigate the curse of dimensionality
- Removes noise and redundant features
- Enables visualization of high-dimensional data
- Can improve the performance of machine learning algorithms
- Preserves important information while discarding less relevant features
Common Dimensionality Reduction Techniques
A statistical procedure that uses an orthogonal transformation to convert a set of observations into a set of linearly uncorrelated variables called principal components.
Common Applications
Reducing high-dimensional data to 2D or 3D for visualization and exploratory data analysis.
Compressing images while preserving important features and reducing storage requirements.
Creating more meaningful features from high-dimensional data to improve machine learning model performance.
Types of Dimensionality Reduction
Feature Selection
Selecting a subset of the original features without transformation.
- Filter methods (statistical measures)
- Wrapper methods (model performance)
- Embedded methods (built into model training)
Feature Extraction
Transforming the original features into a new feature space.
- Principal Component Analysis (PCA)
- Linear Discriminant Analysis (LDA)
- t-Distributed Stochastic Neighbor Embedding (t-SNE)
- Autoencoders