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] 827 790 284 511 466 783 624 628 196 514 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  827  743  841  284  382  309  751  384  802   220
##  [2,]  790  508  120  237  851  586   29  718  145   239
##  [3,]  284  646  318   19  127  215  827  835  802    61
##  [4,]  511  739  625  803  630   17  547  871  713   451
##  [5,]  466  768  978  534  880  118  349  952  742   788
##  [6,]  783  175  911  346  607  627  543  880   26   952
##  [7,]  624  183  581  521  681  739  414  716  621   184
##  [8,]  628  697  969   24  732  126  759  619  406   575
##  [9,]  196  685  519  425  433   12  763  666  657   898
## [10,]  514  442   50  339   56  878  218  186  549   609
## [11,]  251  738  547   84  816  679  760  403  624   277
## [12,]  657  433   23  626  425    9  638  685  146   508
## [13,]  523  435  285  204  409  962  102  422  667   331
## [14,]  201  560  848  780  391  172  342  399  175   110
## [15,]  303  685  261  850  745  940  196  193  478    29
## [16,]  400  409  510  304  130  401  203   20  437   876
## [17,]  183  595  348  100  963  970  625  673  895   739
## [18,]  911  897  169  374  946  434  326  345  361   121
## [19,]  528  946  646  253  455   61  958  434  215   765
## [20,]  381  331  343  633  525  418  357  468  401   714
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 3.07 4.1 3.13 3.72 3.62 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 3.071717 3.482856 3.696256 3.756475 3.768423 3.981704 4.063349 4.176408
##  [2,] 4.104066 4.234811 4.277316 4.314909 4.391883 4.436591 4.496290 4.573288
##  [3,] 3.133906 3.145573 3.405517 3.875179 3.902213 4.154854 4.169846 4.253011
##  [4,] 3.718052 3.770411 3.835693 3.919161 3.981942 4.010090 4.021221 4.042208
##  [5,] 3.622950 3.631121 3.736735 3.749652 3.830653 3.867628 3.869372 3.881259
##  [6,] 3.238448 3.431571 3.468780 3.526893 3.531683 3.654889 3.714632 3.755645
##  [7,] 2.266397 2.469692 2.471813 2.508298 2.544611 2.623631 2.661384 2.847252
##  [8,] 3.400413 3.614318 3.638779 3.703243 3.734166 3.735610 3.790119 3.792057
##  [9,] 4.125997 4.212677 4.344830 4.396136 4.397874 4.448766 4.612523 4.655435
## [10,] 2.866492 3.475343 3.556980 3.613709 3.855725 3.914504 3.986689 4.166008
## [11,] 3.149332 3.188151 3.290095 3.316939 3.379998 3.456063 3.575291 3.589994
## [12,] 3.808868 4.258084 4.281820 4.302814 4.333545 4.448766 4.483504 4.497381
## [13,] 3.923602 4.186758 4.373896 4.379717 4.423305 4.461656 4.635691 4.647018
## [14,] 3.183397 3.242520 3.278325 3.421960 3.640327 3.702407 3.744287 3.759066
## [15,] 3.849542 4.028213 4.159745 4.387797 4.398015 4.409507 4.488994 4.493017
## [16,] 4.713210 5.285954 5.484486 5.560440 5.637751 5.687220 5.694227 5.830702
## [17,] 2.541346 2.775083 2.861422 2.862886 2.878302 2.901064 2.919410 2.973405
## [18,] 3.341492 3.450653 3.501768 3.581125 3.673895 3.674263 3.677091 3.684620
## [19,] 2.548350 2.887469 2.911608 3.205037 3.217258 3.314874 3.334937 3.350510
## [20,] 3.707808 3.753193 3.984069 4.168339 4.213230 4.231129 4.278318 4.302357
##           [,9]    [,10]
##  [1,] 4.260064 4.288347
##  [2,] 4.582641 4.606139
##  [3,] 4.310794 4.333346
##  [4,] 4.072347 4.124709
##  [5,] 3.942098 3.965490
##  [6,] 3.776265 3.807573
##  [7,] 2.858227 2.919281
##  [8,] 3.807089 3.817468
##  [9,] 4.709470 4.753769
## [10,] 4.278016 4.306040
## [11,] 3.604977 3.619126
## [12,] 4.521345 4.550144
## [13,] 4.788668 4.866211
## [14,] 3.839011 3.876835
## [15,] 4.494916 4.549111
## [16,] 6.053192 6.057584
## [17,] 3.034362 3.034531
## [18,] 3.716201 3.748484
## [19,] 3.363391 3.399957
## [20,] 4.340030 4.349927

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                       0.989                      0.933                  0.867
##  2                       0.867                      0.951                  1    
##  3                       0.951                      1                      0.790
##  4                       0.951                      0.957                  0.549
##  5                       1                          1                      1    
##  6                       0.867                      0.997                  0.842
##  7                       0.867                      0.933                  0.744
##  8                       0.951                      0.951                  0.582
##  9                       0.951                      0.913                  0.953
## 10                       0.867                      0.957                  1    
## # 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         0.358        -0.109         -0.131                     0.124 
##  2        -0.0552       -0.136         -0.0639                    0.270 
##  3        -0.0785       -0.00929       -0.00777                  -0.802 
##  4        -0.458        -0.355         -0.366                     0.0316
##  5        -0.133        -0.0245        -0.0975                    0.157 
##  6        -0.125        -0.0787        -0.174                    -1.12  
##  7         0.428         0.291         -0.231                     0.479 
##  8        -0.176        -0.246         -0.196                     0.974 
##  9        -0.180        -0.255         -0.0147                   -0.455 
## 10        -0.149        -0.213         -0.180                     0.951 
## # 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] 0.216 0.213 0.228 0.241 0.238 ...