Dimensionality Reduction Techniques in Machine Learning

Dimensionality reduction is a process used to reduce the number of input variables while preserving essential information. It helps improve model efficiency, reduce overfitting, and enhance interpretability.

Techniques for Dimensionality Reduction:

  1. Feature Selection: Selecting the most relevant features using:

    • Filter Methods (e.g., correlation, mutual information).

    • Wrapper Methods (e.g., Recursive Feature Elimination).

    • Embedded Methods (e.g., Lasso Regression).

  2. Feature Extraction: Transforming data into a lower-dimensional space:

    • Principal Component Analysis (PCA)

    • Linear Discriminant Analysis (LDA)

    • Autoencoders (Neural Networks-based)

Principal Component Analysis (PCA) for Dimensionality Reduction

PCA is an unsupervised technique that projects high-dimensional data into a lower-dimensional space while preserving maximum variance.

Steps of PCA:

  1. Standardization: Normalize data to have zero mean and unit variance.

  2. Compute Covariance Matrix: Identifies relationships between features.

  3. Eigen Decomposition: Compute eigenvalues and eigenvectors of the covariance matrix.

  4. Select Principal Components: Choose the top k eigenvectors corresponding to the largest eigenvalues.

  5. Transform Data: Project data onto the new lower-dimensional space.

PCA for Visualization

  • 2D & 3D Projection: PCA is widely used to visualize high-dimensional datasets by reducing them to 2 or 3 principal components for plotting.

  • Pattern Recognition: Helps in identifying clusters in data, useful in applications like image processing, genetics, and NLP.

Conclusion

PCA efficiently reduces dimensionality, improves model performance, and enables better visualization of complex datasets.