What is PCA in dimensionality reduction?

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Supervised and Unsupervised Learning are two primary types of machine learning, differing mainly in how they process and learn from data.

Neural networks are a type of machine learning model inspired by the structure and function of the human brain. They are designed to recognize patterns and relationships in data through a process of learning.

PCA (Principal Component Analysis) is a statistical technique used in dimensionality reduction to simplify complex datasets with many variables while preserving as much important information as possible.

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What PCA Does:

• Transforms the original variables into a new set of variables called principal components.

• These components are uncorrelated and ordered by the amount of variance (information) they capture from the data.

• The first principal component captures the most variance, the second captures the next most, and so on.

• By selecting the top few principal components, you can reduce the dataset’s dimensions while keeping most of the original data’s variability.

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Why Use PCA in Dimensionality Reduction?

• Reduce complexity: Makes data easier to visualize and analyze.

• Remove redundancy: Eliminates correlated features.

• Improve performance: Speeds up machine learning algorithms and reduces overfitting.

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How PCA Works (Simplified):

1. Center the data (subtract mean).

2. Calculate the covariance matrix.

3. Compute eigenvalues and eigenvectors of the covariance matrix.

4. Sort eigenvectors by eigenvalues (variance explained).

5. Project original data onto the top eigenvectors (principal components).

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