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] 337 274 246 766 539 329 593 796 922 34 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  337  678  354  485  237  552  186  884  315   458
##  [2,]  274  851  933  976  563  434  306  179  460   109
##  [3,]  246  107  335  819  504  307  119  664  809   266
##  [4,]  766   66  835  542  482  873  508  243   94   633
##  [5,]  539  181  266   78  694  818   56  449  833   236
##  [6,]  329  388  842  960  243  154   93  456  808   134
##  [7,]  593   23  667  830  470   14  892  996  799   712
##  [8,]  796  498  614  174  531   34  453  179  273     9
##  [9,]  922  544  174   34  491  182  902  498  290   278
## [10,]   34  900  532  413  225  153  572  843  902   386
## [11,]  176  845  100   20  745  832  523  534  823   479
## [12,]  139  357  856  498  370   85  182  278  224   220
## [13,]  470  778  465  811  961  823  141  302  104   773
## [14,]  593  693    7  534  374   20  321  830  503   844
## [15,]  111  500  583  798  958  512  681  634  215   820
## [16,]  979  408  641  581  372  825  898  644  627    18
## [17,]  676  927  538  994  922  150  182  672  364   324
## [18,]  408  525  966  787  768  609  898  430  148   654
## [19,]  571  240  676  199  994  314  460   17  577   284
## [20,]  100  534   61  112  192  479  465  996  302    14
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 4.4 3.64 3.67 3.05 3.09 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 4.395033 4.589795 4.603207 4.664271 4.740314 4.767237 4.924132 4.933183
##  [2,] 3.637631 4.259387 4.369343 4.480685 4.621630 4.627091 4.707778 4.718599
##  [3,] 3.669831 3.806788 4.199250 4.210395 4.463766 4.470530 4.479801 4.523224
##  [4,] 3.053378 3.261854 3.287635 3.333300 3.555113 3.629050 3.641341 3.670389
##  [5,] 3.092051 3.425935 3.477628 3.530486 3.562070 3.589284 3.618062 3.675332
##  [6,] 2.735375 2.780195 2.846517 3.118594 3.287391 3.443227 3.451687 3.483039
##  [7,] 2.788923 3.036149 3.119447 3.180229 3.262160 3.291503 3.364669 3.392516
##  [8,] 3.786505 3.862875 3.875960 3.880346 3.945621 4.072147 4.088545 4.152295
##  [9,] 2.453201 2.967051 2.974989 3.104128 3.185010 3.191709 3.206891 3.255873
## [10,] 3.560927 3.627175 3.658589 3.692020 3.836290 3.849979 3.962801 3.975738
## [11,] 3.397861 3.480259 3.542899 3.599337 3.656047 3.664770 3.736488 3.753828
## [12,] 2.853666 2.940074 2.977736 3.059686 3.105622 3.139441 3.203300 3.283071
## [13,] 2.531550 2.950760 3.255711 3.294081 3.299178 3.330589 3.461365 3.490697
## [14,] 3.073767 3.277102 3.291503 3.309315 3.330960 3.373050 3.419556 3.428579
## [15,] 4.398089 4.463140 4.501910 4.682387 4.750415 4.847870 4.950003 4.951450
## [16,] 3.424894 3.452362 3.692459 3.708476 3.782683 3.796636 3.830579 3.890667
## [17,] 2.905118 3.353017 3.399958 3.666377 3.920321 3.933761 4.020214 4.066022
## [18,] 3.072292 3.485924 3.489735 3.583584 3.685677 3.691550 3.721304 3.729892
## [19,] 4.913575 5.054053 5.287737 5.310950 5.346754 5.389461 5.479962 5.568654
## [20,] 2.825372 2.887469 3.174962 3.228291 3.251515 3.284541 3.314874 3.334937
##           [,9]    [,10]
##  [1,] 4.950767 5.048756
##  [2,] 4.742350 4.763184
##  [3,] 4.559657 4.579138
##  [4,] 3.671473 3.712238
##  [5,] 3.684008 3.686851
##  [6,] 3.569336 3.597690
##  [7,] 3.395017 3.423078
##  [8,] 4.199830 4.262573
##  [9,] 3.264745 3.343813
## [10,] 3.981353 4.055321
## [11,] 3.813897 3.854260
## [12,] 3.346715 3.447538
## [13,] 3.527052 3.543694
## [14,] 3.428636 3.439355
## [15,] 4.989978 5.027995
## [16,] 3.905504 4.036675
## [17,] 4.135119 4.154608
## [18,] 3.735966 3.824062
## [19,] 5.569669 5.578319
## [20,] 3.363391 3.373050

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                       0.880                          1                      1
##  2                       1                              1                      1
##  3                       0.880                          1                      1
##  4                       1.00                           1                      1
##  5                       1.00                           1                      1
##  6                       0.880                          1                      1
##  7                       0.880                          1                      1
##  8                       1                              1                      1
##  9                       0.924                          1                      1
## 10                       0.954                          1                      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        -0.0307       -0.00396        -0.0498                   -2.64 
##  2        -0.0477       -0.0514         -0.0339                   -0.474
##  3        -0.146        -0.238           0.164                    -2.29 
##  4        -0.0603        0.798           0.460                    -1.21 
##  5        -0.0648       -0.0166         -0.0818                   -0.681
##  6        -0.254        -0.193          -0.121                    -0.267
##  7        -0.0322       -0.451           0.308                    -1.70 
##  8        -0.161        -0.241          -0.232                    -1.92 
##  9        -0.138        -0.170           0.651                    -0.824
## 10        -0.262        -0.454          -0.110                    -0.447
## # 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] 0.189 0.209 0.216 0.27 0.266 ...