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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)

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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.