08. Dimensionality Reduction
AI For Trading C6 L2 A06 Dimensionality Reduction V3.1
Understanding Overfitting and Dimensionality Reduction
Overfitting: Occurs when a model is too complex for available data, often due to excessive features.
Solutions: Two main approaches are expanding data set or selecting fewer features. Gathering more data is difficult, making feature selection crucial.
Feature Elimination: Involves understanding each feature's impact on the model. However, deciding which features to remove isn't simple.
Dimensionality Reduction: Automatically simplifies feature space without manual decisions.
Principal Component Analysis (PCA):
- Most renowned method in dimensionality reduction.
- Transforms data to a new coordinate system where variance is captured on fewer axes.
- Identifies important data trends by creating new axes (principal components).
- Enables reducing dimensions by eliminating less significant axes.
Applications: Useful for managing and simplifying datasets, especially when visualizing high-dimensional data.
Trade-offs: Reduces complexity and risk of overfitting but may lose some data nuances.
Keep in mind that the aim is to achieve computational efficiency while retaining essential data information.
AI For Trading C6 L2 A06 Dimensionality Reduction V2.2
Overview of Dimensionality Reduction and PCA
Principal Component Analysis (PCA) Drawbacks:
- Principal components lack clear real-world interpretation.
- Assumes linear correlation between features; otherwise ineffective.
Situational Examples:
- Non-linear relationships and lack of correlation challenge PCA's utility as demonstrated in example plots.
Alternative Techniques:
LDA (Linear Discriminant Analysis):
Used in supervised learning for classification.
Focuses on separating classes by maximizing variance ratio.
t-SNE (T-distributed Stochastic Neighbor Embedding):
Useful for visualizing high-dimensional data.
Offers non-linear approach unlike PCA, aiding feature selection through deeper data insights.
Consider exploring these techniques further to expand understanding beyond PCA and apply them effectively in various data analysis scenarios.