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] 636 284 509 737 238 257 971 202 841 170 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  636  805  437  199  838  111  725  795  593   243
##  [2,]  284  504  572  258  726  992  690  905   35   991
##  [3,]  509  133   97   17   22  597  926  974  969   703
##  [4,]  737  688   71  757  531  687  656  827  791   570
##  [5,]  238   33  156  699  116  536  714   18  447   357
##  [6,]  257  706  851  916  760  221  446  529  968   309
##  [7,]  971   60  596  453  118  246  647  462  280   937
##  [8,]  202   53   58  415  206  278  321  542  254   515
##  [9,]  841  718   97  387  370  152  974  926  414   147
## [10,]  170  675  602  374  330  938  590  795  657   967
## [11,]  478  863  375  371  974  234  861  382   69   825
## [12,]  697   62  456  996  594  860  944  719  435   509
## [13,]  119  531  800  581  656  925  360  129  240   648
## [14,]  343  793  322   70  594  216   17   83  249   803
## [15,]  917  792  994  192   51  663  210  221  373   734
## [16,]   82  341  276  651  274 1000  751  797  132    27
## [17,]  594    3  133  322   70  969   83  509  911    38
## [18,]  805  111  845  965  715  330  357   10  725   170
## [19,]  992  155  854  607  880  848  912  984  751   185
## [20,]  579  425  557  855  656  674  664  980  452   707
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 3.23 3.91 2.76 3.86 3.91 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 3.233940 3.247491 3.432329 3.475996 3.525090 3.645820 3.686215 3.704800
##  [2,] 3.911108 4.229922 4.398263 4.408850 4.455586 4.549342 4.557152 4.722035
##  [3,] 2.758565 2.966734 3.137071 3.302855 3.358817 3.379048 3.396851 3.399222
##  [4,] 3.862025 4.677194 5.034077 5.364972 5.434077 5.512953 5.554769 5.670642
##  [5,] 3.905281 4.209103 4.451718 4.499129 4.724508 4.775266 4.804957 4.851907
##  [6,] 4.138642 4.227155 4.458585 4.604992 4.659862 4.781641 4.943459 4.985732
##  [7,] 3.137002 3.228795 3.332833 3.392172 3.419672 3.617902 3.670411 3.675168
##  [8,] 3.173675 3.224588 3.400965 3.597171 3.616083 3.641057 3.701916 3.751109
##  [9,] 2.813801 3.322713 3.365303 3.481355 3.518717 3.522506 3.537244 3.601106
## [10,] 2.210230 2.288887 2.714452 2.772969 2.874490 2.948353 2.950053 3.002259
## [11,] 2.907990 3.494212 3.497916 3.599459 3.626131 3.653628 3.661115 3.726571
## [12,] 3.913386 4.031615 4.142594 4.359579 4.377665 4.443450 4.533079 4.544791
## [13,] 4.872277 4.966864 4.972235 5.160121 5.164474 5.234448 5.431538 5.444645
## [14,] 4.295953 4.351428 4.375250 4.384059 4.401406 4.482967 4.498550 4.568035
## [15,] 5.024567 5.234342 5.346780 5.566567 5.600063 5.657185 5.698041 5.802450
## [16,] 5.336579 5.636779 5.690738 5.882752 5.890783 5.891578 5.905012 5.921251
## [17,] 3.037948 3.302855 3.335536 3.417346 3.453594 3.460411 3.639211 3.642213
## [18,] 2.509635 2.594963 2.795106 2.849930 2.982564 3.019074 3.059421 3.110251
## [19,] 4.097389 4.400658 4.429491 4.518798 4.543052 4.562916 4.714266 4.717455
## [20,] 3.096696 3.236308 3.669423 3.890517 3.904964 3.931054 4.142554 4.395414
##           [,9]    [,10]
##  [1,] 3.743823 3.774978
##  [2,] 4.738761 4.740512
##  [3,] 3.412648 3.453275
##  [4,] 5.734580 5.755767
##  [5,] 4.923635 5.004256
##  [6,] 5.055807 5.198930
##  [7,] 3.761874 3.810846
##  [8,] 3.822607 3.825760
##  [9,] 3.613722 3.651251
## [10,] 3.048631 3.092664
## [11,] 3.767352 3.776084
## [12,] 4.557106 4.582614
## [13,] 5.447365 5.463677
## [14,] 4.618178 4.716171
## [15,] 5.830067 5.970378
## [16,] 5.944053 5.999859
## [17,] 3.653846 3.678988
## [18,] 3.146352 3.161656
## [19,] 4.722761 4.723819
## [20,] 4.526058 4.529453

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                           1                      0.870                  0.774
##  2                           1                      0.870                  0.915
##  3                           1                      0.946                  0.770
##  4                           1                      0.895                  0.894
##  5                           1                      0.870                  0.816
##  6                           1                      1                      1    
##  7                           1                      0.902                  0.828
##  8                           1                      1                      0.748
##  9                           1                      0.946                  0.471
## 10                           1                      0.984                  0.974
## # 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        -0.278        -0.00435         -0.131                   -1.06 
##  2        -0.0749       -0.118           -0.282                   -1.01 
##  3        -0.0982       -0.256            0.216                   -0.554
##  4        -0.0957       -0.176           -0.199                   -0.493
##  5        -0.0855       -0.406           -0.487                   -0.833
##  6        -0.0595       -0.264           -0.454                   -1.16 
##  7         0.962        -0.350           -0.716                   -1.11 
##  8        -0.221        -0.132           -0.427                   -0.636
##  9        -0.228        -0.581           -0.237                    0.150
## 10        -0.388        -0.839           -0.392                    0.560
## # 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] 0.26 0.208 0.282 0.174 0.198 ...