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] 522 331 748 797 783 769 134 302 782 108 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  522  745  135  899   54   94  981  367  780   363
##  [2,]  331  840  858  562  515  345  909  703  814   100
##  [3,]  748   24  250    7  392  479  137  579  810   736
##  [4,]  797  758   30  292  823  983   82  398  437   306
##  [5,]  783  520  191  154  319  957  738   91  608   588
##  [6,]  769  115  997  474  768  629  935  509  133   244
##  [7,]  134 1000  736  568  510  954  902  748  294   859
##  [8,]  302  114  389  743  772  660  904   17  549   245
##  [9,]  782  151  488  135  161  823  191  319  552   610
## [10,]  108  495  124  729  469  260  721  357  887   511
## [11,]  471  357  343  201  632   53  241  574  315   866
## [12,]    8  706  904  983  506  531  285  426  302   383
## [13,]  692  604   18  571  713  588  617  766  577   976
## [14,]  173  529  799  949  902  519  859  514  162   736
## [15,]  342  945  588   26  730  230  526  863  380   991
## [16,]  958  190  227  657  485  424  768  115  560   256
## [17,]  228  992  588  772  487  732    8  526  762   156
## [18,]  588  342  577  732  660  980  487  668  566   766
## [19,]  741  966  674  371  513  874  749  541  215   370
## [20,]  892   61  393  783  801  172  422  835  607   628
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 4.06 3.13 3.94 3.42 3.29 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 4.057365 4.499547 4.615946 4.746571 4.764987 4.776526 4.826832 4.830917
##  [2,] 3.132644 3.201004 3.574940 3.639797 3.831307 3.868862 3.922722 3.997139
##  [3,] 3.938531 3.943092 3.960518 4.052555 4.075821 4.247613 4.351326 4.409553
##  [4,] 3.418597 3.647291 3.719420 3.755778 3.764763 3.780412 3.784215 3.798833
##  [5,] 3.294101 3.540613 3.558196 3.593978 3.652203 3.698915 3.737825 3.759327
##  [6,] 3.238448 3.431571 3.518805 3.526893 3.582698 3.654889 3.707655 3.864263
##  [7,] 3.072292 3.485924 3.489735 3.685677 3.721304 3.824062 3.828479 3.869371
##  [8,] 2.469692 2.525892 2.541346 2.568863 2.609080 2.759327 2.781595 2.840275
##  [9,] 3.062838 3.141044 3.195781 3.216842 3.297911 3.356542 3.399645 3.403091
## [10,] 3.605968 3.656766 3.807738 3.813461 3.905923 4.008878 4.041281 4.058931
## [11,] 3.045342 3.553603 3.592151 3.756674 3.780027 3.999451 4.020970 4.067377
## [12,] 3.475064 3.635163 3.728996 3.732867 3.775467 3.802628 3.817044 3.928596
## [13,] 3.616236 3.709744 3.837977 3.887278 3.927038 4.026565 4.088930 4.235365
## [14,] 3.236308 3.669423 3.931054 3.978212 4.056790 4.155755 4.395414 4.429955
## [15,] 2.622165 2.678530 2.800239 2.910490 2.919274 2.920141 3.068432 3.104714
## [16,] 2.491643 3.037649 3.230650 3.331466 3.359248 3.381674 3.392959 3.399999
## [17,] 2.166226 2.608916 2.742256 2.763797 2.811036 2.826947 2.840275 2.845754
## [18,] 2.117253 2.342175 2.522522 2.552946 2.592490 2.594668 2.654381 2.816208
## [19,] 2.516009 2.712644 2.734073 2.908386 3.024370 3.160874 3.166317 3.269707
## [20,] 3.301789 3.357944 3.415477 3.433735 3.433897 3.478375 3.483313 3.568558
##           [,9]    [,10]
##  [1,] 4.851867 4.862725
##  [2,] 4.004922 4.059065
##  [3,] 4.472377 4.480609
##  [4,] 3.837787 3.838603
##  [5,] 3.767822 3.805221
##  [6,] 3.865901 3.885352
##  [7,] 3.929520 3.984988
##  [8,] 2.854118 2.873922
##  [9,] 3.423982 3.445764
## [10,] 4.059009 4.105608
## [11,] 4.124997 4.132393
## [12,] 3.971680 3.972110
## [13,] 4.259835 4.293666
## [14,] 4.523136 4.529453
## [15,] 3.109715 3.235715
## [16,] 3.434338 3.511985
## [17,] 2.874981 2.916131
## [18,] 2.858085 2.910121
## [19,] 3.286231 3.297299
## [20,] 3.601772 3.606580

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                       0.973                      0.981                  0.942
##  2                       0.973                      0.515                  0.523
##  3                       1                          0.848                  0.354
##  4                       0.569                      0.924                  0.143
##  5                       1                          0.836                  0.503
##  6                       1                          0.902                  0.445
##  7                       0.973                      0.822                  0.917
##  8                       1                          0.802                  0.424
##  9                       0.973                      0.822                  0.464
## 10                       1                          0.761                  0.772
## # 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        -0.148          0.816         -0.0442                  -1.36  
##  2        -0.557         -0.0292        -0.621                    0.469 
##  3        -0.0494        -0.196         -0.0961                   0.996 
##  4        -0.179         -0.131         -0.159                   -0.550 
##  5        -0.105         -0.202         -0.202                   -0.564 
##  6         0.787         -0.239          0.0882                   0.0555
##  7         0.237         -0.0447        -0.119                   -0.717 
##  8        -0.180         -0.255         -0.0147                  -0.455 
##  9        -0.121         -0.0918        -0.283                   -1.11  
## 10        -0.170         -0.0392        -0.270                   -0.653 
## # 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] 0.199 0.241 0.215 0.253 0.258 ...