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] 359 212 570 322 24 34 354 152 373 199 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  359  273  973  622  537  567  704  531  589   251
##  [2,]  212  544  985  512  256  675  208  978  900   710
##  [3,]  570   38  949  337  634  360  964  484  408   649
##  [4,]  322  530  292  956  710  883  361  663  850   512
##  [5,]   24  888  650  646   32  803  247  641  962   670
##  [6,]   34    7  288  906  517  354  172  588  881   912
##  [7,]  354  912  288    6  881  172   34  445  517   836
##  [8,]  152   98  519  800  794   15  913  218  763   606
##  [9,]  373  323  333   20  759  727  832  404   51   654
## [10,]  199  318  954  984  428  184  212  975  492   951
## [11,]  952  391  260  689  799  913  840  388  717   401
## [12,]  352  131  125  585  130  558  869  449  998   561
## [13,]  166  436   41  773  350  371  267  586  173   972
## [14,]  792  456  952  649  964  116  506   15  794   969
## [15,]  964  456  792  606  952   56  260  152  669   717
## [16,]  834  161  718  886  306  991   71  813  606    52
## [17,]  540  784  848  365   44  495  894  249  562   217
## [18,]  225  852  545  935  605   65  146  975  763   508
## [19,]  989  438  531  523  273  261  990  118  107    69
## [20,]  741  404  891    9  945  207  780  419  270   727
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 4.04 2.64 4.07 2.75 3.71 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 4.035305 4.038179 4.177173 4.372719 4.448643 4.471075 4.475194 4.526836
##  [2,] 2.641899 3.104684 3.221942 3.237992 3.239236 3.301745 3.317642 3.326276
##  [3,] 4.065915 4.407605 4.497995 4.505718 4.667527 4.684504 4.724088 4.912392
##  [4,] 2.754331 2.918729 2.964791 3.064875 3.133546 3.140060 3.180808 3.225316
##  [5,] 3.710470 3.795016 3.807232 3.887025 4.108874 4.154509 4.174313 4.200468
##  [6,] 3.388935 3.556980 3.772751 4.105836 4.136748 4.336553 4.539583 4.630311
##  [7,] 3.265561 3.288425 3.475343 3.556980 3.750875 3.855725 4.066634 4.107363
##  [8,] 3.586636 3.682744 3.759096 3.800485 3.800792 4.024737 4.031784 4.049032
##  [9,] 3.036149 3.150189 3.182555 3.291503 3.364669 3.395017 3.423078 3.692382
## [10,] 2.636345 2.677292 2.759145 2.812937 2.954664 2.972508 3.004992 3.037446
## [11,] 3.877440 4.057885 4.191101 4.250197 4.308944 4.366451 4.417027 4.456726
## [12,] 3.418311 3.466023 3.659268 3.853933 3.890838 3.931818 3.955120 3.986126
## [13,] 3.473602 3.709277 4.064624 4.405604 4.443858 4.472271 4.487576 4.531966
## [14,] 3.626690 3.781224 3.847783 3.990122 4.104321 4.270507 4.324263 4.374040
## [15,] 2.707680 2.821755 2.941805 3.187454 3.250388 3.292698 3.380915 3.392029
## [16,] 3.231923 4.291241 4.429173 4.587355 5.065862 5.317487 5.576074 5.605470
## [17,] 5.774074 5.989672 6.176424 6.197935 6.322531 6.343355 6.347331 6.373304
## [18,] 2.921099 2.936044 2.995608 3.135549 3.151006 3.357157 3.386441 3.396874
## [19,] 3.409890 3.638739 3.739323 3.769065 3.781679 4.001721 4.033151 4.067418
## [20,] 3.016322 3.263121 3.277102 3.291503 3.309315 3.330960 3.439355 3.489788
##           [,9]    [,10]
##  [1,] 4.548545 4.597727
##  [2,] 3.365591 3.369532
##  [3,] 4.980528 4.990545
##  [4,] 3.267076 3.287998
##  [5,] 4.279224 4.284625
##  [6,] 4.752419 4.804014
##  [7,] 4.215118 4.400167
##  [8,] 4.080342 4.106147
##  [9,] 3.707049 3.712159
## [10,] 3.061104 3.087089
## [11,] 4.632899 4.649404
## [12,] 4.013946 4.018560
## [13,] 4.623144 4.651978
## [14,] 4.403991 4.409067
## [15,] 3.424335 3.521479
## [16,] 5.750151 5.791681
## [17,] 6.504011 6.512254
## [18,] 3.419248 3.468788
## [19,] 4.083570 4.099165
## [20,] 3.615325 3.617184

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                          0.618                  0.992
##  2                       0.983                      0.983                  0.825
##  3                       0.983                      0.952                  0.970
##  4                       1                          0.736                  0.607
##  5                       0.983                      0.758                  0.910
##  6                       0.873                      0.932                  0.880
##  7                       0.983                      0.952                  0.861
##  8                       1                          0.823                  0.970
##  9                       0.871                      0.759                  0.964
## 10                       0.949                      0.991                  0.607
## # 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        -0.158         -0.0951        -0.235                   -0.369 
##  2        -0.0954        -0.168          0.308                    0.133 
##  3        -0.0111        -0.248          0.302                    0.587 
##  4        -0.0437        -0.244          0.831                    0.451 
##  5        -0.0860        -0.237          0.360                    0.254 
##  6        -0.218         -0.233         -0.0306                  -1.52  
##  7        -0.365          0.577          0.910                   -0.409 
##  8        -0.180          0.697          0.571                   -0.287 
##  9        -0.241         -0.0568        -0.148                   -0.0476
## 10        -0.484         -0.309         -0.582                   -0.901 
## # 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] 0.213 0.287 0.191 0.302 0.224 ...