# SVT algorithm and the value of tau.

SVT stands for singular value thresholding. It is an algorithm used in "matrix completion" problems. see http://svt.stanford.edu/ for basics. What is the meaning of "for large values of [tau]..." without actually stating what a "large" value is relative to? I often see such references in mathematical literature and it leaves me puzzled. Thanks

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## 1 Answer

Referring to (P3) on your link:

$$\min_{X \in C} \tau \lVert X \rVert_{*} + \frac{1}{2} \lVert X \rVert_{F}^2$$

A sufficiently large value of $\tau$ would be any value that causes the nucular norm term to be significantly larger than the Frobenius norm term such that omitting the Frobenius norm term will not result in a significantly different result relative to the result obtained from the sum of the nuclear and Frobenius norm terms.

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Ah, Thank you - that was easy to understand and seems so relatively more obvious now. – val Jan 16 '13 at 17:47