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] 810 811 833 903 391 699 143 92 314 391 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  810  319  776  261   37  166  492  840  848   964
##  [2,]  811  894  946  896  272  596  379  978  898   799
##  [3,]  833  956   47  852  281  548  540  472  789   718
##  [4,]  903  428  573  867  750  408  462  593  202   546
##  [5,]  391  178  981   10   19  324  437  537  585   301
##  [6,]  699  895  816  569  719  390  892   21  432   828
##  [7,]  143  868  910  982  861   44   94  724  271   635
##  [8,]   92  467  737  671  210  441  298  665  595   926
##  [9,]  314  342  952  125  955  469  843  113  520   189
## [10,]  391  506  682  692  379  680  313  657  771   237
## [11,]  965  974  197  403  775  862  595  332  434    67
## [12,]   56  690  276  937  880  728  337  211   93   873
## [13,]  673   41  961   58   65   56  635   36  356   853
## [14,]  548  400  891  427  729  675  958  335  484   750
## [15,]  850  905  637  513  907  455  355  490  259   382
## [16,]  757  619  842  883  588   28  317  352  272   692
## [17,]  466  595  766  965   27  694  860  812  457   550
## [18,]  650  841  562  940  634  444  178  455  219   150
## [19,]  499  940  418  437  752  360  504  259  703   537
## [20,]   91  172  221  688  432   39   38  378  616   960
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 3.09 2.75 2.55 4.32 4.43 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 3.088610 3.291602 3.397197 3.402837 3.527949 3.643457 3.748741 3.849347
##  [2,] 2.751551 3.288399 3.621606 3.634743 3.670826 3.674067 3.794746 3.826737
##  [3,] 2.551057 2.934124 3.149285 3.301250 3.339767 3.431880 3.614783 3.626039
##  [4,] 4.315262 4.802885 4.915666 5.047837 5.096255 5.447977 5.478974 5.661682
##  [5,] 4.430561 4.952011 5.055575 5.067698 5.153642 5.163699 5.194464 5.207046
##  [6,] 3.747357 4.188512 4.305541 4.367062 4.375356 4.427646 4.492321 4.817787
##  [7,] 4.180347 4.491967 4.530094 4.651364 4.787794 4.810937 4.826039 4.848569
##  [8,] 3.757888 4.463803 4.466517 4.510118 4.593129 4.650437 4.667709 4.676632
##  [9,] 3.182050 3.419672 3.429446 3.792205 3.832810 3.981910 3.998083 4.052769
## [10,] 4.371005 4.471504 4.510921 4.525895 4.542604 4.544326 4.552659 4.625730
## [11,] 2.287895 2.692867 2.697609 3.095989 3.180094 3.201879 3.315097 3.319824
## [12,] 3.280988 3.352551 3.425248 3.467818 3.527758 3.628436 3.635164 3.656948
## [13,] 3.493480 3.789282 3.901218 3.933761 3.962869 3.979688 4.041869 4.085356
## [14,] 5.003977 5.061926 5.254434 5.508202 5.601588 5.630743 5.723902 5.745775
## [15,] 4.249507 4.962714 5.097261 5.265381 5.265734 5.333571 5.379952 5.387872
## [16,] 4.065915 4.497995 4.535445 4.667527 4.724088 4.980528 5.145195 5.217181
## [17,] 2.766007 2.966594 3.035715 3.048748 3.222205 3.311565 3.405469 3.405926
## [18,] 3.244238 3.740008 3.815576 3.850592 4.003249 4.177621 4.182420 4.204069
## [19,] 3.470828 3.543151 3.565500 3.569898 3.643701 3.698633 3.698943 3.784600
## [20,] 3.475343 3.669566 3.814607 3.926141 4.306589 4.364447 4.388845 4.401926
##           [,9]    [,10]
##  [1,] 3.866521 3.905109
##  [2,] 4.173876 4.379086
##  [3,] 3.636517 3.670123
##  [4,] 5.749056 5.778200
##  [5,] 5.226651 5.229419
##  [6,] 4.822189 4.838125
##  [7,] 4.890339 4.946070
##  [8,] 4.688115 4.691614
##  [9,] 4.108694 4.285727
## [10,] 4.636025 4.669470
## [11,] 3.392430 3.433740
## [12,] 3.669893 3.693790
## [13,] 4.105321 4.110710
## [14,] 5.770430 5.792429
## [15,] 5.402247 5.408303
## [16,] 5.284864 5.291309
## [17,] 3.435292 3.458569
## [18,] 4.207536 4.213908
## [19,] 3.795480 3.833160
## [20,] 4.500277 4.633239

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                       0.809                          1                  0.978
##  2                       0.800                          1                  0.928
##  3                       0.800                          1                  1    
##  4                       0.765                          1                  0.995
##  5                       0.800                          1                  0.988
##  6                       0.819                          1                  0.995
##  7                       0.889                          1                  0.988
##  8                       0.622                          1                  0.995
##  9                       0.703                          1                  0.928
## 10                       1                              1                  0.995
## # 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       -1.15           -0.601          -0.117                  -0.146 
##  2       -0.00107        -0.0374         -0.491                   0.572 
##  3       -0.0616         -0.587           1.47                   -0.490 
##  4       -0.991          -0.718          -0.545                  -1.04  
##  5       -0.320          -0.238          -0.350                   0.997 
##  6       -1.23           -0.458          -0.527                  -2.70  
##  7        0.361           0.902           1.38                    0.337 
##  8        0.810           0.0649          1.85                    0.338 
##  9       -0.217          -0.227          -0.353                  -0.0294
## 10       -0.189           0.561           1.72                    0.361 
## # 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] 0.252 0.225 0.265 0.168 0.188 ...