Multiple Metric Learning Methods in scLearn

Bin Duan

SJTU
binduan@sjtu.edu.cn

2025-05-12

Introduction

Comprehensive summary table of the six metric learning methods used in scLearn

Method	Core Idea	Advantages	Disadvantages	Recommended Sample Size
DCA (Discriminative Component Analysis)	Linear transformation maximizing the between-class / within-class variance ratio (Fisher-style)	Fast, simple, stable; no iterative optimization	Assumes linear class separability; not suitable for complex manifolds	Small to medium
LMNN (Large Margin Nearest Neighbors)	Learns a transformation that maintains class-consistent k-NN relationships with margin constraints	High classification accuracy; interpretable	Computationally expensive; requires many triplets; slow without parallelization	Small to medium
MSL-LMNN (Multi-Similarity Loss-Based Metric Learning)	Enhances LMNN by leveraging multiple similarity cues and continuous loss instead of discrete triplets	More stable optimization; better generalization with fewer pairs	Still requires pairwise comparisons; moderately slow without batching	Medium to large
NCA (Neighborhood Components Analysis)	Maximizes the probability of correct classification under stochastic nearest neighbors	Theoretically elegant; good embedding quality	Sensitive to noise; no margin; costly without approximate neighbors	Small to medium
ITML (Information-Theoretic Metric Learning)	Learns Mahalanobis distance with relative constraints, regularized by information-theoretic divergence	Robust to noise; stable convergence; works with few constraints	Requires careful tuning; slow on high-dimensional data	Small to medium
MMC (Maximum Margin Clustering)	Maximizes inter-class separation while minimizing intra-class spread using scatter matrices	Good for clustering and large-margin separation	High memory usage; expensive eigen decomposition; difficult on large datasets	Medium (with memory)

Installation

library(scLearn)
library(tidyverse) 
library(SingleCellExperiment)
library(M3Drop)

Data preparation

• Reference Cell Database: baron-human

• Query Cell Data: Muraro-human

data(RefCellData)
data(QueryCellData)
stratified_sample <- function(cell_types, n_total = 300, min_per_type = 10) {
  sampled <- lapply(split(seq_along(cell_types), cell_types), function(idx) {
    if(length(idx) > min_per_type) {
      sample(idx, max(min_per_type, round(n_total * length(idx)/length(cell_types))))
    } else {
      idx
    }
  })
   unlist(sampled)
}


set.seed(123)

cell_types <- colData(RefCellData)$cell_type1
sampled_cells <- stratified_sample(cell_types)
RefCellData <- RefCellData[, sampled_cells]
RefCellData

## class: SingleCellExperiment 
## dim: 20125 342 
## metadata(0):
## assays(2): counts logcounts
## rownames(20125): A1BG A1CF ... ZZZ3 pk
## rowData names(10): feature_symbol is_feature_control ... total_counts
##   log10_total_counts
## colnames(342): human3_lib3.final_cell_0081 human3_lib1.final_cell_0121
##   ... human3_lib3.final_cell_0896 human4_lib1.final_cell_0568
## colData names(30): human cell_type1 ... pct_counts_ERCC is_cell_control
## reducedDimNames(0):
## mainExpName: NULL
## altExpNames(0):

cell_types <- colData(QueryCellData)$cell_type1
sampled_cells <- stratified_sample(cell_types)
QueryCellData <- QueryCellData[, sampled_cells]
QueryCellData

## class: SingleCellExperiment 
## dim: 19127 311 
## metadata(0):
## assays(2): normcounts logcounts
## rownames(19127): A1BG-AS1__chr19 A1BG__chr19 ... ZZEF1__chr17
##   ZZZ3__chr1
## rowData names(1): feature_symbol
## colnames(311): D31.7_38 D28.3_4 ... D30.4_58 D31.7_42
## colData names(3): cell_type1 donor batch
## reducedDimNames(0):
## mainExpName: NULL
## altExpNames(0):

Quality control

RefRawcounts <- assays(RefCellData)[[1]]
RefAnn <- as.character(RefCellData$cell_type1)
names(RefAnn) <- colnames(RefCellData)

RefDataQC <- Cell_qc(
  expression_profile = RefRawcounts, 
  sample_information_cellType = RefAnn, 
  sample_information_timePoint = NULL, 
  species = "Hs",
  gene_low = 500, 
  gene_high = 10000, 
  mito_high = 0.1, 
  umi_low = 1500, 
  umi_high = Inf, 
  logNormalize = TRUE, 
  plot = FALSE, 
  plot_path = "./quality_control.pdf")

Filtering rare cell

RefDataQC_filtered <- Cell_type_filter(
  expression_profile = RefDataQC$expression_profile, 
  sample_information_cellType = RefDataQC$sample_information_cellType,
  sample_information_timePoint = NULL,
  min_cell_number = 10)

Feature selection

highest variable genes

RefDataQC_HVG_names <- Feature_selection_M3Drop(
  expression_profile = RefDataQC_filtered$expression_profile,
  log_normalized = TRUE, 
  threshold = 0.05)

QueryData Processing

QueryRawcounts <- assays(QueryCellData)[[1]]
QueryDataQC <- Cell_qc(
  expression_profile = QueryRawcounts, 
  species = "Hs", 
  gene_low = 50, 
  umi_low = 50)

rownames(QueryDataQC$expression_profile) <- gsub("__\\w+\\d+", "", rownames(QueryDataQC$expression_profile))

QueryData_trueLabel <- as.character(QueryCellData$cell_type1)
names(QueryData_trueLabel) <- colnames(QueryCellData)

DCA

Discriminative Component Analysis (DCA) Transformation

• model learning

scLearn_model_learning_result_DCA <- scLearn_model_learning(
  high_varGene_names = RefDataQC_HVG_names,
  expression_profile = RefDataQC_filtered$expression_profile,
  sample_information_cellType = RefDataQC_filtered$sample_information_cellType,
  sample_information_timePoint = NULL,
  method = "DCA",
  bootstrap_times = 1,
  cutoff = 0.01,
  dim_para = 0.999
)

Results：scLearn_model_learning_result_DCAis the final result file containing the processed reference cell matrix.

• high_varGene_names: The set of highly variable genes (324 HVGs)

• simi_threshold_learned: The similarity results between cell types

• trans_matrix_learned: The transformed matrix (23 features * 324 HVGs)

• feature_matrix_learned: After DCA, the matrix of cell type features (these features are obtained by dimensionality reduction of the highly variable gene set) (12 celltype * 23 features)

• cell assignment

scLearn_predict_result_DCA <- scLearn_cell_assignment(
  scLearn_model_learning_result = scLearn_model_learning_result_DCA, 
  expression_profile_query = QueryDataQC$expression_profile, 
  diff = 0.05, 
  threshold_use = TRUE, 
  vote_rate = 0.6)

## [1] "The number of missing features in the query data is  17 "
## [1] "The rate of missing features in the query data is  0.0524691358024691 "

head(scLearn_predict_result_DCA)

##          Query_cell_id Predict_cell_type Additional_information
## D31.7_38      D31.7_38        unassigned             Novel_Cell
## D28.3_4        D28.3_4        unassigned             Novel_Cell
## D30.1_63      D30.1_63            ductal      0.877513396467364
## D31.6_53      D31.6_53            ductal      0.898189213920747
## D30.7_39      D30.7_39            ductal      0.828981549060616
## D31.1_22      D31.1_22            ductal      0.839213242283002

Results: The output consists of three columns of information. The Query_cell_id represents the cell ID, Predict_cell_type indicates the predicted cell type, and Additional_information provides the similarity results. Cells with a Predict_cell_type of unassigned are those that do not intersect with the reference cell set.

• Accuracy

QueryData_CellType_DCA <- QueryData_trueLabel |> 
  as.data.frame() |>
  tibble::rownames_to_column("CellID") |>
  dplyr::rename(trueLabel = QueryData_trueLabel) |>  
  dplyr::inner_join(scLearn_predict_result_DCA |>
                      as.data.frame() |>
                      dplyr::rename(predLabel = Predict_cell_type),
                    by = c("CellID" = "Query_cell_id")) |>
  dplyr::select(CellID, trueLabel, predLabel, everything())

print(
  paste("DCA Accuracy =", 
    sprintf("%1.2f%%",
      100 * sum(QueryData_CellType_DCA$predLabel == QueryData_CellType_DCA$trueLabel) / nrow(QueryData_CellType_DCA))))

## [1] "DCA Accuracy = 81.23%"

LMNN

Implements Large Margin Nearest Neighbor (LMNN) metric learning Transformation

• model learning

scLearn_model_learning_result_LMNN <- scLearn_model_learning(
  high_varGene_names = RefDataQC_HVG_names,
  expression_profile = RefDataQC_filtered$expression_profile,
  sample_information_cellType = RefDataQC_filtered$sample_information_cellType,
  sample_information_timePoint = NULL,
  method = "LMNN",
  bootstrap_times = 1,
  cutoff = 0.01,
  dim_para = 0.999,
  k = 5,
  max_iter = 1
)

• cell assignment

scLearn_predict_result_LMNN <- scLearn_cell_assignment(
  scLearn_model_learning_result = scLearn_model_learning_result_LMNN, 
  expression_profile_query = QueryDataQC$expression_profile, 
  diff = 0.05, 
  threshold_use = TRUE, 
  vote_rate = 0.6)

## [1] "The number of missing features in the query data is  17 "
## [1] "The rate of missing features in the query data is  0.0524691358024691 "

head(scLearn_predict_result_LMNN)

##          Query_cell_id Predict_cell_type Additional_information
## D31.7_38      D31.7_38        unassigned             Novel_Cell
## D28.3_4        D28.3_4        unassigned             Novel_Cell
## D30.1_63      D30.1_63        unassigned             Novel_Cell
## D31.6_53      D31.6_53        unassigned             Novel_Cell
## D30.7_39      D30.7_39        unassigned             Novel_Cell
## D31.1_22      D31.1_22        unassigned             Novel_Cell

• Accuracy

QueryData_CellType_LMNN <- QueryData_trueLabel |> 
  as.data.frame() |>
  tibble::rownames_to_column("CellID") |>
  dplyr::rename(trueLabel = QueryData_trueLabel) |>  
  dplyr::inner_join(scLearn_predict_result_LMNN |>
                      as.data.frame() |>
                      dplyr::rename(predLabel = Predict_cell_type),
                    by = c("CellID" = "Query_cell_id")) |>
  dplyr::select(CellID, trueLabel, predLabel, everything())

print(
  paste("LMNN Accuracy =", 
    sprintf("%1.2f%%",
      100 * sum(QueryData_CellType_LMNN$predLabel == QueryData_CellType_LMNN$trueLabel) / nrow(QueryData_CellType_LMNN))))

## [1] "LMNN Accuracy = 79.94%"

MSL-LMNN

Implements Multi-Similarity Loss-Based Large Margin Nearest Neighbor (LMNN) metric learning Transformation

Note: MSL-LMNN took a long time

• model learning

scLearn_model_learning_result_MSL <- scLearn_model_learning(
  high_varGene_names = RefDataQC_HVG_names,
  expression_profile = RefDataQC_filtered$expression_profile,
  sample_information_cellType = RefDataQC_filtered$sample_information_cellType,
  sample_information_timePoint = NULL,
  method = "MSL",
  bootstrap_times = 1,
  cutoff = 0.01,
  dim_para = 0.999,
  max_iter = 1
)

• cell assignment

scLearn_predict_result_MSL <- scLearn_cell_assignment(
  scLearn_model_learning_result = scLearn_model_learning_result_MSL, 
  expression_profile_query = QueryDataQC$expression_profile, 
  diff = 0.05, 
  threshold_use = TRUE, 
  vote_rate = 0.6)

## [1] "The number of missing features in the query data is  17 "
## [1] "The rate of missing features in the query data is  0.0524691358024691 "

head(scLearn_predict_result_MSL)

##          Query_cell_id Predict_cell_type Additional_information
## D31.7_38      D31.7_38        unassigned             Novel_Cell
## D28.3_4        D28.3_4        unassigned             Novel_Cell
## D30.1_63      D30.1_63        unassigned             Novel_Cell
## D31.6_53      D31.6_53        unassigned             Novel_Cell
## D30.7_39      D30.7_39        unassigned             Novel_Cell
## D31.1_22      D31.1_22        unassigned             Novel_Cell

• Accuracy

QueryData_CellType_MSL <- QueryData_trueLabel |> 
  as.data.frame() |>
  tibble::rownames_to_column("CellID") |>
  dplyr::rename(trueLabel = QueryData_trueLabel) |>  
  dplyr::inner_join(scLearn_predict_result_MSL |>
                      as.data.frame() |>
                      dplyr::rename(predLabel = Predict_cell_type),
                    by = c("CellID" = "Query_cell_id")) |>
  dplyr::select(CellID, trueLabel, predLabel, everything())

print(
  paste("MSL Accuracy =", 
    sprintf("%1.2f%%",
      100 * sum(QueryData_CellType_MSL$predLabel == QueryData_CellType_MSL$trueLabel) / nrow(QueryData_CellType_MSL))))

## [1] "MSL Accuracy = 79.94%"

NCA

Neighborhood Components Analysis (maximizes leave-one-out classification probability)

• model learning

scLearn_model_learning_result_NCA <- scLearn_model_learning(
  high_varGene_names = RefDataQC_HVG_names,
  expression_profile = RefDataQC_filtered$expression_profile,
  sample_information_cellType = RefDataQC_filtered$sample_information_cellType,
  sample_information_timePoint = NULL,
  method = "NCA",
  bootstrap_times = 1,
  cutoff = 0.01,
  dim_para = 0.999,
  max_iter = 1
)

• cell assignment

scLearn_predict_result_NCA <- scLearn_cell_assignment(
  scLearn_model_learning_result = scLearn_model_learning_result_NCA, 
  expression_profile_query = QueryDataQC$expression_profile, 
  diff = 0.05, 
  threshold_use = TRUE, 
  vote_rate = 0.6)

## [1] "The number of missing features in the query data is  17 "
## [1] "The rate of missing features in the query data is  0.0524691358024691 "

head(scLearn_predict_result_NCA)

##          Query_cell_id Predict_cell_type Additional_information
## D31.7_38      D31.7_38        unassigned             Novel_Cell
## D28.3_4        D28.3_4        unassigned             Novel_Cell
## D30.1_63      D30.1_63        unassigned             Novel_Cell
## D31.6_53      D31.6_53        unassigned             Novel_Cell
## D30.7_39      D30.7_39        unassigned             Novel_Cell
## D31.1_22      D31.1_22        unassigned             Novel_Cell

• Accuracy

QueryData_CellType_NCA <- QueryData_trueLabel |> 
  as.data.frame() |>
  tibble::rownames_to_column("CellID") |>
  dplyr::rename(trueLabel = QueryData_trueLabel) |>  
  dplyr::inner_join(scLearn_predict_result_NCA |>
                      as.data.frame() |>
                      dplyr::rename(predLabel = Predict_cell_type),
                    by = c("CellID" = "Query_cell_id")) |>
  dplyr::select(CellID, trueLabel, predLabel, everything())

print(
  paste("NCA Accuracy =", 
    sprintf("%1.2f%%",
      100 * sum(QueryData_CellType_NCA$predLabel == QueryData_CellType_NCA$trueLabel) / nrow(QueryData_CellType_NCA))))

## [1] "NCA Accuracy = 78.32%"

ITML

Information-Theoretic Metric Learning

• model learning

scLearn_model_learning_result_ITML <- scLearn_model_learning(
  high_varGene_names = RefDataQC_HVG_names,
  expression_profile = RefDataQC_filtered$expression_profile,
  sample_information_cellType = RefDataQC_filtered$sample_information_cellType,
  sample_information_timePoint = NULL,
  method = "ITML",
  bootstrap_times = 1,
  cutoff = 0.01,
  dim_para = 0.999,
  max_iter = 1
)

• cell assignment

scLearn_predict_result_ITML <- scLearn_cell_assignment(
  scLearn_model_learning_result = scLearn_model_learning_result_ITML, 
  expression_profile_query = QueryDataQC$expression_profile, 
  diff = 0.05, 
  threshold_use = TRUE, 
  vote_rate = 0.6)

## [1] "The number of missing features in the query data is  17 "
## [1] "The rate of missing features in the query data is  0.0524691358024691 "

head(scLearn_predict_result_ITML)

##          Query_cell_id Predict_cell_type Additional_information
## D31.7_38      D31.7_38        unassigned             Novel_Cell
## D28.3_4        D28.3_4        unassigned             Novel_Cell
## D30.1_63      D30.1_63        unassigned             Novel_Cell
## D31.6_53      D31.6_53        unassigned             Novel_Cell
## D30.7_39      D30.7_39        unassigned             Novel_Cell
## D31.1_22      D31.1_22        unassigned             Novel_Cell

• Accuracy

QueryData_CellType_ITML <- QueryData_trueLabel |> 
  as.data.frame() |>
  tibble::rownames_to_column("CellID") |>
  dplyr::rename(trueLabel = QueryData_trueLabel) |>  
  dplyr::inner_join(scLearn_predict_result_ITML |>
                      as.data.frame() |>
                      dplyr::rename(predLabel = Predict_cell_type),
                    by = c("CellID" = "Query_cell_id")) |>
  dplyr::select(CellID, trueLabel, predLabel, everything())

print(
  paste("ITML Accuracy =", 
    sprintf("%1.2f%%",
      100 * sum(QueryData_CellType_ITML$predLabel == QueryData_CellType_ITML$trueLabel) / nrow(QueryData_CellType_ITML))))

## [1] "ITML Accuracy = 79.94%"

MMC

Maximum Margin Clustering (explicitly optimizes within-class/between-class scatter matrices)

• model learning

scLearn_model_learning_result_MMC <- scLearn_model_learning(
  high_varGene_names = RefDataQC_HVG_names,
  expression_profile = RefDataQC_filtered$expression_profile,
  sample_information_cellType = RefDataQC_filtered$sample_information_cellType,
  sample_information_timePoint = NULL,
  method = "MMC",
  bootstrap_times = 1,
  cutoff = 0.01,
  dim_para = 0.999,
  max_iter = 1
)

• cell assignment

scLearn_predict_result_MMC <- scLearn_cell_assignment(
  scLearn_model_learning_result = scLearn_model_learning_result_MMC, 
  expression_profile_query = QueryDataQC$expression_profile, 
  diff = 0.05, 
  threshold_use = TRUE, 
  vote_rate = 0.6)

## [1] "The number of missing features in the query data is  17 "
## [1] "The rate of missing features in the query data is  0.0524691358024691 "

head(scLearn_predict_result_MMC)

##          Query_cell_id Predict_cell_type Additional_information
## D31.7_38      D31.7_38        unassigned             Novel_Cell
## D28.3_4        D28.3_4            ductal      0.849364909229798
## D30.1_63      D30.1_63            ductal      0.866198056386978
## D31.6_53      D31.6_53        unassigned             Novel_Cell
## D30.7_39      D30.7_39        unassigned             Novel_Cell
## D31.1_22      D31.1_22        unassigned             Novel_Cell

• Accuracy

QueryData_CellType_MMC <- QueryData_trueLabel |> 
  as.data.frame() |>
  tibble::rownames_to_column("CellID") |>
  dplyr::rename(trueLabel = QueryData_trueLabel) |>  
  dplyr::inner_join(scLearn_predict_result_MMC |>
                      as.data.frame() |>
                      dplyr::rename(predLabel = Predict_cell_type),
                    by = c("CellID" = "Query_cell_id")) |>
  dplyr::select(CellID, trueLabel, predLabel, everything())

print(
  paste("MMC Accuracy =", 
    sprintf("%1.2f%%",
      100 * sum(QueryData_CellType_MMC$predLabel == QueryData_CellType_MMC$trueLabel) / nrow(QueryData_CellType_MMC))))

## [1] "MMC Accuracy = 71.20%"

Summary

Method	Accuracy(%)
DCA (Discriminative Component Analysis)	81.23
LMNN (Large Margin Nearest Neighbors)	79.94
MSL-LMNN (Multi-Similarity Loss-Based Metric Learning)	78.32
NCA (Neighborhood Components Analysis)	79.94
ITML (Information-Theoretic Metric Learning)	79.94
MMC (Maximum Margin Clustering)	71.20

The table compares the accuracy of six metric learning methods, with DCA (Discriminative Component Analysis) achieving the highest accuracy at 81.23%. LMNN, NCA, and ITML share identical performance at 79.94%, followed by MSL at 78.32%. MMC (Maximum Margin Clustering) shows the lowest accuracy among the evaluated methods at 71.20%. (RefCellData & QueryCellData)

Key observations:

• DCA outperforms all other methods by a clear margin (1.29% higher than the second-best group).
• Three methods (LMNN, NCA, ITML) demonstrate identical performance levels.
• MMC trails significantly behind other approaches, with a ~8-10% accuracy gap compared to top performers.

System information

sessionInfo()

## R version 4.4.3 (2025-02-28)
## Platform: aarch64-apple-darwin20
## Running under: macOS Sequoia 15.4.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: Asia/Shanghai
## tzcode source: internal
## 
## attached base packages:
## [1] stats4    stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] M3Drop_1.32.0               numDeriv_2016.8-1.1        
##  [3] SingleCellExperiment_1.28.1 SummarizedExperiment_1.36.0
##  [5] Biobase_2.66.0              GenomicRanges_1.58.0       
##  [7] GenomeInfoDb_1.42.3         IRanges_2.40.1             
##  [9] S4Vectors_0.44.0            BiocGenerics_0.52.0        
## [11] MatrixGenerics_1.18.1       matrixStats_1.5.0          
## [13] lubridate_1.9.4             forcats_1.0.0              
## [15] stringr_1.5.1               dplyr_1.1.4                
## [17] purrr_1.0.4                 readr_2.1.5                
## [19] tidyr_1.3.1                 tibble_3.2.1               
## [21] ggplot2_3.5.1               tidyverse_2.0.0            
## [23] scLearn_2.0.0               BiocStyle_2.34.0           
## 
## loaded via a namespace (and not attached):
##   [1] bitops_1.0-9            gridExtra_2.3           inline_0.3.21          
##   [4] rlang_1.1.5             magrittr_2.0.3          compiler_4.4.3         
##   [7] loo_2.8.0               mgcv_1.9-1              systemfonts_1.2.1      
##  [10] vctrs_0.6.5             quadprog_1.5-8          pkgconfig_2.0.3        
##  [13] crayon_1.5.3            fastmap_1.2.0           backports_1.5.0        
##  [16] XVector_0.46.0          caTools_1.18.3          rmarkdown_2.29         
##  [19] tzdb_0.5.0              UCSC.utils_1.2.0        ragg_1.3.3             
##  [22] densEstBayes_1.0-2.2    xfun_0.51               zlibbioc_1.52.0        
##  [25] cachem_1.1.0            jsonlite_2.0.0          DelayedArray_0.32.0    
##  [28] parallel_4.4.3          irlba_2.3.5.1           cluster_2.1.8          
##  [31] R6_2.6.1                dml_1.1.0               bslib_0.9.0            
##  [34] stringi_1.8.4           RColorBrewer_1.1-3      StanHeaders_2.32.10    
##  [37] rpart_4.1.24            jquerylib_0.1.4         Rcpp_1.0.14            
##  [40] bookdown_0.42           rstan_2.32.7            knitr_1.50             
##  [43] base64enc_0.1-3         timechange_0.3.0        Matrix_1.7-2           
##  [46] splines_4.4.3           nnet_7.3-20             tidyselect_1.2.1       
##  [49] rstudioapi_0.17.1       abind_1.4-8             yaml_2.3.10            
##  [52] codetools_0.2-20        gplots_3.2.0            curl_6.2.2             
##  [55] pkgbuild_1.4.7          lattice_0.22-6          withr_3.0.2            
##  [58] rARPACK_0.11-0          evaluate_1.0.3          foreign_0.8-88         
##  [61] desc_1.4.3              RcppParallel_5.1.10     pillar_1.10.1          
##  [64] BiocManager_1.30.25     KernSmooth_2.23-26      checkmate_2.3.2        
##  [67] generics_0.1.3          hms_1.1.3               rstantools_2.4.0       
##  [70] munsell_0.5.1           scales_1.3.0            gtools_3.9.5           
##  [73] glue_1.8.0              Hmisc_5.2-3             tools_4.4.3            
##  [76] data.table_1.17.0       RSpectra_0.16-2         fs_1.6.5               
##  [79] mvtnorm_1.3-3           grid_4.4.3              bbmle_1.0.25.1         
##  [82] QuickJSR_1.7.0          bdsmatrix_1.3-7         colorspace_2.1-1       
##  [85] nlme_3.1-167            GenomeInfoDbData_1.2.13 lfda_1.1.3             
##  [88] htmlTable_2.4.3         Formula_1.2-5           cli_3.6.4              
##  [91] textshaping_1.0.0       S4Arrays_1.6.0          V8_6.0.2               
##  [94] gtable_0.3.6            sass_0.4.9              digest_0.6.37          
##  [97] reldist_1.7-2           SparseArray_1.6.2       htmlwidgets_1.6.4      
## [100] htmltools_0.5.8.1       pkgdown_2.1.1           lifecycle_1.0.4        
## [103] httr_1.4.7              statmod_1.5.0           MASS_7.3-64