SC3聚类 | 拉普拉斯矩阵 | Laplacian matrix | 图论 | R代码
Laplacian和PCA貌似是同一种性质的方法，坐标系变换。只是拉普拉斯属于图论的范畴，术语更加专业了。
要看就把一篇文章看完整，再看其中有什么值得借鉴的，总结归纳理解后的东西才是属于你的。
问题：
1. 这篇文章有哪些亮点决定他能发NM？单细胞，consensus，较好的表现，包装了一些专业的术语，显得自己很专业，其实真正做的东西很少；
2. consensus方法的本质是什么？
3. 工具的评估准则？ARI，silhouette index
4. SC3的最大缺点是什么？速度太慢，超过1000个细胞就非常耗费计算和存储资源
5. 能看懂SC3这个R包的逻辑吗？核心的就4步，多种距离度量，转换，kmeans聚类，consensus；
The main sc3 method explained above is a wrapper that calls several other SC3 methods in the following order:
- sc3_prepare
- sc3_estimate_k - Tracy-Widom theory - random matrix theory (RMT)
- sc3_calc_dists
- sc3_calc_transfs
- sc3_kmeans
- sc3_calc_consens
- sc3_calc_biology
6. 有很多问题没有回答，这篇文章偏技工！核心就是kmeans，打了个复杂的包而已。
- 不同距离的度量有什么差异？
- 为什么要做两种转换PCA和laplacian？
- 为什么选择了kmeans？不知道它有天然的劣势吗
- 做consensus的理论依据是什么？凭什么说做了一致性后结果就更好？
最近在看SC3聚类这篇文章，SC3使用了这个工具。
SC3: consensus clustering of single-cell RNA-seq data
All distance matrices are then transformed using either principal component analysis (PCA) or by calculating the eigenvectors of the associated graph Laplacian (L = I – D–1/2AD–1/2, where I is the identity matrix, A is a similarity matrix (A = e–A′/max(A′)), where A′ is a distance matrix) and D is the degree matrix of A, a diagonal matrix that contains the row-sums of A on the diagonal (Dii = ΣjAij). The columns of the resulting matrices are then sorted in ascending order by their corresponding eigenvalues.
先看下该工具的功能：SC3 package manual
跑一下常规代码：
library(SingleCellExperiment)
library(SC3)
library(scater)
head(ann)
yan[1:3, 1:3]
# create a SingleCellExperiment object
sce <- SingleCellExperiment(
assays = list(
counts = as.matrix(yan),
logcounts = log2(as.matrix(yan) + 1)
),
colData = ann
)
# define feature names in feature_symbol column
rowData(sce)$feature_symbol <- rownames(sce)
# remove features with duplicated names
sce <- sce[!duplicated(rowData(sce)$feature_symbol), ]
# define spike-ins
isSpike(sce, "ERCC") <- grepl("ERCC", rowData(sce)$feature_symbol)
plotPCA(sce, colour_by = "cell_type1")
sce <- sc3(sce, ks = 2:4, biology = TRUE)
# sc3_interactive(sce)
# sc3_export_results_xls(sce)
######################################
sce <- sc3_prepare(sce)
sce <- sc3_estimate_k(sce)
sce <- sc3_calc_dists(sce)
names(metadata(sce)$sc3$distances)
sce <- sc3_calc_transfs(sce)
names(metadata(sce)$sc3$transformations)
metadata(sce)$sc3$distances
sce <- sc3_kmeans(sce, ks = 2:4)
names(metadata(sce)$sc3$kmeans)
col_data <- colData(sce)
head(col_data[ , grep("sc3_", colnames(col_data))])
sce <- sc3_calc_consens(sce)
names(metadata(sce)$sc3$consensus)
names(metadata(sce)$sc3$consensus$`3`)
col_data <- colData(sce)
head(col_data[ , grep("sc3_", colnames(col_data))])
sce <- sc3_calc_biology(sce, ks = 2:4)
sce <- sc3_run_svm(sce, ks = 2:4)
col_data <- colData(sce)
head(col_data[ , grep("sc3_", colnames(col_data))])
接下来会尝试拆一下该工具。
怎么拆这个工具？
这种封装的很好的R包其实比较难拆，一般的通过函数名字就可以看到R代码，但这里你输入函数名，如sc3_calc_dists，看到的只是以下的封装好的代码：
new("nonstandardGenericFunction", .Data = function (object)
{
standardGeneric("sc3_calc_dists")
}, generic = structure("sc3_calc_dists", package = "SC3"), package = "SC3",
group = list(), valueClass = character(0), signature = "object",
default = NULL, skeleton = (function (object)
stop("invalid call in method dispatch to 'sc3_calc_dists' (no default method)",
domain = NA))(object))
暂时还不熟悉这种形式，所以只能通过函数名去GitHub里面查了。
GitHub真的很优秀，可以直接查文件内部代码，可以很快定位到sc3_calc_dists。
再配合这个目录插件，效率提高了不少，https://www.octotree.io/?utm_source=lite&utm_medium=extension
以下是封装前的代码：
#' Calculate distances between the cells.
#'
#' This function calculates distances between the cells. It
#' creates and populates the following items of the \code{sc3} slot of the \code{metadata(object)}:
#' \itemize{
#' \item \code{distances} - contains a list of distance matrices corresponding to
#' Euclidean, Pearson and Spearman distances.
#' }
#'
#' @name sc3_calc_dists
#' @aliases sc3_calc_dists, sc3_calc_dists,SingleCellExperiment-method
#'
#' @param object an object of \code{SingleCellExperiment} class
#'
#' @return an object of \code{SingleCellExperiment} class
#'
#' @importFrom doRNG %dorng%
#' @importFrom foreach foreach %dopar%
#' @importFrom parallel makeCluster stopCluster
#' @importFrom doParallel registerDoParallel
sc3_calc_dists.SingleCellExperiment <- function(object) {
dataset <- get_processed_dataset(object)
# check whether in the SVM regime
if (!is.null(metadata(object)$sc3$svm_train_inds)) {
dataset <- dataset[, metadata(object)$sc3$svm_train_inds]
}
# NULLing the variables to avoid notes in R CMD CHECK
i <- NULL
distances <- c("euclidean", "pearson", "spearman")
message("Calculating distances between the cells...")
if (metadata(object)$sc3$n_cores > length(distances)) {
n_cores <- length(distances)
} else {
n_cores <- metadata(object)$sc3$n_cores
}
cl <- parallel::makeCluster(n_cores, outfile = "")
doParallel::registerDoParallel(cl, cores = n_cores)
# calculate distances in parallel
dists <- foreach::foreach(i = distances) %dorng% {
try({
calculate_distance(dataset, i)
})
}
# stop local cluster
parallel::stopCluster(cl)
names(dists) <- distances
metadata(object)$sc3$distances <- dists
return(object)
}
#' @rdname sc3_calc_dists
#' @aliases sc3_calc_dists
setMethod("sc3_calc_dists", signature(object = "SingleCellExperiment"), sc3_calc_dists.SingleCellExperiment)
通过setMethod链接到一起的。
顺路找到了原函数：
#' Calculate a distance matrix
#'
#' Distance between the cells, i.e. columns, in the input expression matrix are
#' calculated using the Euclidean, Pearson and Spearman metrics to construct
#' distance matrices.
#'
#' @param data expression matrix
#' @param method one of the distance metrics: 'spearman', 'pearson', 'euclidean'
#' @return distance matrix
#'
#' @importFrom stats cor dist
#'
#' @useDynLib SC3
#' @importFrom Rcpp sourceCpp
#'
calculate_distance <- function(data, method) {
return(if (method == "spearman") {
as.matrix(1 - cor(data, method = "spearman"))
} else if (method == "pearson") {
as.matrix(1 - cor(data, method = "pearson"))
} else {
ED2(data)
})
}
#' Distance matrix transformation
#'
#' All distance matrices are transformed using either principal component
#' analysis (PCA) or by calculating the
#' eigenvectors of the graph Laplacian (Spectral).
#' The columns of the resulting matrices are then sorted in
#' descending order by their corresponding eigenvalues.
#'
#' @param dists distance matrix
#' @param method transformation method: either 'pca' or
#' 'laplacian'
#' @return transformed distance matrix
#'
#' @importFrom stats prcomp cmdscale
#'
transformation <- function(dists, method) {
if (method == "pca") {
t <- prcomp(dists, center = TRUE, scale. = TRUE)
return(t$rotation)
} else if (method == "laplacian") {
L <- norm_laplacian(dists)
l <- eigen(L)
# sort eigenvectors by their eigenvalues
return(l$vectors[, order(l$values)])
}
}
#' Calculate consensus matrix
#'
#' Consensus matrix is calculated using the Cluster-based Similarity
#' Partitioning Algorithm (CSPA). For each clustering solution a binary
#' similarity matrix is constructed from the corresponding cell labels:
#' if two cells belong to the same cluster, their similarity is 1, otherwise
#' the similarity is 0. A consensus matrix is calculated by averaging all
#' similarity matrices.
#'
#' @param clusts a matrix containing clustering solutions in columns
#' @return consensus matrix
#'
#' @useDynLib SC3
#' @importFrom Rcpp sourceCpp
#' @export
consensus_matrix <- function(clusts) {
res <- consmx(clusts)
colnames(res) <- as.character(c(1:nrow(clusts)))
rownames(res) <- as.character(c(1:nrow(clusts)))
return(res)
}
- 距离计算
- 转换
- consensus
都在这里。。。
ED2是他们实验室自己用Rcpp写的一个计算欧氏距离的工具。
transformation输入的是对称的距离矩阵（行列都是样本细胞），然后做完PCA，返回了rotation，不知道这样做有什么意义？
还真有用PCA来处理距离相似度矩阵的，MDS，目的就是降维，因为后面要用kmean聚类；
然后对每一个降维了的矩阵用kmeans；
consensus用的是这个算法：Cluster-based Similarity Partitioning Algorithm (CSPA)，做这个的意义何在？输入是每个细胞的多重聚类结果，然后做了一个一致性统一。
参考：
