Sentence examples for distributions of singular values from inspiring English sources

As with the rank, the RIC curves look similar for the small network, but the curves for the 6 ×2048 show very different distributions of singular values for the soft and hard target-trained networks.

We study the distribution of singular values for the matrix of regression coefficients and for the matrix of predicted responses.

It is shown experimentally, that the QR factorization with the complete column pivoting, optionally followed by the LQ factorization of the R-factor, can lead to a substantial decrease of the number of outer parallel iteration steps, whereby the details depend on the condition number and on the distribution of singular values including their multiplicity.

Fig. 4 Distribution of singular values of hidden layer weights.

In addition to the rank of the hidden layer weight matrices, we can also examine the distribution of singular values.

Currently, it is recommended to use the singular values that corresponds to a given percentile, such as the 95th of the distribution of singular values derived from the random data.

We verified using multiple randomised matrices that the null distribution of singular values is very tight (Figure S2), allowing significance to be estimated from as little as 5 permutations.

The procedure was repeated 500 times to generate a sampling distribution of singular values under the null hypothesis.

Using multiple randomisations we verified that the null distribution of singular values was very tight, as expected since null singular values reflect a global property of the randomised data, which should be robust to further randomisations of the data.

SVD was subsequently reapplied to the normalised adjusted data and the spectrum of singular values compared to the null distribution obtained by considering random matrices [ 37, 38].

Within a Bayesian framework, Knapick et al. (2012) proposed a solution by using the singular value decomposition of T such that the decay of singular values is mimicked in the prior distribution of θ.