Running SIMLR

Daniele Ramazzotti

Bo Wang

Luca De Sano

Serafim Batzoglou

October 31, 2024

Source: vignettes/v2_running_SIMLR.Rmd

The external R package igraph is required for the computation of the normalized mutual information to assess the results of the clustering.

## 
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union

We now run SIMLR as an example on an input dataset from Buettner, Florian, et al. “Computational analysis of cell-to-cell heterogeneity in single-cell RNA-sequencing data reveals hidden subpopulations of cells.” Nature biotechnology 33.2 (2015): 155-160. For this dataset we have a ground true of 3 cell populations, i.e., clusters.

set.seed(11111)
data(BuettnerFlorian)
example = SIMLR(X = BuettnerFlorian$in_X, c = BuettnerFlorian$n_clust, cores.ratio = 0)
## Computing the multiple Kernels.
## Performing network diffiusion.
## Iteration:  1 
## Iteration:  2 
## Iteration:  3 
## Iteration:  4 
## Iteration:  5 
## Iteration:  6 
## Iteration:  7 
## Iteration:  8 
## Iteration:  9 
## Iteration:  10 
## Iteration:  11
## Warning in SIMLR(X = BuettnerFlorian$in_X, c = BuettnerFlorian$n_clust, : Maybe
## you should set a larger value of c.
## Performing t-SNE.
## Epoch: Iteration # 100  error is:  0.08998739 
## Epoch: Iteration # 200  error is:  0.06089897 
## Epoch: Iteration # 300  error is:  0.06045714 
## Epoch: Iteration # 400  error is:  0.06012935 
## Epoch: Iteration # 500  error is:  0.05987104 
## Epoch: Iteration # 600  error is:  0.05965852 
## Epoch: Iteration # 700  error is:  0.05948183 
## Epoch: Iteration # 800  error is:  0.05933143 
## Epoch: Iteration # 900  error is:  0.05919999 
## Epoch: Iteration # 1000  error is:  0.05908594 
## Performing Kmeans.
## Performing t-SNE.
## Epoch: Iteration # 100  error is:  11.69701 
## Epoch: Iteration # 200  error is:  0.6657623 
## Epoch: Iteration # 300  error is:  0.4418035 
## Epoch: Iteration # 400  error is:  0.5574686 
## Epoch: Iteration # 500  error is:  0.6270695 
## Epoch: Iteration # 600  error is:  0.361243 
## Epoch: Iteration # 700  error is:  0.3024225 
## Epoch: Iteration # 800  error is:  0.2892506 
## Epoch: Iteration # 900  error is:  0.281246 
## Epoch: Iteration # 1000  error is:  0.2676769

We now compute the normalized mutual information between the inferred clusters by SIMLR and the true ones. This measure with values in [0,1], allows us to assess the performance of the clustering with higher values reflecting better performance.

nmi_1 = compare(BuettnerFlorian$true_labs[,1], example$y$cluster, method="nmi")
print(nmi_1)
## [1] 0.888298

As a further understanding of the results, we now visualize the cell populations in a plot.

plot(example$ydata, 
    col = c(topo.colors(BuettnerFlorian$n_clust))[BuettnerFlorian$true_labs[,1]], 
    xlab = "SIMLR component 1",
    ylab = "SIMLR component 2",
    pch = 20,
    main="SIMILR 2D visualization for BuettnerFlorian")
Visualization of the 3 cell populations retrieved by SIMLR on the dataset by Florian, et al.

Visualization of the 3 cell populations retrieved by SIMLR on the dataset by Florian, et al.

We also run SIMLR feature ranking on the same inputs to get a rank of the key genes with the related pvalues.

set.seed(11111)
ranks = SIMLR_Feature_Ranking(A=BuettnerFlorian$results$S,X=BuettnerFlorian$in_X)
## 1 
## 2 
## 3 
## 4 
## 5 
## 6 
## 7 
## 8 
## 9 
## 10 
## 11 
## 12 
## 13 
## 14 
## 15 
## 16 
## 17 
## 18 
## 19 
## 20 
## 21 
## 22 
## 23 
## 24 
## 25 
## 26 
## 27 
## 28 
## 29 
## 30 
## 31 
## 32 
## 33 
## 34 
## 35 
## 36 
## 37 
## 38 
## 39 
## 40 
## 41 
## 42 
## 43 
## 44 
## 45 
## 46 
## 47 
## 48 
## 49 
## 50 
## 51 
## 52 
## 53 
## 54 
## 55 
## 56 
## 57 
## 58 
## 59 
## 60 
## 61 
## 62 
## 63 
## 64 
## 65 
## 66 
## 67 
## 68 
## 69 
## 70 
## 71 
## 72 
## 73 
## 74 
## 75 
## 76 
## 77 
## 78 
## 79 
## 80 
## 81 
## 82 
## 83 
## 84 
## 85 
## 86 
## 87 
## 88 
## 89 
## 90 
## 91 
## 92 
## 93 
## 94 
## 95 
## 96 
## 97 
## 98 
## 99 
## 100
head(ranks$pval)
## [1] 1.086748e-128  1.189327e-90  5.504924e-80  4.652359e-75  5.593957e-73
## [6]  3.373056e-69
head(ranks$aggR)
## [1] 5701 1689 7549   57 2653 8081

Similarly, we show an example for SIMLR large scale on an input dataset being a reduced version of the dataset provided in Buettner, Zeisel, Amit, et al. “Cell types in the mouse cortex and hippocampus revealed by single-cell RNA-seq.” Science 347.6226 (2015): 1138-1142. For this dataset we have a ground true of 9 cell populations, i.e., clusters. But we should notice that here we use for computational reasons a reduced version of the data, so please refer to the original publication for the full data.

set.seed(11111)
data(ZeiselAmit)
example_large_scale = SIMLR_Large_Scale(X = ZeiselAmit$in_X, c = ZeiselAmit$n_clust, kk = 10)
## Performing fast PCA.
## Performing k-nearest neighbour search.
## Computing the multiple Kernels.
## Performing the iterative procedure  5  times.
## Iteration:  1 
## Iteration:  2 
## Iteration:  3 
## Iteration:  4 
## Iteration:  5 
## Performing Kmeans.
## Performing t-SNE.
## The main loop will be now performed with a maximum of 300 iterations.
## Performing iteration 1.
## Performing iteration 2.
## Performing iteration 3.
## Performing iteration 4.
## Performing iteration 5.
## Performing iteration 6.
## Performing iteration 7.
## Performing iteration 8.
## Performing iteration 9.
## Performing iteration 10.
## Performing iteration 11.
## Performing iteration 12.
## Performing iteration 13.
## Performing iteration 14.
## Performing iteration 15.
## Performing iteration 16.
## Performing iteration 17.
## Performing iteration 18.
## Performing iteration 19.
## Performing iteration 20.
## Performing iteration 21.
## Performing iteration 22.
## Performing iteration 23.
## Performing iteration 24.
## Performing iteration 25.
## Performing iteration 26.
## Performing iteration 27.
## Performing iteration 28.
## Performing iteration 29.
## Performing iteration 30.
## Performing iteration 31.
## Performing iteration 32.
## Performing iteration 33.
## Performing iteration 34.
## Performing iteration 35.
## Performing iteration 36.
## Performing iteration 37.
## Performing iteration 38.
## Performing iteration 39.
## Performing iteration 40.
## Performing iteration 41.
## Performing iteration 42.
## Performing iteration 43.
## Performing iteration 44.
## Performing iteration 45.
## Performing iteration 46.
## Performing iteration 47.
## Performing iteration 48.
## Performing iteration 49.
## Performing iteration 50.
## Performing iteration 51.
## Performing iteration 52.
## Performing iteration 53.
## Performing iteration 54.
## Performing iteration 55.
## Performing iteration 56.
## Performing iteration 57.
## Performing iteration 58.
## Performing iteration 59.
## Performing iteration 60.
## Performing iteration 61.
## Performing iteration 62.
## Performing iteration 63.
## Performing iteration 64.
## Performing iteration 65.
## Performing iteration 66.
## Performing iteration 67.
## Performing iteration 68.
## Performing iteration 69.
## Performing iteration 70.
## Performing iteration 71.
## Performing iteration 72.
## Performing iteration 73.
## Performing iteration 74.
## Performing iteration 75.
## Performing iteration 76.
## Performing iteration 77.
## Performing iteration 78.
## Performing iteration 79.
## Performing iteration 80.
## Performing iteration 81.
## Performing iteration 82.
## Performing iteration 83.
## Performing iteration 84.
## Performing iteration 85.
## Performing iteration 86.
## Performing iteration 87.
## Performing iteration 88.
## Performing iteration 89.
## Performing iteration 90.
## Performing iteration 91.
## Performing iteration 92.
## Performing iteration 93.
## Performing iteration 94.
## Performing iteration 95.
## Performing iteration 96.
## Performing iteration 97.
## Performing iteration 98.
## Performing iteration 99.
## Performing iteration 100.
## Performing iteration 101.
## Performing iteration 102.
## Performing iteration 103.
## Performing iteration 104.
## Performing iteration 105.
## Performing iteration 106.
## Performing iteration 107.
## Performing iteration 108.
## Performing iteration 109.
## Performing iteration 110.
## Performing iteration 111.
## Performing iteration 112.
## Performing iteration 113.
## Performing iteration 114.
## Performing iteration 115.
## Performing iteration 116.
## Performing iteration 117.
## Performing iteration 118.
## Performing iteration 119.
## Performing iteration 120.
## Performing iteration 121.
## Performing iteration 122.
## Performing iteration 123.
## Performing iteration 124.
## Performing iteration 125.
## Performing iteration 126.
## Performing iteration 127.
## Performing iteration 128.
## Performing iteration 129.
## Performing iteration 130.
## Performing iteration 131.
## Performing iteration 132.
## Performing iteration 133.
## Performing iteration 134.
## Performing iteration 135.
## Performing iteration 136.
## Performing iteration 137.
## Performing iteration 138.
## Performing iteration 139.
## Performing iteration 140.
## Performing iteration 141.
## Performing iteration 142.
## Performing iteration 143.
## Performing iteration 144.
## Performing iteration 145.
## Performing iteration 146.
## Performing iteration 147.
## Performing iteration 148.
## Performing iteration 149.
## Performing iteration 150.
## Performing iteration 151.
## Performing iteration 152.
## Performing iteration 153.
## Performing iteration 154.
## Performing iteration 155.
## Performing iteration 156.
## Performing iteration 157.
## Performing iteration 158.
## Performing iteration 159.
## Performing iteration 160.
## Performing iteration 161.
## Performing iteration 162.
## Performing iteration 163.
## Performing iteration 164.
## Performing iteration 165.
## Performing iteration 166.
## Performing iteration 167.
## Performing iteration 168.
## Performing iteration 169.
## Performing iteration 170.
## Performing iteration 171.
## Performing iteration 172.
## Performing iteration 173.
## Performing iteration 174.
## Performing iteration 175.
## Performing iteration 176.
## Performing iteration 177.
## Performing iteration 178.
## Performing iteration 179.
## Performing iteration 180.
## Performing iteration 181.
## Performing iteration 182.
## Performing iteration 183.
## Performing iteration 184.
## Performing iteration 185.
## Performing iteration 186.
## Performing iteration 187.
## Performing iteration 188.
## Performing iteration 189.
## Performing iteration 190.
## Performing iteration 191.
## Performing iteration 192.
## Performing iteration 193.
## Performing iteration 194.
## Performing iteration 195.
## Performing iteration 196.
## Performing iteration 197.
## Performing iteration 198.
## Performing iteration 199.
## Performing iteration 200.
## Performing iteration 201.
## Performing iteration 202.
## Performing iteration 203.
## Performing iteration 204.
## Performing iteration 205.
## Performing iteration 206.
## Performing iteration 207.
## Performing iteration 208.
## Performing iteration 209.
## Performing iteration 210.
## Performing iteration 211.
## Performing iteration 212.
## Performing iteration 213.
## Performing iteration 214.
## Performing iteration 215.
## Performing iteration 216.
## Performing iteration 217.
## Performing iteration 218.
## Performing iteration 219.
## Performing iteration 220.
## Performing iteration 221.
## Performing iteration 222.
## Performing iteration 223.
## Performing iteration 224.
## Performing iteration 225.
## Performing iteration 226.
## Performing iteration 227.
## Performing iteration 228.
## Performing iteration 229.
## Performing iteration 230.
## Performing iteration 231.
## Performing iteration 232.
## Performing iteration 233.
## Performing iteration 234.
## Performing iteration 235.
## Performing iteration 236.
## Performing iteration 237.
## Performing iteration 238.
## Performing iteration 239.
## Performing iteration 240.
## Performing iteration 241.
## Performing iteration 242.
## Performing iteration 243.
## Performing iteration 244.
## Performing iteration 245.
## Performing iteration 246.
## Performing iteration 247.
## Performing iteration 248.
## Performing iteration 249.
## Performing iteration 250.
## Performing iteration 251.
## Performing iteration 252.
## Performing iteration 253.
## Performing iteration 254.
## Performing iteration 255.
## Performing iteration 256.
## Performing iteration 257.
## Performing iteration 258.
## Performing iteration 259.
## Performing iteration 260.
## Performing iteration 261.
## Performing iteration 262.
## Performing iteration 263.
## Performing iteration 264.
## Performing iteration 265.
## Performing iteration 266.
## Performing iteration 267.
## Performing iteration 268.
## Performing iteration 269.
## Performing iteration 270.
## Performing iteration 271.
## Performing iteration 272.
## Performing iteration 273.
## Performing iteration 274.
## Performing iteration 275.
## Performing iteration 276.
## Performing iteration 277.
## Performing iteration 278.
## Performing iteration 279.
## Performing iteration 280.
## Performing iteration 281.
## Performing iteration 282.
## Performing iteration 283.
## Performing iteration 284.
## Performing iteration 285.
## Performing iteration 286.
## Performing iteration 287.
## Performing iteration 288.
## Performing iteration 289.
## Performing iteration 290.
## Performing iteration 291.
## Performing iteration 292.
## Performing iteration 293.
## Performing iteration 294.
## Performing iteration 295.
## Performing iteration 296.
## Performing iteration 297.
## Performing iteration 298.
## Performing iteration 299.
## Performing iteration 300.

We compute the normalized mutual information between the inferred clusters by SIMLR large scale and the true ones.

nmi_2 = compare(ZeiselAmit$true_labs[,1], example_large_scale$y$cluster, method="nmi")
print(nmi_2)
## [1] 0.04158302

As a further understanding of the results, also in this case we visualize the cell populations in a plot.

plot(example_large_scale$ydata, 
    col = c(topo.colors(ZeiselAmit$n_clust))[ZeiselAmit$true_labs[,1]], 
    xlab = "SIMLR component 1",
    ylab = "SIMLR component 2",
    pch = 20,
    main="SIMILR 2D visualization for ZeiselAmit")
Visualization of the 9 cell populations retrieved by SIMLR large scale on the dataset by Zeisel, Amit, et al.

Visualization of the 9 cell populations retrieved by SIMLR large scale on the dataset by Zeisel, Amit, et al.

Now, as a final example, we also provide the results of two heuristics (see the original SIMLR paper) to estimate the number of clusters from data.

set.seed(53900)
NUMC = 2:5
res_example = SIMLR_Estimate_Number_of_Clusters(BuettnerFlorian$in_X,
    NUMC = NUMC,
    cores.ratio = 0)

Best number of clusters, K1 heuristic:

NUMC[which.min(res_example$K1)]
## [1] 2

K2 heuristic:

NUMC[which.min(res_example$K2)]
## [1] 2

Results of the two heuristics:

res_example
## $K1
## [1] -63.04223 -19.49278 -23.77182  13.30109
## 
## $K2
## [1] -94.56335 -25.99037 -29.71477  15.96130