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arXiv · 1701.00711

Approximation of Gram-Schmidt Orthogonalization by Data Matrix

Gen Li·Yuantao Gu
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Abstract

For a matrix ${\bf A}$ with linearly independent columns, this work studies to use its normalization $\bar{\bf A}$ and ${\bf A}$ itself to approximate its orthonormalization $\bf V$. We theoretically analyze the order of the approximation errors as $\bf A$ and $\bar{\bf A}$ approach ${\bf V}$, respectively. Our conclusion is able to explain the fact that a high dimensional Gaussian matrix can well approximate the corresponding truncated Haar matrix. For applications, this work can serve as a foundation of a wide variety of problems in signal processing such as compressed subspace clustering.

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Gen Li, Yuantao Gu. 2016-12-31. Approximation of Gram-Schmidt Orthogonalization by Data Matrix. https://arxiv.org/abs/1701.00711

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