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About this paper
Jan Quan, Johan Suykens, Panagiotis Patrinos
A re-examination of Principal Component Analysis through Difference-of-Convex duality yields novel theoretical formulations and algorithms, fundamentally linking simultaneous iteration to DCA. This approach also introduces a kernelizable dual for robust PCA, showing first-order methods can outperform state-of-the-art eigensolvers on new formulations and effectively handle outliers.
Key insights
- Simultaneous iteration, a classical method for eigenvalue computation, is fundamentally an instance of the Difference-of-Convex Algorithm (DCA).
- For PCA-like problems, unitary invariance in the primal DC formulation is the key property enabling kernelizability and out-of-sample applicability of the dual.
- The performance of optimization methods for PCA is highly dependent on the choice of primal vs. dual formulation, matrix dimensions, and spectral properties of the data.
Summary by alphaXiv.
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