An Implicit Form of Krasulina's k-PCA Update without the Orthonormality Constraint
national conference on artificial intelligence, 2020.
We shed new insights on the two commonly used updates for the online $k$-PCA problem, namely, Krasulina's and Oja's updates. We show that Krasulina's update corresponds to a projected gradient descent step on the Stiefel manifold of the orthonormal $k$-frames, while Oja's update amounts to a gradient descent step using the unprojected g...More
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