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数据预处理中的缺失值问题

2017-12-5 16:12| 发布者: 炼数成金_小数| 查看: 14736| 评论: 0|原作者: 晔无殊|来自: R语言中文社区
摘要: 缺失值从数据分布上可被分为三类 (Gelman and Hill 2006, Little and Rubin (2002)) :missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR)。完全随机缺失(MCAR): ...
可视化 方法
1. 简介
1.1 缺失值的分类
缺失值从数据分布上可被分为三类 (Gelman and Hill 2006, Little and Rubin (2002)) :missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR)。
完全随机缺失(MCAR):某一变量缺失值不依赖于其他任何原因的完全随机缺失
随机缺失(MAR):某一变量的缺失与其他变量相关但与该变量本身的数值不相关
非随机缺失(NMAR):某一变量的缺失和该变量本身的数值相关, e.g., 仪器的较低检测线:某被检测物质的含量低于该检测线则会产生非随机缺失(left-censored missing)

目前大部分填补缺失值的方法都是基于MCAR和MAR,这两种情况也相对比较难区别,因此本文会将这两种情况合并起来讨论。

1.2 缺失值的可视化
我一般拿到数据的第一件事就是用Amelia package (Honaker, King, and Blackwell 2011) 里面的missmap function看一下缺失值的分布情况。
require(magrittr)
require(Amelia)
load(file="MVI.RData")
missmap(test_na, col=c("black", "grey"), legend=FALSE, main = 'Missing Map')
# 对于某一变量的缺失值识别可用is.na()sum(is.na(test_na$Var_1))
## [1] 43

1.3 为什么要对缺失值进行处理
对于MCAR,直接删除缺失的样本一般不会对结果产生偏差,但会减少样本数量;对于非完全随机确实特别是MNAR,如果缺失值较多则会对结果产生很大的偏移。另一方面,很多后续的统计检验要求完整的没有缺失值的数据集, e.g., principal components analysis (PCA).

2. 目前常用的缺失值处理方法
2.1 行删除
2.1.1 直接删除有缺失值的样本
最简单粗暴的方法就是直接na.omit(),但是我们可以看到原来198个样本被删到了只剩4个。

test_na_rm <- na.omit(test_na)
dim(test_na)
## [1] 198  30
dim(test_na_rm)
## [1]  4 30

2.1.2 80%法则
80%法则 (Bijlsma et al. 2006)认为,当某一物质的非缺失部分低于总样本量的80%时,建议删除该物质。Modified 80%法则认为, 当某一物质的非缺失部分低于所有生物学亚组的80%时,建议删除该物质。
# remove variables with missing > 20% mis_prop <- sapply(test_na, function(x) sum(is.na(x))/length(x))var_rm <- names(mis_prop)[mis_prop > 1 - 0.8]var_rm # remove 7 variables
## [1] "Var_1"  "Var_2"  "Var_4"  "Var_6"  "Var_11" "Var_16" "Var_21"
test_na_rm <- test_na[, !colnames(test_na) %in% var_rm]test_na_rm <- na.omit(test_na_rm)
dim(test_na)
## [1] 198  30
dim(test_na_rm)
## [1] 83 23
去掉7个不符合80%法则的物质以后再用na.omit()删除有缺失的样本,最终的样本数量维持在了83个。

2.2 单变量填补
用单一变量的均值/中位数/二分之一最小值/零值进行补值,这种方法会导致数据分布的偏移,方差偏小,PCA上会看到一条补值导致的直线等问题。

2.2.1 MCAR/MAR
对于MCAR/MAR,可以用均值/中位数补值。
# meantest_na_mean_imp <- lapply(test_na, function(x) {    x[is.na(x)] <- mean(x, na.rm = T)    x
  })test_na_mean_imp_df <- do.call(cbind.data.frame, test_na_mean_imp)
# mediantest_na_median_imp <- lapply(test_na, function(x) {    x[is.na(x)] <- median(x, na.rm = T)    x
  })test_na_median_imp_df <- do.call(cbind.data.frame, test_na_median_imp)

2.2.2 MNAR
对于left-censored MNAR可以用二分之一最小值/零值进行补值。
# half of minimumtest_na_hm_imp <- lapply(test_na, function(x) {    x[is.na(x)] <- min(x, na.rm = T)/2
    x
  })test_na_hm_imp_df <- do.call(cbind.data.frame, test_na_hm_imp)
# zerotest_na_zero_imp_df <- test_natest_na_zero_imp_df[is.na(test_na_zero_imp_df)] <- 0

2.3 多变量填补
多变量填补的前提是其他变量对于该变量的可预测性,用其他变量作为independent variable,含有缺失值的该变量作为dependent variable,建立模型,用模型来预测该变量中的缺失值。

2.3.1 MCAR/MAR
目前常用的补值方法大部分都是针对MCAR/MAR的情况:missForest (Stekhoven and Bühlmann 2012), k-nearest neighbors (kNN) (Troyanskaya et al. 2001), singular value decomposition (SVD) (T. Hastie, Tibshirani, and Sherlock 1999, Stacklies et al. (2007)), 等等。
# 请先安装missForest packagerequire(missForest)# missForesttest_na_missForest_imp_df <- missForest(test_na)[[1]]
##   missForest iteration 1 in progress...done!
##   missForest iteration 2 in progress...done!
##   missForest iteration 3 in progress...done!
##   missForest iteration 4 in progress...done!
##   missForest iteration 5 in progress...done!
# 请先安装impute packagerequire(impute)# kNNtest_na_kNN_imp_df <-  test_na %>% data.matrix() %>% impute.knn() %>% extract2(1) %>% data.frame()
# 请先安装imputeLCMD packagerequire(imputeLCMD)# SVDSVD_wrapper <- function(data, K = 5) {  data_sc_res <- scale_recover(data, method = 'scale')  data_sc <- data_sc_res[[1]]  data_sc_param <- data_sc_res[[2]]  result <- data_sc %>% impute.wrapper.SVD(., K = K) %>% 
    scale_recover(., method = 'recover', param_df = data_sc_param) %>% extract2(1)  return(result)
}test_na_SVD_imp_df <- SVD_wrapper(test_na) %>% data.frame()

2.3.2 MNAR
目前对于MNAR的算法开发非常有限,如quantile regression imputation of left-censored data (QRILC) (Lazar et al. 2016), gibbs sampler based left-censored missing value imputation approach (GSimp) (Wei et al. 2017).
# 请先安装imputeLCMD packagerequire(imputeLCMD)# QRILCQRILC_wrapper <- function(data, ...) {  zero_idx <- which(data == 0, arr.ind = T)  data_temp <- data
  data_temp[zero_idx] <- NA
  result <- data_temp %>% log() %>% impute.QRILC(., ...) %>% extract2(1) %>% exp()  result[zero_idx] <- 0
  return(result)
}test_na_QRILC_imp_df <- QRILC_wrapper(test_na)
# GSimpsource('GSimp.R')sim_GS_wrapper <- function(data) {  result <- data %>% multi_impute(., iters_each=50, iters_all=10, initial='qrilc', 
                                  lo=-Inf, hi='min', n_cores=1, imp_model='glmnet_pred')  return(result$data_imp)
}test_na_GSimp_imp_df <- sim_GS_wrapper(test_na)
## Iteration 1 start...end!
## Iteration 2 start...end!
## Iteration 3 start...end!
## Iteration 4 start...end!
## Iteration 5 start...end!
## Iteration 6 start...end!
## Iteration 7 start...end!
## Iteration 8 start...end!
## Iteration 9 start...end!
## Iteration 10 start...end!
Core functions for GSimp are available at: GitHub(地址:https://github.com/WandeRum/GSimp)

3. 不同补值方法的结果比较
请参考以下两篇文章: Missing Value Imputation Approach for Mass Spectrometry-based Metabolomics Data (Wei et al. 2017), GSimp: A Gibbs sampler based left-censored missing value imputation approach for metabolomics studies (Wei et al. 2017)。结果显示:在代谢组学的数据中,对于MCAR/MAR的缺失,推荐使用missForest进行补值; 对于left-censored MNAR的缺失,推荐使用GSimp进行补值。 注:以上方法还需在其他类型的数据中进行系统性的比较。

4. 缺失值补值可视化软件 – MetImp
我们将以上各种补值方法 (GSimp很快也会添加进去) 做成了一个免费的web-tool: MetImp(地址:https://metabolomics.cc.hawaii.edu/software/MetImp/)
Step 1: 上传数据,数据格式请保持和我们网站上example data一致; 即横行为样本,纵列为物质,第一行为物质名称,第一列为样本名称,第二列为组别信息;
Step 2: 选择缺失值是属于MCAR/MAR, 还是MNAR;
Step 3: 选择物质删除标准,非缺失部分低于总样本量的百分之多少时删除该物质;
Step 4: Run;
Step 5: 下载补值后的完整数据。
请cite我们的文章:
Runmin Wei, Jingye Wang, Mingming Su, Erik Jia, Tianlu Chen, and Yan Ni.
"Missing Value Imputation Approach for Mass Spectrometry-based Metabolomics Data." Scientific Reports (under revision).
Runmin Wei, Jingye Wang, Erik Jia, Tianlu Chen, Yan Ni, and Wei Jia.
“GSimp: A Gibbs sampler based left-censored missing value imputation approach for metabolomics studies.” PLOS Computational Biology (under revision).

5. 参考文献
Bijlsma, Sabina, Ivana Bobeldijk, Elwin R. Verheij, Raymond Ramaker, Sunil Kochhar, Ian A. Macdonald, Ben Van Ommen, and Age K. Smilde. 2006. “Large-scale human metabolomics studies: A strategy for data (pre-) processing and validation.” Analytical Chemistry 78 (2):567–74. https://doi.org/10.1021/ac051495j.
Gelman, Andrew, and Jennifer Hill. 2006. Data analysis using regression and multilevel/hierarchical models.https://doi.org/10.2277/0521867061.
Hastie, Trevor, Robert Tibshirani, and Gavin Sherlock. 1999. “Imputing missing data for gene expression arrays.” Technical Report, Division of Biostatistics, Stanford University, 1–9.
Honaker, James, Gary King, and Matthew Blackwell. 2011. “AMELIA II : A Program for Missing Data.” Journal of Statistical Software 45 (7):1–54. https://doi.org/10.1.1.149.9611.
Lazar, Cosmin, Laurent Gatto, Myriam Ferro, Christophe Bruley, and Thomas Burger. 2016. “Accounting for the Multiple Natures of Missing Values in Label-Free Quantitative Proteomics Data Sets to Compare Imputation Strategies.” Journal of Proteome Research 15 (4):1116–25. https://doi.org/10.1021/acs.jproteome.5b00981.
Little, Roderick J a, and Donald B Rubin. 2002. Statistical Analysis with Missing Data. https://doi.org/10.2307/1533221.
Stacklies, Wolfram, Henning Redestig, Matthias Scholz, Dirk Walther, and Joachim Selbig. 2007. “pcaMethods - A bioconductor package providing PCA methods for incomplete data.” Bioinformatics 23 (9):1164–7.https://doi.org/10.1093/bioinformatics/btm069.
Stekhoven, Daniel J., and Peter Bühlmann. 2012. “Missforest-Non-parametric missing value imputation for mixed-type data.” Bioinformatics 28 (1):112–18. https://doi.org/10.1093/bioinformatics/btr597.
Troyanskaya, O, M Cantor, G Sherlock, P Brown, T Hastie, R Tibshirani, D Botstein, and R B Altman. 2001. “Missing value estimation methods for DNA microarrays.” Bioinformatics (Oxford, England) 17 (6):520–25.https://doi.org/10.1093/bioinformatics/17.6.520.
Runmin Wei, Jingye Wang, Erik Jia, Tianlu Chen, Yan Ni, and Wei Jia. 2017. “GSimp: A Gibbs sampler based left-censored missing value imputation approach for metabolomics studies.” bioRxiv. https://doi.org/10.1101/177410.
Runmin Wei, Jingye Wang, Mingming Su, Erik Jia, Tianlu Chen, and Yan Ni. 2017. "Missing Value Imputation Approach for Mass Spectrometry-based Metabolomics Data." bioRxiv. https://doi.org/10.1101/171967.

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