I would like to plot in R following contour plots representing two dimensional cumulative distributon functions (CDF)
A CDF in 2 or more dimensions is not unique (Lopes et al. The two-dimensional Kolmogorov-Smirnov test) that's why there are 4 alternative plots (and probably some more).
So far I have no R/Matlab code to show. I don't think it's difficult but most likely very time consuming. There might out there something I could use.
EDIT
Type 1 & 4 are more or less covered, but any help with 2 & 3 would be really appreciated.
EDIT2
Types 2 & 3 using geom_rect - as simple as it gets!
The sequence of recangles is ordered wrt the eucleadian distance of the data. This means, if we assume this generic ordering, there is possibly only one version of defining a 2D CDF instead of two. That would confirm the statement of Lopes et al.and other that there are only 2^N-1 (here 3) ways to define the CDF.
Any thoughts?
Related
I have a matrix with 4 variables whereas 3 variables are parameters and the 4th variable gives the mean sum of squares for simulation results with the corresponding variables. Now I'd like to create a ternary plot with R where the triangle corresponding to the 3 parameter values should be colored by the mean sum of squares value. Alternatively, I'd like to plot interpolated mean sum of squares in the whole simplex triangle.
I was already looking for some functions or code that does what I'm looking for. But I didn't succeed.
Nevertheless, here's an example code of how my data set looks like (for which I'd like to create the ternary plot):
grid <- as.matrix(expand.grid(seq(0,0.5,0.025), seq(0,0.5,0.025), seq(-0.25,0.25,0.025)))
data <- cbind (grid, runif(9261,0,2))
I'd be very thankful if you'd provide R code that can create the plot I'd like to get. Maybe there's even a pre-implemented function in a package that I haven't found?!
Thanks a lot in advance for your help!
I am back at college learning maths and I want to try and use some this knowledge to create some svg with d3.js.
If I have a function f(x) = x^3 - 3x^2 + 3x - 1
I would take the following steps:
Find the x intercepts for when y = 0
Find the y intercept when x = 0
Find the stationary points when dy\dx = 0
I would then have 2 x values from point 3 to plug into the original equation.
I would then draw a nature table do judge the flow of the graph or curve.
Plot the known points from the above and sketch the graph.
Translating what I would do on pen and paper into code instructions is what I really could do with any sort of advice on the following:
How can I programmatically factorise point 1 of the above to find the x-intercepts for when y = 0. I honestly do not know where to even start.
How would I programmatically find dy/dx and the values for the stationary points.
If I actually get this far then what should I use in d3 to join the points on the graph.
Your other "steps" have nothing to do with d3 or plotting.
Find the x intercepts for when y = 0
This is root finding. Look for algorithms to help with this.
Find the y intercept when x = 0
Easy: substitute to get y = 1.
Find the stationary points when dy\dx = 0
Take the first derivative to get 3x^2 - 12x + 9 and repeat the root finding step. Easy to get using quadratic equation.
I would then have 2 x values from point 3 to plug into the original
equation. I would then draw a nature table do judge the flow of the
graph or curve. Plot the known points from the above and sketch the
graph.
I would just draw the curve. Pick a range for x and go.
It's great to learn d3. You'll end up with something like this:
https://maurizzzio.github.io/function-plot/
For a cubic polynomial, there are closed formulas available to find all the particular points that you want (https://en.wikipedia.org/wiki/Cubic_function), and it is a sound approach to determine them.
Anyway, you will have to plot the smooth curve, which means that you will need to compute close enough points and draw a polyline that joins them.
Doing this, you are actually performing the first steps of numerical root isolation, with such an accuracy that the approximate and exact roots will be practically undistinguishable.
So an easy combined solution is to draw the curve as a polyline and find the intersections with the X axis as well as extrema using this polyline representation, rather than by means of more sophisticated methods.
This approach works for any continuous curve and is very easy to implement. So you actually draw the curve to find particular points rather than conversely as is done by analytical methods.
For best results on complicated curves, you can adapt the point density based on the local curvature, but this is another story.
Hi I am using partitioning around medoids algorithm for clustering using the pam function in clustering package. I have 4 attributes in the dataset that I clustered and they seem to give me around 6 clusters and I want to generate a a plot of these clusters across those 4 attributes like this 1: http://www.flickr.com/photos/52099123#N06/7036003411/in/photostream/lightbox/ "Centroid plot"
But the only way I can draw the clustering result is either using a dendrogram or using
plot (data, col = result$clustering) command which seems to generate a plot similar to this
[2] : http://www.flickr.com/photos/52099123#N06/7036003777/in/photostream "pam results".
Although the first image is a centroid plot I am wondering if there are any tools available in R to do the same with a medoid plot Note that it also prints the size of each cluster in the plot. It would be great to know if there are any packages/solutions available in R that facilitate to do this or if not what should be a good starting point in order to achieve plots similar to that in Image 1.
Thanks
Hi All,I was trying to work out the problem the way Joran told but I think I did not understand it correctly and have not done it the right way as it is supposed to be done. Anyway this is what I have done so far. Following is how the file looks like that I tried to cluster
geneID RPKM-base RPKM-1cm RPKM+4cm RPKMtip
GRMZM2G181227 3.412444267 3.16437442 1.287909035 0.037320722
GRMZM2G146885 14.17287135 11.3577013 2.778514642 2.226818648
GRMZM2G139463 6.866752401 5.373925806 1.388843962 1.062745344
GRMZM2G015295 1349.446347 447.4635291 29.43627879 29.2643755
GRMZM2G111909 47.95903081 27.5256729 1.656555758 0.949824883
GRMZM2G078097 4.433627458 0.928492841 0.063329249 0.034255945
GRMZM2G450498 36.15941083 9.45235616 0.700105077 0.194759794
GRMZM2G413652 25.06985426 15.91342458 5.372151214 3.618914949
GRMZM2G090087 21.00891969 18.02318412 17.49531186 10.74302155
following is the Pam clustering output
GRMZM2G181227
1
GRMZM2G146885
2
GRMZM2G139463
2
GRMZM2G015295
2
GRMZM2G111909
2
GRMZM2G078097
3
GRMZM2G450498
3
GRMZM2G413652
2
GRMZM2G090087
2
AC217811.3_FG003
2
Using the above two files I generated a third file that somewhat looks like this and has cluster information in the form of cluster type K1,K2,etc
geneID RPKM-base RPKM-1cm RPKM+4cm RPKMtip Cluster_type
GRMZM2G181227 3.412444267 3.16437442 1.287909035 0.037320722 K1
GRMZM2G146885 14.17287135 11.3577013 2.778514642 2.226818648 K2
GRMZM2G139463 6.866752401 5.373925806 1.388843962 1.062745344 K2
GRMZM2G015295 1349.446347 447.4635291 29.43627879 29.2643755 K2
GRMZM2G111909 47.95903081 27.5256729 1.656555758 0.949824883 K2
GRMZM2G078097 4.433627458 0.928492841 0.063329249 0.034255945 K3
GRMZM2G450498 36.15941083 9.45235616 0.700105077 0.194759794 K3
GRMZM2G413652 25.06985426 15.91342458 5.372151214 3.618914949 K2
GRMZM2G090087 21.00891969 18.02318412 17.49531186 10.74302155 K2
I certainly don't think that this is the file that joran would have wanted me to create but I could not think of anything else thus I ran lattice on the above file using the following code.
clusres<- read.table("clusinput.txt",header=TRUE,sep="\t");
jpeg(filename = "clusplot.jpeg", width = 800, height = 1078,
pointsize = 12, quality = 100, bg = "white",res=100);
parallel(~clusres[2:5]|Cluster_type,clusres,horizontal.axis=FALSE);
dev.off();
and I get a picture like this
Since I want one single line as the representative of the whole cluster at four different points this output is wrong moreover I tried playing with lattice but I can not figure out how to make it accept the Rpkm values as the X coordinate It always seems to plot so many lines against a maximum or minimum value at the Y coordinate which I don't understand what it is.
It will be great if anybody can help me out. Sorry If my question still seems absurd to you.
I do not know of any pre-built functions that generate the plot you indicate, which looks to me like a sort of parallel coordinates plot.
But generating such a plot would be a fairly trivial exercise.
Add a column of cluster labels (K1,K2, etc.) to your original data set, based on your clustering algorithm's output.
Use one of the many, many tools in R for aggregating data (plyr, aggregate, etc.) to calculate the relevant summary statistics by cluster on each of the four variables. (You haven't said what the first graph is actually plotting. Mean and sd? Median and MAD?)
Since you want the plots split into six separate panels, or facets, you will probably want to plot the data using either ggplot or lattice, both of which provide excellent support for creating the same plot, split across a single grouping vector (i.e. the clusters in your case).
But that's about as specific as anyone can get, given that you've provided so little information (i.e. no minimal runnable example, as recommended here).
How about using clusplot from package cluster with partitioning around medoids? Here is a simple example (from the example section):
require(cluster)
#generate 25 objects, divided into 2 clusters.
x <- rbind(cbind(rnorm(10,0,0.5), rnorm(10,0,0.5)),
cbind(rnorm(15,5,0.5), rnorm(15,5,0.5)))
clusplot(pam(x, 2)) #`pam` does you partitioning
Is there a simple way to plot the difference between two probability density functions?
I can plot the pdfs of my data sets (both are one-dimensional vectors with roughly 11000 values) on the same plot together to get an idea of the overlap/difference but it would be more useful to me if I could see a plot of the difference.
something along the lines of the following (though this obviously doesn't work):
> plot(density(data1)-density(data2))
I'm relatively new to R and have been unable to find what I'm looking for on any of the forums.
Thanks in advance
This should work:
plot(x =density(data1, from= range(c(data1, data2))[1],
to=range(c(data1, data2))[2] )$x,
y= density(data1, from= range(c(data1, data2))[1],
to=range(c(data1, data2))[2] )$y-
density(data2, from= range(c(data1, data2))[1],
to=range(c(data1, data2))[2] )$y )
The trick is to make sure the densities have the same limits. Then you can plot their differences at the same locations.My understanding of the need for the identical limits comes from having made the error of not taking that step in answering a similar question on Rhelp several years ago. Too bad I couldn't remember the right arguments.
It looks like you need to spend a little time learning how to use R (or any other language, for that matter). Help files are your friend.
From the output of ?density :
Value [i.e. the data returned by the function]
If give.Rkern is true, the number R(K), otherwise an object with class
"density" whose underlying structure is a list containing the
following components.
x the n coordinates of the points where the density is estimated.
y the estimated density values. These will be non-negative, but can
be zero [remainder of "value" deleted for brevity]
So, do:
foo<- density(data1)
bar<- density(data2)
plot(foo$y-bar$y)
I need to get a plot of a Lorentz curve of a cumulative variable as a function of the number of observations. I want both axes to be displayed on a percentage basis (e.g. say observations are the number of buyers and the y variable is the amount they bought, buyers are already ranked in descending order, I want to get the plot that says "The top 10% buyers purchased 90% of the total bought"). My dataset is a couple million observations.
What is the best way to do this? Sub-questions:
If I need to add two variables for the quantiles of total observations and total $ bought (so as to use them to plot), what is the object that returns the row number? I tried:
user_quantile <- row(df)/nrow(df)
but I get a matrix of identical columns (user_quantile.1, user_quantile.2) of which I only need one column.
Is there instead any way to skip adding percentages as variables and only have them for axes values?
The plot has way to many points than I need to get the line. What is the best approach to minimize the computational effort and get a nice graph?
Thanks.
You may want to acquaint yourself with the excellent RSeek search engine for R content. One quick query for Lorentz curve (and Lorenz curve) lead to these packages:
ineq: Measuring inequality, concentration, and poverty
reldist: Relative Distribution Methods
GeoXp: Interactive exploratory spatial data analysis
lawstat: An R package for biostatistics, public policy and law
all of which seem to supply a Lorenz curve function.
In order to get the plot done you need first to arrange the raw data.
1) You can use the cut2() function from the Hmisc package to cut the data in quantiles. Check the documentation, it's not hard. It's similar to the cut() from the base package.
2) After using the cut2() function with the income data, you need to compute the frequency of each decile. Use table() for that. Then calculate percentages of income for each decile.
3) Now you should have a very small table with the following columns:
Decile, cumulative % of total income.
Add another column with the 45 degree line. Just add a constant cumulative % of income.
finaltable$cumulative_equality_line = seq(0.1, 1, by = 0.1)
4) You can use base graphics or ggplot2 for plotting. I guess you can do it with the info of step 3 or perhaps check out specific plotting questions.
I'll have to do it soon, but i already have the final table. I'll post the code for plotting once i do it.
Good luck!