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] 385 523 842 370 459 786 545 185 390 185 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  385  302  253  704  156  392  853  857  187   922
##  [2,]  523  900  384  560  790  599  495  489  644   565
##  [3,]  842  548    6   74  372  612  824  550  929   167
##  [4,]  370  592  518   60  367  747  786   22  357   537
##  [5,]  459  645  904  606  677   42  292  779  426   101
##  [6,]  786  651  842  510  386  563  768  727    3   976
##  [7,]  545  890   84  366  243  509  333  238  934   766
##  [8,]  185  998  489    9   26  748  852  169  565   646
##  [9,]  390    8  728   66  819  389  998   78  650   722
## [10,]  185    2  282  852  851  560  376   59   82   565
## [11,]  345  687  180  177  392  704  195  288  633   531
## [12,]  117  429  611  196  241  463  886   27  328   513
## [13,]  956  491  614  554  757  680  795  914  682   298
## [14,]   72  349  309  164  267  117  429  217  162   326
## [15,]  599  722   63  851   26  646  644    2  439   565
## [16,]  879  924  856  832  419  388  319  314  622   659
## [17,]  850   84  284  369  934  444  911   51   70   360
## [18,]  255  988  122  691  830  780  329  521   77   754
## [19,]  411  869   67  787  518  354   60  691  521   122
## [20,]  519  340  199  416  875  342  713  544  938    37
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 2.93 3.35 3.29 4.21 4.02 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 2.934807 3.011332 3.016751 3.041276 3.115193 3.143164 3.178666 3.191518
##  [2,] 3.351119 3.650990 4.095008 4.206182 4.235428 4.350250 4.373396 4.392919
##  [3,] 3.290888 3.911146 3.926375 3.983958 4.119979 4.182650 4.189109 4.233163
##  [4,] 4.209103 4.346599 4.969283 5.004522 5.022780 5.043362 5.046867 5.100007
##  [5,] 4.024740 4.211203 4.460094 4.532959 4.568434 4.571980 4.623731 4.631122
##  [6,] 3.285947 3.420973 3.556735 3.632301 3.712904 3.784941 3.871373 3.913881
##  [7,] 3.348652 3.469219 4.023168 4.047665 4.187657 4.254687 4.396174 4.478943
##  [8,] 4.582641 4.682708 4.938197 5.100889 5.189825 5.272487 5.286979 5.290724
##  [9,] 4.506636 5.100889 5.324985 5.355285 5.491075 5.520704 5.607854 5.672028
## [10,] 5.652755 5.949307 5.958460 6.051648 6.078806 6.087200 6.206025 6.342065
## [11,] 2.780195 2.846517 3.282821 3.287391 3.450488 3.490798 3.493728 3.504874
## [12,] 2.973577 2.973670 3.013207 3.018629 3.126406 3.142318 3.152739 3.212486
## [13,] 2.947010 3.133154 3.361468 3.418536 3.426967 3.601187 3.696938 3.725041
## [14,] 2.603422 3.280572 3.478222 3.490121 3.492663 3.593597 3.646447 3.648670
## [15,] 3.408298 4.105685 4.237876 4.425122 4.502597 4.512711 4.569172 4.577794
## [16,] 3.266432 3.983039 4.199958 4.585742 4.722467 4.797333 4.846697 5.028735
## [17,] 4.302399 4.338485 4.466796 4.686618 4.709518 4.712367 4.720591 4.834547
## [18,] 3.805116 3.939331 3.963862 4.061989 4.116736 4.131508 4.138642 4.151666
## [19,] 3.174668 3.233375 3.262967 3.285306 3.307915 3.380307 3.411497 3.518862
## [20,] 3.425833 3.466023 3.619415 3.656178 3.873374 3.963417 4.032484 4.090213
##           [,9]    [,10]
##  [1,] 3.242820 3.278678
##  [2,] 4.438370 4.467971
##  [3,] 4.264294 4.310539
##  [4,] 5.106651 5.230399
##  [5,] 4.648924 4.683237
##  [6,] 3.926375 3.983435
##  [7,] 4.555771 4.876762
##  [8,] 5.378112 5.501689
##  [9,] 5.698508 5.780566
## [10,] 6.371971 6.372856
## [11,] 3.618053 3.629939
## [12,] 3.238886 3.264479
## [13,] 3.734132 3.806068
## [14,] 3.650747 3.663923
## [15,] 4.714625 4.740133
## [16,] 5.034995 5.091078
## [17,] 4.931211 4.945244
## [18,] 4.185250 4.295264
## [19,] 3.537164 3.611575
## [20,] 4.137645 4.144629

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…¹ pCREB…² pBTK(…³ pS6(Y…⁴ cPARP…⁵ pPLCg…⁶ pSrc(…⁷ Ki67(…⁸ pErk1…⁹
##            <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
##  1         1       0.915   1       0.716  1        0.984   0.998   0.978       1
##  2         0.932   0.960   0.989   1      1        0.998   0.975   0.924       1
##  3         0.854   0.842   0.989   0.751  1        0.984   0.914   0.836       1
##  4         0.923   0.915   0.958   0.882  1        0.911   0.940   1           1
##  5         0.854   0.915   0.915   0.939  1        0.971   0.940   0.994       1
##  6         0.887   0.915   0.958   0.945  0.0862   0.971   0.749   0.814       1
##  7         0.945   0.915   0.859   0.894  1        0.930   0.952   0.994       1
##  8         0.854   0.915   0.794   0.894  1        0.971   0.990   0.994       1
##  9         0.921   0.915   0.989   0.867  1        0.984   0.944   0.765       1
## 10         1       0.960   1       0.716  1        0.984   0.963   0.994       1
## # … with 990 more rows, 25 more variables: `pSTAT3(Gd158)Di.IL7.qvalue` <dbl>,
## #   `pAKT(Tb159)Di.IL7.qvalue` <dbl>, `pBLNK(Gd160)Di.IL7.qvalue` <dbl>,
## #   `pP38(Tm169)Di.IL7.qvalue` <dbl>, `pSTAT5(Nd150)Di.IL7.qvalue` <dbl>,
## #   `pSyk(Dy162)Di.IL7.qvalue` <dbl>, `tIkBa(Er166)Di.IL7.qvalue` <dbl>,
## #   `pCrkL(Lu175)Di.IL7.change` <dbl>, `pCREB(Yb176)Di.IL7.change` <dbl>,
## #   `pBTK(Yb171)Di.IL7.change` <dbl>, `pS6(Yb172)Di.IL7.change` <dbl>,
## #   `cPARP(La139)Di.IL7.change` <dbl>, `pPLCg2(Pr141)Di.IL7.change` <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)D…¹ CD3(C…² CD3(C…³ CD235…⁴ CD3(C…⁵ CD45(…⁶ CD19(…⁷ CD22(…⁸ IgD(N…⁹
##            <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
##  1       -0.0784  1.08     0.860  -0.631  0.449    1.96    0.766  1.87    0.921 
##  2        0.373   0.507    1.21   -0.671  1.01     2.67    2.14   1.66   -0.213 
##  3       -0.170  -0.705   -0.617  -0.318 -0.209    0.429   1.16   0.191  -0.0542
##  4        0.233  -0.102    2.27   -0.120  0.775    3.54    1.57  -0.0189 -0.463 
##  5       -0.240   1.83     0.154  -0.419  0.685    1.06    1.86   0.798   1.26  
##  6        0.689   1.67     1.65    0.479  0.624    2.66    1.05   1.12    1.32  
##  7       -0.131  -0.0374   0.673  -0.318  1.16     1.72    0.484  2.10   -0.240 
##  8        0.438   0.288    0.570  -1.90   0.0718   2.38    2.51  -0.423   1.41  
##  9        0.435  -0.253    0.570   0.243 -0.130    1.37    1.48   1.23    0.0774
## 10       -0.252  -0.143    1.82    0.560  0.670    1.15    0.320 -0.159   1.94  
## # … with 20 more rows, 42 more variables: `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>, `PreBCR(Ho165)Di` <dbl>,
## #   `CD43(Er167)Di` <dbl>, `CD38(Er168)Di` <dbl>, `CD40(Er170)Di` <dbl>,
## #   `CD33(Yb173)Di` <dbl>, `HLA-DR(Yb174)Di` <dbl>, Time <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] 0.292 0.215 0.224 0.189 0.211 ...