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For a linear system, the response to a stimulus is often superposed by itsresponses to other decomposed stimuli. In quantum mechanics, a state is thesuperposition of multiple eigenstates. Here, by taking advantage of the phasedifference, a common feature as we identified in data sets, we propose eigencomponent analysis (ECA), an interpretable linear learning model thatincorporates the principle of quantum mechanics into the design of algorithmdesign for feature extraction, classification, dictionary and deep learning,and adversarial generation, etc. The simulation of ECA, possessing a measurable$class\text{-}label$ $\mathcal{H}$, on a classical computer outperforms theexisting classical linear models. Eigen component analysis network (ECAN), anetwork of concatenated ECA models, enhances ECA and gains the potential to benot only integrated with nonlinear models, but also an interface for deepneural networks to implement on a quantum computer, by analogizing a data setas recordings of quantum states. Therefore, ECA and ECAN promise to expand thefeasibility of linear learning models, by adopting the strategy of quantummachine learning to replace heavy nonlinear models with succinct linearoperations in tackling complexity.

Eigen component analysis: A quantum theory incorporated machine learning technique to find linearly maximum separable components