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Quantum Mechanics Meets Pca: an (un)expected Convergence

Towards Data Science 11:23 am on May 22, 2024

Linear algebra in PCA reveals total variance through eigenvalues, with the first principal component (v_1) indicating highest variance direction due to its significant contribution. This mirrors quantum mechanics where state vectors and energy operators form the basis for understanding physical systems. The overlap is evident when considering eigenvectors of the energy operator as a basis in PCA, revealing an intuitive link between "energy" values (principal components) and their significance within quantum states.

Principle Component Analysis (PCA):
Total variance represented by eigenvalues; highest variance in the first component.
Eigenvalues' magnitudes reflect their importance to total variance, ordered from largest to smallest.
Connection between quantum mechanics and PCA: eigenvectors of energy operators as basis for both.
Quantum states correlate with principal components; first component indicates highest "energy" contribution.

https://towardsdatascience.com/quantum-mechanics-meets-pca-an-un-expected-convergence-5e04bcb16376

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Quantum Mechanics Meets Pca: an (un)expected Convergence

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