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基于参考点预测的动态多目标优化算法
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基于参考点预测的动态多目标优化算法
官方公共微信用R软件画热图全教程
to analyse an Acute
lymphocytic leukemia (ALL) microarray dataset, producing a heatmap
(with dendrograms) of genes differentially expressed between two
types of leukemia.
There is a follow on page dealing with how to do this
using RPy.
The original citation for the raw data is "Gene expression
profile of adult T-cell acute lymphocytic leukemia identifies
distinct subsets of patients with different response to therapy and
survival" by Chiaretti et al. Blood 2004. ()
The analysis is a "step by step" recipe based on this paper,
. Their , which we recreate, is reproduced here:
Heatmaps from R
Assuming you have a recent version of R (from ) and
(see ), the example dataset can
be downloaded as the BioConductor ALL package.
You should be able to install this from within R as follows:
& source("http://www.bioconductor.org/biocLite.R")
& biocLite("ALL")
Running bioCLite version 0.1
with R version
Alternatively, you can download the package by hand from
If you are using Windows, download ALL_1.0.2.zip (or
similar) and save it. Then from within the R program, use the menu
option "Packages", "Install package(s) from local zip files..." and
select the ZIP file.
On Linux, download ALL_1.0.2.tar.gz (or similar) and
use sudo R CMD INSTALL ALL_1.0.2.tar.gz at the command
With that out of the way, you should be able to start R and load
this package with the library and data commands:
& library("ALL")
Loading required package: Biobase
Loading required package: tools
Welcome to Bioconductor
Vignettes contain introductory material.
simply type: openVignette()
For details on reading vignettes, see
the openVignette help page.
& data("ALL")
If you inspect the resulting ALL variable, it contains 128
samples with 12625 genes, and associated phenotypic data.
Expression Set (exprSet) with
12625 genes
128 samples
phenoData object with 21 variables and 128 cases
Patient ID
diagnosis:
Date of diagnosis
Gender of the patient
Age of the patient at entry
does the patient have B-cell or T-cell ALL
remission:
Complete remission(CR), refractory(REF) or NA. Derived from CR
Original remisson data
Date complete remission if achieved
did the patient have t(4;11) translocation. Derived from citog
did the patient have t(9;22) translocation. Derived from citog
cyto.normal:
Was cytogenetic test normal? Derived from citog
original citogenetics data, deletions or t(4;11), t(9;22) status
molecular biology
fusion protein:
which of p190, p210 or p190/210 for bcr/able
multi-drug resistant
ploidy: either diploid or hyperd.
Continuous complete remission? Derived from f.u
Relapse? Derived from f.u
transplant:
did the patient receive a bone marrow transplant? Derived from f.u
follow up data available
date last seen:
date patient was last seen
We can looks at the results of molecular biology testing for the
128 samples:
& ALL$mol.biol
[1] BCR/ABL
ALL1/AF4 NEG
[10] BCR/ABL
E2A/PBX1 NEG
[19] BCR/ABL
ALL1/AF4 BCR/ABL
Levels: ALL1/AF4 BCR/ABL E2A/PBX1 NEG NUP-98 p15/p16
Ignoring the samples which came back negative on this test
(NEG), most have been classified as having a translocation between
chromosomes 9 and 22 (BCR/ABL), or a translocation between
chromosomes 4 and 11 (ALL1/AF4).
For the purposes of this example, we are only interested in
these two subgroups, so we will create a filtered version of the
dataset using this as a selection criteria:
& eset &- ALL[, ALL$mol.biol %in% c("BCR/ABL", "ALL1/AF4")]
The resulting variable, eset, contains just 47 samples
- each with the full 12,625 gene expression levels.
This is far too much data to draw a heatmap with, but we can do
one for the first 100 genes as follows:
& heatmap(exprs(eset[1:100,]))
According to the BioConductor paper we are following, the next
step in the analysis was to use the lmFit function (from the limma
package) to look for genes differentially expressed between the two
groups. The fitted model object is further processed by the eBayes
function to produce empirical Bayes test statistics for each gene,
including moderated t-statistics, p-values and log-odds of
differential expression.
& library(limma)
& f &- factor(as.character(eset$mol.biol))
& design &- model.matrix(~f)
& fit &- eBayes(lmFit(eset,design))
If the limma package isn't installed, you'll need to install it
& source("http://www.bioconductor.org/biocLite.R")
& biocLite("limma")
Running bioCLite version 0.1
with R version
We can now reproduce
from the paper.
& topTable(fit, coef=2)
1914_at -3...581e-27 56.32653
37809_at -3...570e-20 44.23832
36873_at -3...670e-20 43.97298
40763_at -3...381e-18 38.64615
3...401e-16 35.10692
41448_at -2...456e-15 33.61391
33358_at -2...289e-13 28.76471
37978_at -1...996e-10 21.60216
1...033e-10 21.27732
1...875e-09 20.89145
The leftmost numbers are row indices, ID is the Affymetrix
HGU95av2 accession number, M is the log ratio of expression, A is
the log average expression, t the moderated t-statistic, and B is
the log odds of differential expression.
Next, we select those genes that have adjusted p-values below
0.05, using a very stringent Holm method to select a small number
(165) of genes.
& selected
&- p.adjust(fit$p.value[, 2]) &0.05
& esetSel &- eset [selected, ]
The variable esetSel has data on (only) 165 genes for
all 47 samples . We can easily produce a heatmap as follows (in
R-2.1.1 this defaults to a yellow/red "heat" colour scheme):
& heatmap(exprs(esetSel))
If you have the topographical colours installed
(yellow-green-blue), you can do this:
& heatmap(exprs(esetSel), col=topo.colors(100))
This is getting very close to , except they have added a red/blue banner across
the top to really emphasize how the hierarchical clustering has
correctly split the data into the two groups (10 and 37
patients).
To do that, we can use the heatmap function's optional argument
of ColSideColors. I created a small function to
map the eselSet$mol.biol values to red (#FF0000) and blue
(#0000FF), which we can apply to each of the molecular biology
results to get a matching list of colours for our columns:
& color.map &- function(mol.biol) { if (mol.biol=="ALL1/AF4") "#FF0000" else "#0000FF" }
& patientcolors &- unlist(lapply(esetSel$mol.bio, color.map))
& heatmap(exprs(esetSel), col=topo.colors(100), ColSideColors=patientcolors)
Looks pretty close now, doesn't it:
To recap, this is "all" we needed to type into R to achieve
library("ALL")
data("ALL")
eset &- ALL[, ALL$mol.biol %in% c("BCR/ABL", "ALL1/AF4")]
library("limma")
f &- factor(as.character(eset$mol.biol))
design &- model.matrix(~f)
fit &- eBayes(lmFit(eset,design))
&- p.adjust(fit$p.value[, 2]) &0.05
esetSel &- eset [selected, ]
color.map &- function(mol.biol) { if (mol.biol=="ALL1/AF4") "#FF0000" else "#0000FF" }
patientcolors &- unlist(lapply(esetSel$mol.bio, color.map))
heatmap(exprs(esetSel), col=topo.colors(100), ColSideColors=patientcolors)
Heatmaps in R - More Options
One subtle point in the previous examples is that the
heatmap function has automatically scaled the colours for
each row (i.e. each gene has been individually normalised across
patients). This can be disabled using
scale="none", which you might want to do if you
have already done your own normalisation (or this may not be
appropriate for your data):
heatmap(exprs(esetSel), col=topo.colors(75),
scale="none", ColSideColors=patientcolors, cexRow=0.5)
You might also have noticed in the above snippet, that I have
shrunk the row captions which were so big they overlapped each
other. The relevant options are cexRow and
So far so good - but what if you wanted a key to the colours
shown? The heatmap function doesn't offer this, but the
good news is that heatmap.2 from the gplots
library does. In fact, it offers a lot of other features, many of
which I deliberately turn off in the following example:
library("gplots")
heatmap.2(exprs(esetSel), col=topo.colors(75), scale="none", ColSideColors=patientcolors,
key=TRUE, symkey=FALSE, ="none", trace="none", cexRow=0.5)
By default, heatmap.2 will also show a trace on each
data point (removed this with trace="none"). If
you ask for a key (using key=TRUE) this function
will actually give you a combined "color key and histogram", but
that can be overridden (with
<="none").
Don't like the colour scheme? Try using the functions
bluered/redblue for a red-white-blue spread, or
redgreen/greenred for the red-black-green colour
scheme often used with two-colour microarrays:
library("gplots")
heatmap.2(exprs(esetSel), col=redgreen(75), scale="row", ColSideColors=patientcolors,
key=TRUE, symkey=FALSE, ="none", trace="none", cexRow=0.5)
Heatmaps from Python
So, how can we do that from within Python? One way is using
this is discussed on .
P.S. If you want to use heatmap.2 from within python
using RPy, use the syntax heatmap_2 due to the differences
in how R and Python handle full stops and underscores.
What about other microarray data?
Well, I have also documented how you can
as a BioConductor expression
set object. As long as you can get your data into R as a matrix or
data frame, converting it into an exprSet shouldn't be too
This was all written and tested using Windows XP and R-2.1.1,
but it should all work on other platforms.
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一个网格划分实例的详解该题目条件如下图所示：Part 1：本部分将平台考虑成蓝色的虚线1.& & 画左边的第一部分，有多种方案。方法一：最简单的一种就是不用布置任何初始的2dmesh直接用one volume画，画出来的质量相当不错。One volume是非常简单而且强大的画法，只要是一个有一个方向可以mapped的实体都可以用这个方法来画网格，而事实上，很多不能map的单元也都可以用这个命令来画，所以在对三维实体进行网格划分的时候，收件推荐用one volume来试下效果，如果效果不错的话，就没有必要先做二维单元后再来画。方法二：先在其一个面上生成2D的mesh，在来利用general选项，这样的优点是可以做出很漂亮的网格。 相比之下：方法二所做出来的网格质量要比一要高。2.& & 画第二段的网格，同样演示两种方法：方法一：直接用3D&solid map&one volume 方法二：从该段图形来看，左端面实际上由3个面组成，右端面由一个部分组成，故可以先将左端面的另两个部分的面网格补齐，再用general选项来拉伸，但是，问题是左面砖红色的部分仅为3D单元，而没有可供拉伸的源面网格，故，应该先用face命令生成二维网格后，再来拉伸，其每一步的结果分见下： 在用general选项时，有个问题需要注意：在前面我们说过，source geom和elemes to drag二选一都可以，但是这里就不一样了，因为source geom选面的话，只能选择一个面，而此处是3个面，所以这里只能选elemesto drag而不能选择source geom.在即将对第三段画网格时候，出现了问题：第三段两根黑色的边界线处应该和第二段的网格协调，也就是说，在两部分的共享边上，线的相交处应该产生单元节点，要控制这一步，偶想了很久，最后想出一个办法，就先在第二段的表面上将第二段的表面分开，但并不剖分体。3.& & 画第3段的网格：利用one volume 画，当然也可以用general，注意那个平台是用蓝色虚线影藏掉了的，所以，这个特征实际上没有什么重要影响。第四段的画法同样很简单，直接用one volume画即可。剩下的就是画圆台部分：用one volume 注意圆台中间有些地方是不规则的六面体，那是由于圆台的上表面和下表面不一样大而导致的。剩下的半个圆台就直接在用one volume就行了。总结：创造三维六面体网格最强大的功能就是one volume，如果用该命令得不到满意的网格，再采用先利用automesh生成面网格后，再来用general来产生体网格的方式。Part 2：考虑平台该问题的难点在于：考虑了平台的存在之后，第三部分的单元划分时就不能再继续采用one volume，因为有平台之后，该部分就变成了nomapped区域。另外，为了保证和第一二部分单元的协调，就必须做出相应的剖分。1.& & 必要的几何剖分。 2.& & 对所选出来的部分进行再次几何剖分去掉一根边界线（togglecommand） Using Project commandProject again利用quick edit中的命令node andline利用solidedit&trim with lines&sweep line将体沿那条曲线剖下去然后再利用solid edit&trim with nodes命令来剖分，注意要勾选extendedtrimmer。剖分完毕，就完成了本题目最重要的内容，剩下的全都先用one volume来画，不行的话，就用general修改 总结：1.& & 经常需要使用建立临时的节点和线来作为辅助点和线，构造节点的方法要熟练掌握。完了之后，利用clear temp nodes删除即可。2.& & 常用的几个命令： solid map。3.& & 要得到实体单元：最常用的两个命令：one volume and general4.& & 选择实体：先按住鼠标左键不放，然后再按住shift键，然后再移动鼠标点选。
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