Math Problem Statement
Given data points (2, 3, −1),(−1, 0, −1),(2, 4, 1),(−1, −3, 1),(−2, −4, 0), perform PCA step by-step to reduce data dimension into k = 2
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Principal Component Analysis (PCA)
Dimensionality Reduction
Formulas
Covariance matrix formula: Cov(X) = (1/n) * Σ(X_i - μ)(X_i - μ)^T
Eigenvalue decomposition: Cov(X) * v = λ * v
Theorems
Spectral theorem
Eigenvalue and eigenvector properties
Suitable Grade Level
Undergraduate level
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