Author: Daniele RamazzottiBo WangLuca De SanoSerafim Batzoglou

# Running SIMLR

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

    library(igraph)

    ##
    ## Attaching package: 'igraph'

    ## The following objects are masked from 'package:stats':
    ##
    ##     decompose, spectrum

    ## The following object is masked from 'package:base':
    ##
    ##     union

    library(SIMLR)

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
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    ## 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:  0.09963693
    ## Epoch: Iteration # 200  error is:  0.06058465
    ## Epoch: Iteration # 300  error is:  0.05917217
    ## Epoch: Iteration # 400  error is:  0.05894224
    ## Epoch: Iteration # 500  error is:  0.05875543
    ## Epoch: Iteration # 600  error is:  0.05859694
    ## Epoch: Iteration # 700  error is:  0.05846076
    ## Epoch: Iteration # 800  error is:  0.05834064
    ## Epoch: Iteration # 900  error is:  0.05823708
    ## Epoch: Iteration # 1000  error is:  0.05814519
    ## Performing Kmeans.
    ## Performing t-SNE.
    ## Epoch: Iteration # 100  error is:  10.68672
    ## Epoch: Iteration # 200  error is:  0.7104486
    ## Epoch: Iteration # 300  error is:  0.5736699
    ## Epoch: Iteration # 400  error is:  0.7495346
    ## Epoch: Iteration # 500  error is:  0.4888358
    ## Epoch: Iteration # 600  error is:  0.7009221
    ## Epoch: Iteration # 700  error is:  0.5901729
    ## Epoch: Iteration # 800  error is:  0.4479219
    ## Epoch: Iteration # 900  error is:  0.4278976
    ## Epoch: Iteration # 1000  error is:  0.4230764

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.

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)

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    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.
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    ## Performing Kmeans.
    ## Performing t-SNE.
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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.

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