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] 267 609 899 731 196 597 8 7 64 827 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  267  282  995  850  438  623  325   86  947   483
##  [2,]  609  434  408  570  841  392  888  427  164   576
##  [3,]  899  742  331  480  942  323  200  598  879   151
##  [4,]  731  131  924  397  615  568  271  968  625   503
##  [5,]  196  174  363   11  925  739  745  622  545   559
##  [6,]  597  214   64  245   69    8  181  341  616   559
##  [7,]    8    9  197   99  672  934   64  616  170   727
##  [8,]    7   34   64  353    6   99  616  141  768    69
##  [9,]   64  616  353  869  181  597  696  110  170   950
## [10,]  827  417  442  553  897  450  634   67  308   170
## [11,]  622  196  947  363  807  195  174  438  172     5
## [12,]   33  435  144  320  645   73  733   48  869   354
## [13,]  620  586  418  109  990  679  921  538  234   919
## [14,]  902  218  822  687  834  865  764  673  941   394
## [15,]  363  839  739  460  623  864  883  804    5   947
## [16,]  424  559  479  934  739  877  584  983  515   307
## [17,]  479  269  102   55  883  221  704  332  372   300
## [18,]  534  431  296  263  352   41  503  127  815   846
## [19,]  355  440  266  721  689   79  568  525  843   330
## [20,]  745  195   11  293  290  438  821  894  947   363
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 2.56 4.51 4.35 3.08 3.12 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 2.564155 3.339232 3.678814 3.705585 3.708406 3.713332 3.713587 3.717871
##  [2,] 4.510690 4.550859 4.573888 4.579418 4.867458 5.046789 5.086669 5.174128
##  [3,] 4.352202 4.600549 4.623144 4.835635 4.848014 4.889187 4.916895 4.969283
##  [4,] 3.075094 3.503807 3.726603 3.792677 3.820885 3.877766 3.879786 3.952217
##  [5,] 3.123578 3.126652 3.281805 3.343012 3.425534 3.555591 3.571135 3.599752
##  [6,] 2.473366 2.743782 2.823186 2.855793 2.897474 2.952073 2.975193 3.008461
##  [7,] 2.641899 3.189302 3.239236 3.298887 3.321811 3.404989 3.431209 3.445228
##  [8,] 2.641899 2.824527 2.877447 2.908134 2.952073 2.961004 2.973848 3.015275
##  [9,] 2.545865 2.840335 2.995501 3.019087 3.040590 3.058576 3.079463 3.119821
## [10,] 2.707680 2.821755 2.902729 2.941805 3.080338 3.214857 3.250388 3.292698
## [11,] 2.453201 2.470231 2.967051 3.104128 3.167093 3.185010 3.191709 3.218411
## [12,] 2.046750 2.505417 2.739721 2.746293 2.848480 2.895432 3.004853 3.024012
## [13,] 4.321551 4.502277 4.552564 4.603309 4.636783 4.656170 4.680338 4.709247
## [14,] 2.049721 2.134410 2.373197 2.399796 2.570987 2.642107 2.659695 2.759566
## [15,] 3.382568 3.486147 3.566865 3.624838 3.629024 3.704721 3.824715 3.830374
## [16,] 2.690266 3.042903 3.055655 3.085945 3.112783 3.180471 3.219082 3.244668
## [17,] 3.095164 3.098691 3.297911 3.379533 3.394414 3.448939 3.491857 3.563927
## [18,] 3.205816 3.702407 3.744287 3.759066 3.839011 3.881543 3.882930 3.952275
## [19,] 3.526604 4.241187 4.311942 4.371984 4.429282 4.508412 4.597442 4.622240
## [20,] 3.615463 3.707808 3.753193 3.800756 3.984069 4.088078 4.126504 4.168339
##           [,9]    [,10]
##  [1,] 3.816347 3.825843
##  [2,] 5.298361 5.304528
##  [3,] 4.970772 4.997647
##  [4,] 4.019366 4.028348
##  [5,] 3.601231 3.642188
##  [6,] 3.048458 3.060811
##  [7,] 3.490355 3.505098
##  [8,] 3.045286 3.062585
##  [9,] 3.125789 3.163069
## [10,] 3.319018 3.340254
## [11,] 3.255873 3.343012
## [12,] 3.088299 3.138187
## [13,] 4.737838 4.755523
## [14,] 2.777708 2.795061
## [15,] 3.842300 3.850378
## [16,] 3.254884 3.265306
## [17,] 3.635052 3.653628
## [18,] 3.975931 4.013522
## [19,] 4.629036 4.634261
## [20,] 4.213230 4.231129

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                              1                  0.943
##  2                       1                              1                  0.761
##  3                       1                              1                  0.974
##  4                       1                              1                  1    
##  5                       0.999                          1                  0.804
##  6                       0.976                          1                  0.578
##  7                       0.966                          1                  0.866
##  8                       0.966                          1                  0.517
##  9                       0.966                          1                  0.852
## 10                       0.976                          1                  0.981
## # 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        -0.557         -0.0292        -0.621                     0.469
##  2        -0.0914        -0.135         -0.271                     0.558
##  3        -0.180         -0.255         -0.0147                   -0.455
##  4        -0.0403        -0.496         -0.108                    -1.01 
##  5        -0.0663        -0.0284        -0.180                     0.385
##  6         0.702         -0.114          0.282                     0.181
##  7         0.702         -0.162         -0.412                     0.563
##  8        -0.0296        -0.0715        -0.589                    -0.786
##  9        -0.0882         1.04           0.385                    -0.361
## 10        -0.216          0.771          0.140                     0.125
## # 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] 0.253 0.183 0.197 0.244 0.263 ...