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] 975 783 871 911 678 561 174 527 152 952 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  975  321  732  221   49  816  394  819  700    13
##  [2,]  783  635  277  697  125  244  667  644  883   404
##  [3,]  871  362  803  163  121  589  663  947  354   526
##  [4,]  911  358  305  708  429  680  122  794  681   242
##  [5,]  678  278  617   94   26    7  868  985  487   816
##  [6,]  561  136  165  152  713  169  876  586  400   647
##  [7,]  174  976  395  662  742  625  787  278  868   685
##  [8,]  527  428  485  215  749   53  489  451   16   240
##  [9,]  152  455  791  728  468  136  113  166  561    28
## [10,]  952  234  174    7  770  395  209  782  781   285
## [11,]  861  382  696  231  879  432  549  412  206   994
## [12,]  285  909  792  232  852  595   24  651  490   782
## [13,]  757   81  952  324  669  395  651  852  751   511
## [14,]  979  122  996  735  410  327  580  667  281   827
## [15,]  856  830  609  794  565  576  861  696  271   258
## [16,]  517  749  512  722  215  428   64  485  913    53
## [17,]  496  661  814  793  575   95  806  670  552   182
## [18,]  318  320  830  696   15  856  994  608  854   918
## [19,]   44  827  295  549  588  281  936  944  327   735
## [20,]  369  652  452  310  387  812  191  492  651   389
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 3.72 3.87 2.96 2.88 2.58 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 3.723428 3.760809 3.914977 4.018204 4.112165 4.138905 4.143516 4.178350
##  [2,] 3.869308 4.242402 4.335811 4.353181 4.402773 4.543152 4.557389 4.573768
##  [3,] 2.961884 3.265195 3.267385 3.340423 3.379025 3.389055 3.428510 3.462020
##  [4,] 2.877684 3.498250 3.527949 3.606120 3.622966 3.720628 3.788851 3.882383
##  [5,] 2.579222 3.234159 3.265297 3.351763 3.428287 3.503782 3.504496 3.510774
##  [6,] 2.485762 3.154017 3.429964 3.506096 3.669237 3.742693 3.785822 3.810819
##  [7,] 2.166226 2.375891 2.469439 2.482662 2.585580 2.608916 2.742256 2.750633
##  [8,] 5.131131 5.336579 5.703112 5.890783 5.891578 5.944053 5.981509 5.999859
##  [9,] 3.292670 3.736173 3.849177 3.940421 3.944156 4.069371 4.124803 4.235465
## [10,] 3.264471 3.287994 3.303976 3.355336 3.378307 3.385581 3.405819 3.413346
## [11,] 2.491643 3.037649 3.392959 3.399999 3.434338 3.511985 3.525676 3.530482
## [12,] 3.815895 3.951312 3.978292 4.009095 4.078269 4.095559 4.102395 4.291013
## [13,] 3.063972 3.163539 3.217766 3.239427 3.246037 3.251005 3.281831 3.294002
## [14,] 4.017774 4.407108 4.443624 4.477922 4.497634 4.548213 4.590462 4.645345
## [15,] 1.991096 2.537125 2.702714 2.774993 2.812816 2.841366 2.844674 2.867829
## [16,] 3.694205 3.714277 3.778572 4.095550 4.686074 5.051553 5.193347 5.311071
## [17,] 5.835787 6.100983 6.138841 6.210533 6.219095 6.346594 6.389606 6.511899
## [18,] 3.087960 3.255221 3.284561 3.303000 3.566917 3.597512 3.708648 3.720469
## [19,] 3.526604 4.371984 4.421682 4.597442 4.597678 4.627651 4.629036 4.680737
## [20,] 2.869548 2.876851 3.074811 3.266154 3.292981 3.377377 3.407014 3.443274
##           [,9]    [,10]
##  [1,] 4.222727 4.226467
##  [2,] 4.620796 4.631275
##  [3,] 3.467390 3.497579
##  [4,] 3.903263 3.915071
##  [5,] 3.532714 3.540736
##  [6,] 3.857591 3.965888
##  [7,] 2.763797 2.894083
##  [8,] 6.019691 6.165635
##  [9,] 4.274129 4.288405
## [10,] 3.431261 3.463302
## [11,] 3.579136 3.772070
## [12,] 4.299045 4.310667
## [13,] 3.377825 3.407321
## [14,] 4.665953 4.680896
## [15,] 2.978875 2.996549
## [16,] 5.410265 5.433805
## [17,] 6.526201 6.531005
## [18,] 3.733213 3.753155
## [19,] 4.741965 4.758651
## [20,] 3.462538 3.474743

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                       0.950                      0.840                  0.623
##  2                       0.886                      0.999                  0.674
##  3                       0.896                      1                      0.875
##  4                       0.875                      0.949                  0.617
##  5                       0.964                      1                      0.552
##  6                       0.803                      1                      0.909
##  7                       0.886                      0.840                  0.674
##  8                       0.976                      1                      0.575
##  9                       0.803                      0.981                  0.969
## 10                       0.886                      1                      0.623
## # 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       -0.482          -0.448         -0.482                    -1.63 
##  2       -0.236          -0.0968        -0.220                    -0.340
##  3       -0.630          -0.0807         0.0549                   -1.49 
##  4       -0.0656         -0.471         -0.0767                    0.202
##  5       -0.650          -0.0338        -0.779                    -1.05 
##  6       -0.375          -0.291         -0.559                     0.863
##  7        0.565          -0.432         -0.352                    -0.366
##  8       -0.330          -0.382         -1.10                     -0.459
##  9       -0.00120        -0.0421        -0.0498                   -1.38 
## 10       -0.124          -0.370         -0.210                    -0.860
## # 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] 0.234 0.21 0.278 0.249 0.28 ...