使用R或Matlab进行二元分布的三维图

Question

我想知道是否有人可以告诉我你是如何绘制与此类似的东西 带有样本直方图的根据两条曲线下面的代码生成。使用R或Matlab，但最好使用R

# bivariate normal with a gibbs sampler...

gibbs<-function (n, rho) 
{
  mat <- matrix(ncol = 2, nrow = n)
  x <- 0
  y <- 0
  mat[1, ] <- c(x, y)
  for (i in 2:n) {
    x <- rnorm(1, rho * y, (1 - rho^2))
    y <- rnorm(1, rho * x,(1 - rho^2))
    mat[i, ] <- c(x, y)
  }
  mat
}



bvn<-gibbs(10000,0.98)
par(mfrow=c(3,2))
plot(bvn,col=1:10000,main="bivariate normal distribution",xlab="X",ylab="Y")
plot(bvn,type="l",main="bivariate normal distribution",xlab="X",ylab="Y")

hist(bvn[,1],40,main="bivariate normal distribution",xlab="X",ylab="")
hist(bvn[,2],40,main="bivariate normal distribution",xlab="Y",ylab="")
par(mfrow=c(1,1))`

提前致谢

致以最诚挚的问候，

JC T。

Answer 1

您可以通过编程方式在Matlab中完成。

结果如下：

代码：

% Generate some data.
data = randn(10000, 2);

% Scale and rotate the data (for demonstration purposes).
data(:,1) = data(:,1) * 2;
theta = deg2rad(130);
data = ([cos(theta) -sin(theta); sin(theta) cos(theta)] * data')';

% Get some info.
m = mean(data);
s = std(data);
axisMin = m - 4 * s;
axisMax = m + 4 * s;

% Plot data points on (X=data(x), Y=data(y), Z=0)
plot3(data(:,1), data(:,2), zeros(size(data,1),1), 'k.', 'MarkerSize', 1);

% Turn on hold to allow subsequent plots.
hold on

% Plot the ellipse using Eigenvectors and Eigenvalues.
data_zeroMean = bsxfun(@minus, data, m);
[V,D] = eig(data_zeroMean' * data_zeroMean / (size(data_zeroMean, 1)));
[D, order] = sort(diag(D), 'descend');
D = diag(D);
V = V(:, order);
V = V * sqrt(D);
t = linspace(0, 2 * pi);
e = bsxfun(@plus, 2*V * [cos(t); sin(t)], m');
plot3(...
    e(1,:), e(2,:), ...
    zeros(1, nPointsEllipse), 'g-', 'LineWidth', 2);

maxP = 0;
for side = 1:2
    % Calculate the histogram.
    p = [0 hist(data(:,side), 20) 0];
    p = p / sum(p);
    maxP = max([maxP p]);
    dx = (axisMax(side) - axisMin(side)) / numel(p) / 2.3;
    p2 = [zeros(1,numel(p)); p; p; zeros(1,numel(p))]; p2 = p2(:);
    x = linspace(axisMin(side), axisMax(side), numel(p));
    x2 = [x-dx; x-dx; x+dx; x+dx]; x2 = max(min(x2(:), axisMax(side)), axisMin(side));

    % Calculate the curve.
    nPtsCurve = numel(p) * 10;
    xx = linspace(axisMin(side), axisMax(side), nPtsCurve);

    % Plot the curve and the histogram.
    if side == 1
        plot3(xx, ones(1, nPtsCurve) * axisMax(3 - side), spline(x,p,xx), 'r-', 'LineWidth', 2);
        plot3(x2, ones(numel(p2), 1) * axisMax(3 - side), p2, 'k-', 'LineWidth', 1);
    else
        plot3(ones(1, nPtsCurve) * axisMax(3 - side), xx, spline(x,p,xx), 'b-', 'LineWidth', 2);
        plot3(ones(numel(p2), 1) * axisMax(3 - side), x2, p2, 'k-', 'LineWidth', 1);
    end

end

% Turn off hold.
hold off

% Axis labels.
xlabel('x');
ylabel('y');
zlabel('p(.)');

axis([axisMin(1) axisMax(1) axisMin(2) axisMax(2) 0 maxP * 1.05]);
grid on;

Answer 2

我必须承认，我认为这是一个挑战因为我正在寻找不同的方式来展示其他数据集。我通常按​​照其他答案中显示的scatterhist 2D图表的方式做了一些事情，但我想在rgl试试一段时间。

我使用你的函数来生成数据

gibbs<-function (n, rho) {
    mat <- matrix(ncol = 2, nrow = n)
    x <- 0
    y <- 0
    mat[1, ] <- c(x, y)
    for (i in 2:n) {
        x <- rnorm(1, rho * y, (1 - rho^2))
        y <- rnorm(1, rho * x, (1 - rho^2))
        mat[i, ] <- c(x, y)
    }
    mat
}
bvn <- gibbs(10000, 0.98)

设置

我使用rgl进行硬提升，但我不知道如何在不进入car的情况下获得置信椭圆。我猜还有其他方法来攻击这个。

library(rgl) # plot3d, quads3d, lines3d, grid3d, par3d, axes3d, box3d, mtext3d
library(car) # dataEllipse

处理数据

获取直方图数据而不绘制它，然后我提取密度并将它们标准化为概率。 *max变量用于简化将来的绘图。

hx <- hist(bvn[,2], plot=FALSE)
hxs <- hx$density / sum(hx$density)
hy <- hist(bvn[,1], plot=FALSE)
hys <- hy$density / sum(hy$density)

## [xy]max: so that there's no overlap in the adjoining corner
xmax <- tail(hx$breaks, n=1) + diff(tail(hx$breaks, n=2))
ymax <- tail(hy$breaks, n=1) + diff(tail(hy$breaks, n=2))
zmax <- max(hxs, hys)

地板上的基本散点图

应根据分布将比例设置为适当的值。不可否认，X和Y标签的放置并不精美，但根据数据重新定位不应太难。

## the base scatterplot
plot3d(bvn[,2], bvn[,1], 0, zlim=c(0, zmax), pch='.',
       xlab='X', ylab='Y', zlab='', axes=FALSE)
par3d(scale=c(1,1,3))

后墙上的直方图

我无法弄清楚如何在整个3D渲染中将它们自动绘制在平面上，所以我必须手动制作每个矩形。

## manually create each histogram
for (ii in seq_along(hx$counts)) {
    quads3d(hx$breaks[ii]*c(.9,.9,.1,.1) + hx$breaks[ii+1]*c(.1,.1,.9,.9),
            rep(ymax, 4),
            hxs[ii]*c(0,1,1,0), color='gray80')
}
for (ii in seq_along(hy$counts)) {
    quads3d(rep(xmax, 4),
            hy$breaks[ii]*c(.9,.9,.1,.1) + hy$breaks[ii+1]*c(.1,.1,.9,.9),
            hys[ii]*c(0,1,1,0), color='gray80')
}

摘要行

## I use these to ensure the lines are plotted "in front of" the
## respective dot/hist
bb <- par3d('bbox')
inset <- 0.02 # percent off of the floor/wall for lines
x1 <- bb[1] + (1-inset)*diff(bb[1:2])
y1 <- bb[3] + (1-inset)*diff(bb[3:4])
z1 <- bb[5] + inset*diff(bb[5:6])

## even with draw=FALSE, dataEllipse still pops up a dev, so I create
## a dummy dev and destroy it ... better way to do this?
dev.new()
de <- dataEllipse(bvn[,1], bvn[,2], draw=FALSE, levels=0.95)
dev.off()

## the ellipse
lines3d(de[,2], de[,1], z1, color='green', lwd=3)

## the two density curves, probability-style
denx <- density(bvn[,2])
lines3d(denx$x, rep(y1, length(denx$x)), denx$y / sum(hx$density), col='red', lwd=3)
deny <- density(bvn[,1])
lines3d(rep(x1, length(deny$x)), deny$x, deny$y / sum(hy$density), col='blue', lwd=3)

美化

grid3d(c('x+', 'y+', 'z-'), n=10)
box3d()
axes3d(edges=c('x-', 'y-', 'z+'))
outset <- 1.2 # place text outside of bbox *this* percentage
mtext3d('P(X)', edge='x+', pos=c(0, ymax, outset * zmax))
mtext3d('P(Y)', edge='y+', pos=c(xmax, 0, outset * zmax))

最终产品

使用rgl的一个好处是你可以用鼠标旋转它并找到最佳视角。缺少为这个SO页面制作动画，完成上述所有操作应该可以让您获得播放时间。 （如果你旋转它，你将能够看到线条略微位于直方图的前方并稍微高于散点图;否则我发现了交叉点，所以它在某些地方看起来是非连续的。）

最后，我发现这有点让人分心（2D变体已经足够了）：显示z轴意味着数据有第三个维度; Tufte特别不鼓励这种行为（Tufte，“Envisioning Information，”1990）。但是，具有更高的维度，这种使用RGL的技术将允许对模式进行重要的观察。

（对于记录，Win7 x64，使用R-3.0.3在32位和64位测试，rgl v0.93.996，车载v2.0-19。）

Answer 3

使用bvn <- as.data.frame(gibbs(10000,0.98))创建数据框。 R中的几个2d解决方案：

---

1：快速＆amp;使用psych包的脏解决方案：

library(psych)
scatter.hist(x=bvn$V1, y=bvn$V2, density=TRUE, ellipse=TRUE)

导致：

---

2：一个不错的＆amp;使用ggplot2的漂亮解决方案：

library(ggplot2)
library(gridExtra)
library(devtools)
source_url("https://raw.github.com/low-decarie/FAAV/master/r/stat-ellipse.R") # needed to create the 95% confidence ellipse

htop <- ggplot(data=bvn, aes(x=V1)) + 
  geom_histogram(aes(y=..density..), fill = "white", color = "black", binwidth = 2) + 
  stat_density(colour = "blue", geom="line", size = 1.5, position="identity", show_guide=FALSE) +
  scale_x_continuous("V1", limits = c(-40,40), breaks = c(-40,-20,0,20,40)) + 
  scale_y_continuous("Count", breaks=c(0.0,0.01,0.02,0.03,0.04), labels=c(0,100,200,300,400)) + 
  theme_bw() + theme(axis.title.x = element_blank())

blank <- ggplot() + geom_point(aes(1,1), colour="white") +
  theme(axis.ticks=element_blank(), panel.background=element_blank(), panel.grid=element_blank(),
        axis.text.x=element_blank(), axis.text.y=element_blank(), axis.title.x=element_blank(), axis.title.y=element_blank())

scatter <- ggplot(data=bvn, aes(x=V1, y=V2)) + 
  geom_point(size = 0.6) + stat_ellipse(level = 0.95, size = 1, color="green") +
  scale_x_continuous("label V1", limits = c(-40,40), breaks = c(-40,-20,0,20,40)) + 
  scale_y_continuous("label V2", limits = c(-20,20), breaks = c(-20,-10,0,10,20)) + 
  theme_bw()

hright <- ggplot(data=bvn, aes(x=V2)) + 
  geom_histogram(aes(y=..density..), fill = "white", color = "black", binwidth = 1) + 
  stat_density(colour = "red", geom="line", size = 1, position="identity", show_guide=FALSE) +
  scale_x_continuous("V2", limits = c(-20,20), breaks = c(-20,-10,0,10,20)) + 
  scale_y_continuous("Count", breaks=c(0.0,0.02,0.04,0.06,0.08), labels=c(0,200,400,600,800)) + 
  coord_flip() + theme_bw() + theme(axis.title.y = element_blank())

grid.arrange(htop, blank, scatter, hright, ncol=2, nrow=2, widths=c(4, 1), heights=c(1, 4))

导致：

---

3： ggplot2的紧凑型解决方案：

library(ggplot2)
library(devtools)
source_url("https://raw.github.com/low-decarie/FAAV/master/r/stat-ellipse.R") # needed to create the 95% confidence ellipse

ggplot(data=bvn, aes(x=V1, y=V2)) + 
  geom_point(size = 0.6) + 
  geom_rug(sides="t", size=0.05, col=rgb(.8,0,0,alpha=.3)) + 
  geom_rug(sides="r", size=0.05, col=rgb(0,0,.8,alpha=.3)) + 
  stat_ellipse(level = 0.95, size = 1, color="green") +
  scale_x_continuous("label V1", limits = c(-40,40), breaks = c(-40,-20,0,20,40)) + 
  scale_y_continuous("label V2", limits = c(-20,20), breaks = c(-20,-10,0,10,20)) + 
  theme_bw()

导致：

Answer 4

Matlab的实现称为scatterhist，需要统计工具箱。不幸的是它不是3D，它是一个扩展的2D图。

% some example data
x = randn(1000,1);
y = randn(1000,1);

h = scatterhist(x,y,'Location','SouthEast',...
                'Direction','out',...
                'Color','k',...
                'Marker','o',...
                'MarkerSize',4);

legend('data')
legend boxoff
grid on

它还允许对数据集进行分组：

load fisheriris.mat;
x = meas(:,1);        %// x-data
y = meas(:,2);        %// y-data
gnames = species;     %// assigning of names to certain elements of x and y


scatterhist(x,y,'Group',gnames,'Location','SouthEast',...
            'Direction','out',...
            'Color','kbr',...
            'LineStyle',{'-','-.',':'},...
            'LineWidth',[2,2,2],...
            'Marker','+od',...
            'MarkerSize',[4,5,6]);

Answer 5

R实施

加载库＆＃34; car＆＃34;。我们只使用dataEllipse函数根据数据的百分比绘制椭圆（0.95表示95％的数据落在椭圆内）。

library("car")

gibbs<-function (n, rho) 
 {
   mat <- matrix(ncol = 2, nrow = n)
   x <- 0
   y <- 0
   mat[1, ] <- c(x, y)
   for (i in 2:n) {
   x <- rnorm(1, rho * y, (1 - rho^2))
   y <- rnorm(1, rho * x,(1 - rho^2))
   mat[i, ] <- c(x, y)
   }
   mat
 }

bvn<-gibbs(10000,0.98)

打开PDF设备：

OUTFILE <- "bivar_dist.pdf"

pdf(OUTFILE)

首先设置布局

layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), widths=c(3,1), heights=c(1,3), TRUE)

制作散点图

par(mar=c(5.1,4.1,0.1,0))

评论的线条可用于绘制散点图而不用＆＃34; car＆＃34;从我们使用dataEllipse函数的包

# plot(bvn[,2], bvn[,1], 
#      pch=".",cex = 1, col=1:length(bvn[,2]),
#      xlim=c(-0.6, 0.6),
#      ylim=c(-0.6,0.6),
#      xlab="X",
#      ylab="Y")
# 
# grid(NULL, NULL, lwd = 2)


dataEllipse(bvn[,2], bvn[,1],
        levels = c(0.95),
        pch=".",
        col=1:length(bvn[,2]),
        xlim=c(-0.6, 0.6),
        ylim=c(-0.6,0.6),
        xlab="X",
        ylab="Y",
        center.cex = 1
        )

绘制顶行中X变量的直方图

     par(mar=c(0,4.1,3,0))

     hist(bvn[,2],
          ann=FALSE,axes=FALSE,
          col="light blue",border="black",
          )
     title(main = "Bivariate Normal Distribution")

绘制散点图右侧的Y变量直方图

     yhist <- hist(bvn[,1],
                   plot=FALSE
                  )

     par(mar=c(5.1,0,0.1,1))

     barplot(yhist$density,
             horiz=TRUE,
             space=0,
             axes=FALSE,
             col="light blue",
             border="black"
             )

 dev.off(which = dev.cur())

      dataEllipse(bvn[,2], bvn[,1],
                  levels = c(0.5, 0.95),
                  pch=".",
                  col= 1:length(bvn[,2]),
                  xlim=c(-0.6, 0.6),
                  ylim=c(-0.6,0.6),
                  xlab="X",
                  ylab="Y",
                  center.cex = 1
                 )

Answer 6

我在上面使用了@ jaap的代码并将其转换为稍微更通用的功能。代码可以来源here。注意：我没有在@jaap的代码中添加任何新内容，只是进行了一些小修改并将其包装在函数中。希望它有用。

density.hist <- function(df, x=NULL, y=NULL) {

require(ggplot2)
require(gridExtra)
require(devtools)

htop <- ggplot(data=df, aes_string(x=x)) + 
  geom_histogram(aes(y=..density..), fill = "white", color = "black", bins=100) + 
  stat_density(colour = "blue", geom="line", size = 1, position="identity", show.legend=FALSE) +
  theme_bw() + theme(axis.title.x = element_blank())

blank <- ggplot() + geom_point(aes(1,1), colour="white") +
  theme(axis.ticks=element_blank(), panel.background=element_blank(), panel.grid=element_blank(),
  axis.text.x=element_blank(), axis.text.y=element_blank(), axis.title.x=element_blank(), 
  axis.title.y=element_blank())

scatter <- ggplot(data=df, aes_string(x=x, y=y)) + 
  geom_point(size = 0.6) + stat_ellipse(type = "norm", linetype = 2, color="green",size=1) +
  stat_ellipse(type = "t",color="green",size=1) +
  theme_bw() + labs(x=x, y=y)

hright <- ggplot(data=df, aes_string(x=x)) + 
  geom_histogram(aes(y=..density..), fill = "white", color = "black", bins=100) + 
  stat_density(colour = "red", geom="line", size = 1, position="identity", show.legend=FALSE) +
  coord_flip() + theme_bw() + theme(axis.title.y = element_blank())

grid.arrange(htop, blank, scatter, hright, ncol=2, nrow=2, widths=c(4, 1), heights=c(1, 4))

}