K-nearest neighbors:

We read in input.scone.csv, which is our file modified (and renamed) from the get.marker.names() function. The K-nearest neighbor generation is derived from the Fast Nearest Neighbors (FNN) R package, within our function Fnn(), which takes as input the “input markers” to be used, along with the concatenated data previously generated, and the desired k. We advise the default selection to the total number of cells in the dataset divided by 100, as has been optimized on existing mass cytometry datasets. The output of this function is a matrix of each cell and the identity of its k-nearest neighbors, in terms of its row number in the dataset used here as input.

library(Sconify)
# Markers from the user-generated excel file
marker.file <- system.file('extdata', 'markers.csv', package = "Sconify")
markers <- ParseMarkers(marker.file)

# How to convert your excel sheet into vector of static and functional markers
markers
## $input
##  [1] "CD3(Cd110)Di"           "CD3(Cd111)Di"           "CD3(Cd112)Di"          
##  [4] "CD235-61-7-15(In113)Di" "CD3(Cd114)Di"           "CD45(In115)Di"         
##  [7] "CD19(Nd142)Di"          "CD22(Nd143)Di"          "IgD(Nd145)Di"          
## [10] "CD79b(Nd146)Di"         "CD20(Sm147)Di"          "CD34(Nd148)Di"         
## [13] "CD179a(Sm149)Di"        "CD72(Eu151)Di"          "IgM(Eu153)Di"          
## [16] "Kappa(Sm154)Di"         "CD10(Gd156)Di"          "Lambda(Gd157)Di"       
## [19] "CD24(Dy161)Di"          "TdT(Dy163)Di"           "Rag1(Dy164)Di"         
## [22] "PreBCR(Ho165)Di"        "CD43(Er167)Di"          "CD38(Er168)Di"         
## [25] "CD40(Er170)Di"          "CD33(Yb173)Di"          "HLA-DR(Yb174)Di"       
## 
## $functional
##  [1] "pCrkL(Lu175)Di"  "pCREB(Yb176)Di"  "pBTK(Yb171)Di"   "pS6(Yb172)Di"   
##  [5] "cPARP(La139)Di"  "pPLCg2(Pr141)Di" "pSrc(Nd144)Di"   "Ki67(Sm152)Di"  
##  [9] "pErk12(Gd155)Di" "pSTAT3(Gd158)Di" "pAKT(Tb159)Di"   "pBLNK(Gd160)Di" 
## [13] "pP38(Tm169)Di"   "pSTAT5(Nd150)Di" "pSyk(Dy162)Di"   "tIkBa(Er166)Di"
# Get the particular markers to be used as knn and knn statistics input
input.markers <- markers[[1]]
funct.markers <- markers[[2]]

# Selection of the k. See "Finding Ideal K" vignette
k <- 30

# The built-in scone functions
wand.nn <- Fnn(cell.df = wand.combined, input.markers = input.markers, k = k)
# Cell identity is in rows, k-nearest neighbors are columns
# List of 2 includes the cell identity of each nn, 
#   and the euclidean distance between
#   itself and the cell of interest

# Indices
str(wand.nn[[1]])
##  int [1:1000, 1:30] 397 493 328 257 66 831 467 719 629 797 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  397  248  595  226  310  745  476  241  730   809
##  [2,]  493  176  966    7  559  149  594   66  477   614
##  [3,]  328  742  147  136  594   89  329  558  914   297
##  [4,]  257  316  458  761  523  729  633  547  681   722
##  [5,]   66  618  222  167   47  435  437  663  654    82
##  [6,]  831  144  780  437  772   85  752  655  505    52
##  [7,]  467  251  559  142  522  829  631  950  665   590
##  [8,]  719  660   56  557  267  773  530  822  499   735
##  [9,]  629  726  212  502  109  394  920  257  567    78
## [10,]  797  541  164  645  398  973  587  252  515   543
## [11,]  849  904  606  387  492  856  909  450  511   957
## [12,]  428  954  755  309   36  200  427  997  245   356
## [13,]  617  515  751  350  833  974  704  798  362   631
## [14,]  974  957  429   53   43  457  602  663  613   781
## [15,]  485  459  956   97  844  572  386  615   38   645
## [16,]  783  838   87  576  990  899  949  148  612   835
## [17,]  791  268  961  845   79  375  733  411  666   139
## [18,]  780  218  917  116  952  908   82  203  276   657
## [19,]  911  704  454  974  833  286  120  104  294   350
## [20,]  241  220  729  158  820  951  595  764  706   487
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 3.65 3.76 2.95 3.26 2.84 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 3.645414 3.709156 4.029866 4.133649 4.134326 4.144389 4.150857 4.153028
##  [2,] 3.760809 3.952757 3.985408 3.989476 4.047919 4.062999 4.075113 4.199003
##  [3,] 2.945146 3.165788 3.324877 3.327581 3.385618 3.470366 3.536828 3.561370
##  [4,] 3.259101 3.261762 3.666321 3.687049 3.791091 3.802243 3.802274 3.805394
##  [5,] 2.835728 3.500711 3.552670 3.585326 3.706476 3.749412 3.754423 3.769125
##  [6,] 3.338399 3.382568 3.566865 3.624838 3.704721 3.757948 3.822214 3.824715
##  [7,] 2.767854 2.806661 2.987004 2.991700 3.122293 3.130170 3.170648 3.189350
##  [8,] 3.915565 4.107313 4.291177 4.400052 4.413866 4.444378 4.574260 4.593292
##  [9,] 3.499473 3.594728 3.677234 3.760076 3.805075 4.009335 4.018692 4.065416
## [10,] 2.958366 3.266185 3.310175 3.432619 3.561533 3.644414 3.664861 3.682744
## [11,] 3.139290 3.254699 3.264064 3.399754 3.474589 3.505483 3.516638 3.627091
## [12,] 2.554459 3.042187 3.873224 4.134249 4.236226 4.353519 4.603931 4.636049
## [13,] 2.551453 2.957247 3.008799 3.145082 3.148818 3.165821 3.178897 3.266841
## [14,] 3.465510 3.536116 3.616258 3.618091 3.643756 3.741816 3.762439 3.767415
## [15,] 3.719667 4.026514 4.176736 4.270014 4.291213 4.377162 4.378579 4.390021
## [16,] 3.708425 4.258050 4.305388 4.807121 5.106599 5.137192 5.161567 5.257490
## [17,] 5.163658 5.323673 5.328068 5.352525 5.355876 5.384779 5.425869 5.463509
## [18,] 3.276811 3.301880 3.315433 3.382013 3.481479 3.566801 3.578287 3.578380
## [19,] 3.137002 3.332833 3.392172 3.572659 3.670411 3.715041 3.813584 3.840656
## [20,] 3.802450 3.897873 3.909321 3.912981 4.139994 4.206469 4.214673 4.235914
##           [,9]    [,10]
##  [1,] 4.296063 4.296554
##  [2,] 4.203501 4.215571
##  [3,] 3.664144 3.676124
##  [4,] 3.814260 3.843571
##  [5,] 3.779799 3.785346
##  [6,] 3.830374 3.831685
##  [7,] 3.201493 3.217548
##  [8,] 4.597965 4.654596
##  [9,] 4.204764 4.285100
## [10,] 3.683244 3.695702
## [11,] 3.689276 3.712615
## [12,] 4.679682 4.708707
## [13,] 3.269239 3.335537
## [14,] 3.797406 3.816846
## [15,] 4.436698 4.441487
## [16,] 5.287662 5.368870
## [17,] 5.481784 5.485570
## [18,] 3.595170 3.608271
## [19,] 3.868350 3.893680
## [20,] 4.291757 4.372950

Finding scone values:

This function iterates through each KNN, and performs a series of calculations. The first is fold change values for each maker per KNN, where the user chooses whether this will be based on medians or means. The second is a statistical test, where the user chooses t test or Mann-Whitney U test. I prefer the latter, because it does not assume any properties of the distributions. Of note, the p values are adjusted for false discovery rate, and therefore are called q values in the output of this function. The user also inputs a threshold parameter (default 0.05), where the fold change values will only be shown if the corresponding statistical test returns a q value below said threshold. Finally, the “multiple.donor.compare” option, if set to TRUE will perform a t test based on the mean per-marker values of each donor. This is to allow the user to make comparisons across replicates or multiple donors if that is relevant to the user’s biological questions. This function returns a matrix of cells by computed values (change and statistical test results, labeled either marker.change or marker.qvalue). This matrix is intermediate, as it gets concatenated with the original input matrix in the post-processing step (see the relevant vignette). We show the code and the output below. See the post-processing vignette, where we show how this gets combined with the input data, and additional analysis is performed.

wand.scone <- SconeValues(nn.matrix = wand.nn, 
                      cell.data = wand.combined, 
                      scone.markers = funct.markers, 
                      unstim = "basal")

wand.scone
## # A tibble: 1,000 × 34
##    `pCrkL(Lu175)Di.IL7.qvalue` pCREB(Yb176)Di.IL7.qvalu…¹ pBTK(Yb171)Di.IL7.qv…²
##                          <dbl>                      <dbl>                  <dbl>
##  1                       1                          0.911                  1    
##  2                       0.892                      0.973                  0.944
##  3                       1                          0.954                  0.778
##  4                       0.876                      0.997                  0.604
##  5                       0.995                      0.950                  0.990
##  6                       1                          0.997                  0.857
##  7                       0.892                      0.988                  0.911
##  8                       1                          0.950                  0.519
##  9                       1                          0.973                  0.970
## 10                       1                          1                      0.663
## # ℹ 990 more rows
## # ℹ abbreviated names: ¹​`pCREB(Yb176)Di.IL7.qvalue`,
## #   ²​`pBTK(Yb171)Di.IL7.qvalue`
## # ℹ 31 more variables: `pS6(Yb172)Di.IL7.qvalue` <dbl>,
## #   `cPARP(La139)Di.IL7.qvalue` <dbl>, `pPLCg2(Pr141)Di.IL7.qvalue` <dbl>,
## #   `pSrc(Nd144)Di.IL7.qvalue` <dbl>, `Ki67(Sm152)Di.IL7.qvalue` <dbl>,
## #   `pErk12(Gd155)Di.IL7.qvalue` <dbl>, `pSTAT3(Gd158)Di.IL7.qvalue` <dbl>, …

For programmers: performing additional per-KNN statistics

If one wants to export KNN data to perform other statistics not available in this package, then I provide a function that produces a list of each cell identity in the original input data matrix, and a matrix of all cells x features of its KNN.

I also provide a function to find the KNN density estimation independently of the rest of the “scone.values” analysis, to save time if density is all the user wants. With this density estimation, one can perform interesting analysis, ranging from understanding phenotypic density changes along a developmental progression (see post-processing vignette for an example), to trying out density-based binning methods (eg. X-shift). Of note, this density is specifically one divided by the aveage distance to k-nearest neighbors. This specific measure is related to the Shannon Entropy estimate of that point on the manifold (https://hal.archives-ouvertes.fr/hal-01068081/document).

I use this metric to avoid the unusual properties of the volume of a sphere as it increases in dimensions (https://en.wikipedia.org/wiki/Volume_of_an_n-ball). This being said, one can modify this vector to be such a density estimation (example http://www.cs.haifa.ac.il/~rita/ml_course/lectures_old/KNN.pdf), by treating the distance to knn as the radius of a n-dimensional sphere and incoroprating said volume accordingly.

An individual with basic programming skills can iterate through these elements to perform the statistics of one’s choosing. Examples would include per-KNN regression and classification, or feature imputation. The additional functionality is shown below, with the example knn.list in the package being the first ten instances:

# Constructs KNN list, computes KNN density estimation
wand.knn.list <- MakeKnnList(cell.data = wand.combined, nn.matrix = wand.nn)
wand.knn.list[[8]]
## # A tibble: 30 × 51
##    `CD3(Cd110)Di` `CD3(Cd111)Di` `CD3(Cd112)Di` `CD235-61-7-15(In113)Di`
##             <dbl>          <dbl>          <dbl>                    <dbl>
##  1         -0.161        0.888          -1.28                    -0.470 
##  2         -0.147       -0.234          -0.0636                  -2.14  
##  3         -1.07        -0.650           0.0482                  -1.15  
##  4         -0.201       -0.220           0.723                   -1.64  
##  5         -0.221       -0.00163        -0.186                   -1.05  
##  6         -1.26        -0.980          -0.244                   -1.77  
##  7         -0.438       -0.0758         -0.118                   -0.678 
##  8         -0.233        0.549           0.631                    0.0991
##  9          0.392       -0.0429         -0.335                   -2.89  
## 10          0.371       -0.357           0.355                   -0.604 
## # ℹ 20 more rows
## # ℹ 47 more variables: `CD3(Cd114)Di` <dbl>, `CD45(In115)Di` <dbl>,
## #   `CD19(Nd142)Di` <dbl>, `CD22(Nd143)Di` <dbl>, `IgD(Nd145)Di` <dbl>,
## #   `CD79b(Nd146)Di` <dbl>, `CD20(Sm147)Di` <dbl>, `CD34(Nd148)Di` <dbl>,
## #   `CD179a(Sm149)Di` <dbl>, `CD72(Eu151)Di` <dbl>, `IgM(Eu153)Di` <dbl>,
## #   `Kappa(Sm154)Di` <dbl>, `CD10(Gd156)Di` <dbl>, `Lambda(Gd157)Di` <dbl>,
## #   `CD24(Dy161)Di` <dbl>, `TdT(Dy163)Di` <dbl>, `Rag1(Dy164)Di` <dbl>, …
# Finds the KNN density estimation for each cell, ordered by column, in the 
# original data matrix
wand.knn.density <- GetKnnDe(nn.matrix = wand.nn)
str(wand.knn.density)
##  num [1:1000] 0.229 0.236 0.265 0.252 0.257 ...