$\ell_1$-norm constrained multi-block sparse canonical correlation analysis via proximal gradient descent. (arXiv:2201.05289v1 [stat.ME])

Multi-block CCA constructs linear relationships explaining coherent
variations across multiple blocks of data. We view the multi-block CCA problem
as finding leading generalized eigenvectors and propose to solve it via a
proximal gradient descent algorithm with $\ell_1$ constraint for high
dimensional data. In particular, we use a decaying sequence of constraints over
proximal iterations, and show that the resulting estimate is rate-optimal under
suitable assumptions. Although several previous works have demonstrated such
optimality for the $\ell_0$ constrained problem using iterative …

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