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Fig. 2 | Genome Biology

Fig. 2

From: CellFishing.jl: an ultrafast and scalable cell search method for single-cell RNA sequencing

Fig. 2

Benchmarks of randomized SVD. a Elapsed time of different SVD algorithms. The blue, orange, and green points indicate the elapsed time of the full, truncated, and randomized SVD, respectively. b Relative errors of the randomized SVD. The error bars denote the standard deviation of ten trials. The relative error of the ith largest singular value σi is defined as \(\left |1 - \frac {\hat \sigma _{i}}{\sigma _{i}}\right |\), where \(\hat \sigma _{i}\) is an approximated value of σi. The error bars denote the standard deviation of ten trials. The approximation error for a real matrix A with a low-rank matrix is bounded by a singular value as illustrated in the following formula: minrank(X)≤j||AX||=σj+1, where ||·|| denotes the operator norm of a matrix

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