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Principal Component Analysis

Hunt for the direction a cloud of points spreads most, find that it is an eigenvector of the covariance matrix, and flatten the data onto it — in two dimensions and in three. Then watch a change of units fool it.

Builds onEigenvectors and Eigenvalues Random Variables and Expectation Change of Basis

PCA computed in your browser · seeded synthetic clouds

Act 1 of 6 · Spreadstep 1 of 22

X[n, d] =[40, 2]C[2, 2]

Speed

40 points with two features, x₁ and x₂, and no labels. Their mean is (0.64, 0.22). Spread is measured by variance: 0.729 along x₁ and 1.314 along x₂, 2.043 in total. PCA asks which direction holds the most of it.

\bar x = \tfrac{1}{40} \textstyle\sum_i x_i = (0.64,\ 0.22)

Principal Component Analysis

Builds onEigenvectors and Eigenvalues Random Variables and Expectation Change of Basis

PCA computed in your browser · seeded synthetic clouds

Act 1 of 6 · Spreadstep 1 of 22

X[n, d] =[40, 2]C[2, 2]

Speed

\bar x = \tfrac{1}{40} \textstyle\sum_i x_i = (0.64,\ 0.22)

DSAverse

Principal Component Analysis

See also

Principal Component Analysis

See also