## Parallel Jaccard Benchmarks

We have implemented a naive but fast parallel version of Jaccard Coefficient estimation for the Phenograph method, thus obtaing a speed boot of about 20X when comparade with previous serial implementation.

Tets were performed using a dataset composed by 32900 cells and using different numbers of neighbors for each cell (i.e. 15, 25, 50, 100, 250). Each jaccard estimation method (serial and parallel) was run two times. See code below for details.

test | elapsed | relative | cell neighbors number |
---|---|---|---|

Parallel Jaccard | 54.822 | 1.000 | 250 |

Serial Jaccard |
1293.185 | 23.589 |
250 |

Parallel Jaccard | 7.192 | 1.000 | 100 |

Serial Jaccard |
161.533 | 22.460 |
100 |

Parallel Jaccard | 1.614 | 1.000 | 50 |

Serial Jaccard |
38.642 | 23.942 |
50 |

Parallel Jaccard | 0.372 | 1.000 | 25 |

Serial Jaccard |
9.546 | 25.661 |
25 |

Parallel Jaccard | 0.114 | 1.000 | 15 |

Serial Jaccard |
3.366 | 29.526 |
15 |

Below the code used to generate the above table using PBMCs dataset from HERE.

```
library(gficf)
library(uwot)
library(RcppParallel)
library(rbenchmark)
# Step 1: load PBMC dstsdet
pbmc = readRDS("/path/to/Purified.PBMC.RAW.rds")
data = gficf::gficf(M = pbmc,cell_proportion_max = 1,cell_proportion_min = .05,storeRaw = F,normalize = F)
rm(pbmc);gc()
# Step 2: Reduce data with PCA
data = gficf::runPCA(data = data,dim = 10)
# Benchmarks
RcppParallel::setThreadOptions(numThreads = 6)
res = NULL
for (neigh.number in c(15,25,50,100,250))
{
message(paste("Testing neigh = ",neigh.number))
neigh.idx = uwot:::find_nn(data$pca$cells,k=neigh.number+1,include_self = T,n_threads = 6,verbose = F,method = "annoy")$idx
neigh.idx = neigh.idx[,-1]
# compare performance of serial and parallel
tmp <- benchmark(gficf:::jaccard_coeff(neigh.idx,T),
gficf:::rcpp_parallel_jaccard_coef(neigh.idx,T),
replications=2,
order="elapsed")
tmp$neigh_number = neigh.number
res = rbind(tmp,res)
}
print(res[,c("test","elapsed","relative","neigh_number")])
```

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