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] 151 182 98 329 516 998 768 788 83 827 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  151  211  879  631  967  229  456  846  778   618
##  [2,]  182  628  154   24  526  112   42   44  756   296
##  [3,]   98  105  204  927  880  290  193  152  665   906
##  [4,]  329  435  163  414   26  281  804  128  821   758
##  [5,]  516  430  130   35  392  129  505  568  929   163
##  [6,]  998  476    7  871  462  171  613   17  372   695
##  [7,]  768  388  876  161  690  531   17  294  871   904
##  [8,]  788  698  438  544  637  493  578  303  477   560
##  [9,]   83  804  680  732  770  710  542  505  163   382
## [10,]  827  231  832  477  146  619  419  578  400   416
## [11,]  207  684  955  694  580  982  453  260  813   481
## [12,]  115  373  712  956  977  862  103  893  312   258
## [13,]  573  975  912  402  300  985  183  355  964   226
## [14,]  397  603  835  430  629  420  186  163  929   185
## [15,]  230   57  170  231  192  509   98  927  485   983
## [16,]  985  306  543  914  871  161  998   38  876   369
## [17,]  876  531    7  497   68  296  161  768  455   401
## [18,]  912  594  190  468  949  801  820  658  300   498
## [19,]  807  404  735  400  697  319  205  373  920   320
## [20,]  355  805  479  825  985   38  396  161   16   871
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 2.83 3.07 2.76 3.18 4.26 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 2.830166 3.118466 3.309226 3.417577 3.470278 3.473444 3.514027 3.573422
##  [2,] 3.069267 3.148104 3.338633 3.472081 3.482895 3.569087 3.599660 3.617268
##  [3,] 2.756064 3.101829 3.208460 3.240576 3.340364 3.379686 3.380470 3.409709
##  [4,] 3.178829 3.374849 3.593361 3.624553 3.671397 3.776295 3.850098 3.853116
##  [5,] 4.263774 4.359537 4.392323 4.449738 4.471956 4.574700 4.610302 4.611345
##  [6,] 2.995882 3.238647 3.863275 3.933989 4.090073 4.096591 4.205574 4.272677
##  [7,] 3.306132 3.319166 3.462312 3.478612 3.495325 3.584387 3.591139 3.655244
##  [8,] 3.900709 4.359579 4.370300 4.377665 4.443450 4.444762 4.544791 4.557106
##  [9,] 3.471128 3.631353 3.834755 3.836526 3.849196 3.913398 3.962134 4.153947
## [10,] 2.898468 3.268903 3.350932 3.380427 3.411248 3.450779 3.513848 3.534031
## [11,] 3.183397 3.205816 3.242520 3.278325 3.421960 3.475945 3.640327 3.876835
## [12,] 2.871365 3.102100 3.109491 3.547660 3.580165 3.672785 3.693242 3.719736
## [13,] 3.461833 4.020903 4.048636 4.128494 4.143845 4.172098 4.260912 4.331258
## [14,] 4.061455 4.304531 4.321065 4.435504 4.498026 4.509705 4.525498 4.608804
## [15,] 2.396558 3.103443 3.105622 3.259011 3.324790 3.459256 3.467396 3.479397
## [16,] 2.912644 3.025148 3.175566 3.201198 3.215821 3.244561 3.285467 3.411283
## [17,] 3.136938 3.339877 3.591139 3.694872 3.746387 3.752660 3.760497 3.886972
## [18,] 3.859810 3.882399 3.910523 4.090203 4.100428 4.168162 4.175512 4.199732
## [19,] 2.761806 2.800912 2.865841 2.954585 2.999526 3.034984 3.064435 3.111426
## [20,] 3.458017 3.485632 3.550795 3.611620 3.653345 3.700618 3.732034 3.739261
##           [,9]    [,10]
##  [1,] 3.582380 3.619918
##  [2,] 3.635197 3.862350
##  [3,] 3.428570 3.453297
##  [4,] 3.967070 4.100474
##  [5,] 4.723101 4.796276
##  [6,] 4.302237 4.326643
##  [7,] 3.678692 3.718329
##  [8,] 4.573960 4.582614
##  [9,] 4.171481 4.231706
## [10,] 3.550266 3.579120
## [11,] 3.882930 3.912304
## [12,] 3.725640 3.734865
## [13,] 4.365954 4.384890
## [14,] 4.716813 4.728539
## [15,] 3.554798 3.653757
## [16,] 3.412400 3.427536
## [17,] 3.896328 3.919972
## [18,] 4.275730 4.358250
## [19,] 3.116395 3.119821
## [20,] 3.819886 3.825954

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                       0.484                      1                      0.988
##  2                       0.906                      0.985                  0.985
##  3                       0.918                      0.651                  0.934
##  4                       0.875                      0.872                  0.972
##  5                       0.760                      0.952                  0.984
##  6                       0.938                      0.907                  0.954
##  7                       0.888                      0.848                  0.989
##  8                       0.533                      0.736                  0.972
##  9                       0.982                      0.886                  0.972
## 10                       0.586                      0.736                  0.972
## # 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       -0.219          -0.126          0.0327                    0.456
##  2       -0.00923        -0.0951        -0.0519                   -0.802
##  3       -0.308          -0.503         -0.592                     0.431
##  4       -0.185           0.101         -0.121                    -0.442
##  5       -0.288           0.929          0.653                     0.654
##  6        0.486           0.946          0.318                     0.123
##  7       -0.131          -0.106         -0.294                     0.683
##  8        0.640           0.203          0.757                     0.141
##  9       -0.113          -0.176          0.456                    -0.695
## 10        0.396          -0.107         -0.0873                   -0.144
## # 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] 0.268 0.255 0.281 0.234 0.202 ...