SNE(t-distributed stochastic neighbor embedding)是用于降维的一种机器学习算法，是由 Laurens van der Maaten 和 Geoffrey Hinton在08年提出来。此外，t-SNE 是一种非线性降维算法，非常适用于高维数据降维到2维或者3维，进行可视化。t-SNE是由SNE(Stochastic Neighbor Embedding, SNE; Hinton and Roweis, 2002)发展而来。t-SNE本质是一种嵌入模型，能够将高维空间中的数据映射到低维空间中，并保留数据集的局部特性。t-SNE降维方法，降维的效果相对于PCA更好，还可以进行可视化分析等，是目前很好用的降维算法之一。

软件安装

设置清华镜像，加快包的安装如下：

options("repos" = c(CRAN="https://mirrors.tuna.tsinghua.edu.cn/CRAN/"))
if(!require(Rtsne))
  install.packages("Rtsne")

数据读取

这里我们准备了三个数据集，一个是例子中给出来的，一个是乳腺癌患者活检数据集，另一个是单细胞转录组的数据集。

1. 埃德加·安德森的虹膜数据

DescriptionThis famous (Fisher's or Anderson's) iris data set gives the measurements in centimeters of the variables sepal length and width and petal length and width, respectively, for 50 flowers from each of 3 species of iris. The species are Iris setosa, versicolor, and virginica.UsageirisFormatiris is a data frame with 150 cases (rows) and 5 variables (columns) named Sepal.Length, Sepal.Width, Petal.Length, Petal.Width, and Species.

library(Rtsne)
library(ggplot2)
data("iris")
iris_unique <- unique(iris)  # Remove duplicates
iris_matrix <- as.matrix(iris_unique[, 1:4])
head(iris_matrix)
##   Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1          5.1         3.5          1.4         0.2
## 2          4.9         3.0          1.4         0.2
## 3          4.7         3.2          1.3         0.2
## 4          4.6         3.1          1.5         0.2
## 5          5.0         3.6          1.4         0.2
## 6          5.4         3.9          1.7         0.4

2. 乳腺癌患者活检数据

我们已经多次使用过这个数据集了，class是二分类的结果变量恶性还是良性的。

DescriptionThis breast cancer database was obtained from the University of Wisconsin Hospitals, Madison from Dr. William H. Wolberg. He assessed biopsies of breast tumours for 699 patients up to 15 July 1992; each of nine attributes has been scored on a scale of 1 to 10, and the outcome is also known. There are 699 rows and 11 columns.UsagebiopsyFormatThis data frame contains the following columns:IDsample code number (not unique).V1clump thickness.V2uniformity of cell size.V3uniformity of cell shape.V4marginal adhesion.V5single epithelial cell size.V6bare nuclei (16 values are missing).V7bland chromatin.V8normal nucleoli.V9mitoses.class"benign" or "malignant".

library(MASS)
data("biopsy")
head(biopsy)
##        ID V1 V2 V3 V4 V5 V6 V7 V8 V9     class
## 1 1000025  5  1  1  1  2  1  3  1  1    benign
## 2 1002945  5  4  4  5  7 10  3  2  1    benign
## 3 1015425  3  1  1  1  2  2  3  1  1    benign
## 4 1016277  6  8  8  1  3  4  3  7  1    benign
## 5 1017023  4  1  1  3  2  1  3  1  1    benign
## 6 1017122  8 10 10  8  7 10  9  7  1 malignant
data <- unique(na.omit(biopsy[, -1]))
head(data)
##   V1 V2 V3 V4 V5 V6 V7 V8 V9     class
## 1  5  1  1  1  2  1  3  1  1    benign
## 2  5  4  4  5  7 10  3  2  1    benign
## 3  3  1  1  1  2  2  3  1  1    benign
## 4  6  8  8  1  3  4  3  7  1    benign
## 5  4  1  1  3  2  1  3  1  1    benign
## 6  8 10 10  8  7 10  9  7  1 malignant

3. 单细胞转录组数据集

单细胞数据我们可以从scatter这个软件包获取，但是目前失效了，我到github上下载了一下，同样可以使用：

library(scater)
library(scRNAseq)
load("sc_example_counts.RData")
load("sc_example_cell_info.RData")
head(sc_example_cell_info)
##              Cell Mutation_Status Cell_Cycle Treatment
## Cell_001 Cell_001        positive          S    treat1
## Cell_002 Cell_002        positive         G0    treat1
## Cell_003 Cell_003        negative         G1    treat1
## Cell_004 Cell_004        negative          S    treat1
## Cell_005 Cell_005        negative         G1    treat2
## Cell_006 Cell_006        negative         G0    treat1
sc_example_counts = unique(sc_example_counts)
sc_example_counts[1:5, 1:5]
##           Cell_001 Cell_002 Cell_003 Cell_004 Cell_005
## Gene_0001        0      123        2        0        0
## Gene_0002      575       65        3     1561     2311
## Gene_0003        0        0        0        0     1213
## Gene_0004        0        1        0        0        0
## Gene_0005        0        0       11        0        0

参数说明

Barnes-Hut implementation of t-Distributed Stochastic Neighbor EmbeddingDescriptionWrapper for the C++ implementation of Barnes-Hut t-Distributed Stochastic Neighbor Embedding. t-SNE is a method for constructing a low dimensional embedding of high-dimensional data, distances or similarities. Exact t-SNE can be computed by setting theta=0.0.UsageRtsne(X, ...)

Rtsne输入对象必须为矩阵；
dims参数设置降维后的维度，默认为2；
theta参数取值越大，结果的准确率越低，默认为0.5，theta此处设置为0.0 ，可以计算出t-SNE的准确值，但是运行时间会比较长；
pca表示是否对输入的数据进行pca分析，此处设置TRUE。

例子实操

1. iris数据集的降维

读入矩阵，构造模型，给出结果：

# Set a seed if you want reproducible results
set.seed(123)
tsne_out <- Rtsne(iris_matrix, pca = FALSE, perplexity = 30, theta = 0)  # Run TSNE
res <- as.data.frame(tsne_out$Y)
res$Class = iris_unique$Species
length(unique(res$Class))
## [1] 3
# 绘制降维后图形
ggplot(res, aes(x = V1, y = V2, color = Class)) + geom_point(size = 1.25) + labs(title = "t-SNE",
    x = "TSNE1", y = "TSNE2") + theme(plot.title = element_text(hjust = 0.5)) + theme_bw()

2. biopsy数据集的降维

读入矩阵，构造模型，给出结果：

set.seed(123)
tsne <- Rtsne(as.matrix(data[, 1:9]), pca = TRUE, perplexity = 10, theta = 0)  # Run TSNE
res <- as.data.frame(tsne$Y)
res$Class = data$class
length(unique(res$Class))
## [1] 2
head(res)
##           V1        V2     Class
## 1  -7.126002  32.10630    benign
## 2 -20.002728 -20.17814    benign
## 3 -12.207140  41.77637    benign
## 4   8.327698 -24.82569    benign
## 5  11.560514  34.23023    benign
## 6  14.006864 -56.03128 malignant
# 绘制降维后图形
ggplot(res, aes(x = V1, y = V2, color = Class)) + geom_point(size = 1.25) + labs(title = "t-SNE",
    x = "TSNE1", y = "TSNE2") + theme(plot.title = element_text(hjust = 0.5)) + theme_bw()

4. 单细胞转录组数据集降维

set.seed(123)
tsne <- Rtsne(as.matrix(t(sc_example_counts)), pca = FALSE, perplexity = 10, theta = 0)  # Run TSNE
res <- as.data.frame(tsne$Y)
res$Class = sc_example_cell_info[sc_example_cell_info$Cell %in% colnames(sc_example_counts),
    ]$Cell_Cycle
length(unique(res$Class))
## [1] 4
head(res)
##          V1         V2 Class
## 1 -52.47414  29.539762     S
## 2  24.23850 -12.023524    G0
## 3  28.90259  48.070417    G1
## 4  72.40250   9.639261     S
## 5 -41.68105  53.376565    G1
## 6  38.48649  12.414251    G0
ggplot(res, aes(x = V1, y = V2, color = Class)) + geom_point(size = 1.25) + labs(title = "t-SNE",
    x = "TSNE1", y = "TSNE2") + theme(plot.title = element_text(hjust = 0.5)) + theme_bw()

我这里都给大家分析三个数据集的，方便大家选择适合自己的数据方法，另外需要代码的将这期教程转发朋友圈，并配文“学生信，找桓峰基因，铸造成功的你！”即可获得！

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References:

Maaten, L. Van Der, 2014. Accelerating t-SNE using Tree-Based Algorithms. Journal of Machine Learning Research, 15, p.3221-3245.

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MachineLearning 12. 机器学习之降维方法t-S

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