Eigen component analysis: A quantum theory incorporated machine learning technique to find linearly maximum separable components
This work addresses the problem of improving linear models for machine learning tasks by leveraging quantum-inspired strategies, though it appears incremental as it builds on existing linear and quantum machine learning concepts.
The authors proposed eigen component analysis (ECA), a linear learning model incorporating quantum mechanics principles to enhance feature extraction and classification, which outperformed existing classical linear models in simulations. They also introduced ECAN, a network of ECA models, to integrate with nonlinear models and potentially interface with quantum computers.
For a linear system, the response to a stimulus is often superposed by its responses to other decomposed stimuli. In quantum mechanics, a state is the superposition of multiple eigenstates. Here, by taking advantage of the phase difference, a common feature as we identified in data sets, we propose eigen component analysis (ECA), an interpretable linear learning model that incorporates the principle of quantum mechanics into the design of algorithm design 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 the existing classical linear models. Eigen component analysis network (ECAN), a network of concatenated ECA models, enhances ECA and gains the potential to be not only integrated with nonlinear models, but also an interface for deep neural networks to implement on a quantum computer, by analogizing a data set as recordings of quantum states. Therefore, ECA and ECAN promise to expand the feasibility of linear learning models, by adopting the strategy of quantum machine learning to replace heavy nonlinear models with succinct linear operations in tackling complexity.