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Closed 9 years ago.
I am a programmer, but when I am faced complex mathematical formulas I am often stuck.
Please suggest a good video lecture resource that teaches reading math symbols, quantifiers etc.
This formula means nothing without a context. It seems to be the derivation of the partial derivative of Ep with respect to yhp, which turns out to be the negative of the sum of products of δop and wpo, with o ranging from 1 to No:
def partial_of_E_wrt_y(p):
acc = 0
for o in range(1, No):
acc = acc + delta[p][o] * w[p][o]
return -acc
E, y and δ may be tensors because of the use of superscript indexes. This would also means that δopwpo could be a tensor product. Or it could be that the author simply likes using superscript indexes without any association with tensors, a convention I have seen in some texts on machine learning. If δ has not been given any other interpretation, it's possible it stands for the Kronecker delta, which would mean δop = 1 if o=p, and 0 otherwise.
Related
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Closed 10 years ago.
When I try to visualize my integer data with histogram(mydata,breaks=c(0,n)), R usually doesnt care about how many breaks (usually 1 bar for each sample) do I use and it plots n-1 bars (first two bars are summed into one).
In most cases I use barplot(table(mydata))
And there is one more way to do it
How to separate the two leftmost bins of a histogram in R
but I think its not "clear" way.
So how do you visualize frequency of your integer data?
Which one is right?
Thank you a lot
hist(dataset, breaks=seq(min(dataset)-0.5, max(dataset)+0.5, by=1) )
Another option (for thos situations where you know these are integers would be:
require(lattice)
barchart(table(dataset), horizontal=FALSE)
Or:
barplot(table(dataset))
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Closed 10 years ago.
I'm new in random numbers generators field. I would like to use the Mersenne-Twister algorithm since it has the longest period respect to other algorithms.
Which R function implements this algorithm? I used
"?sample" but no information about which algorithm is used, is there.
Another question is: which is the best seed to set in the random number generation?
Finally: is R the best tool to generate random numbers?
The default algorithm used by R is Mersenne-Twister.
There is no best seed. It depends on your application. Do you want it to be the same set of numbers every time you run your code? Use the same seed(s). If not, perhaps using the current time will suit your needs.
The best tool to generate random numbers is something that does not use a deterministic PRNG (such as Mersenne-Twister). Instead look into something such as random.org. I think it will really benefit you to read up on True randomness vs. Pseudo randomness.
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Closed 9 years ago.
When providing example code, "foo" and "bar" are commonly used to represent "arbitrary values", to the point they are almost standard notation.
Are there more "standard" terms for when you want to show more than two arbitrary values?
ie. Is there a standard list of terms whose first two are "foo" and "bar"?
Those are known as "Metasyntatic variables". I would not consider any of them standard, but Wikipedia offers the following as common in the U.S.:
foo
bar
baz
qux
quux
corge
grault
garply
waldo
fred
plugh
xyzzy
thud
Source: http://en.wikipedia.org/wiki/Metasyntactic_variable
Personally, I have only seen foo, bar, baz and xyzzy used from the list. The list was cited from RFC 3092.
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Closed 10 years ago.
I'm looking for a basic implementation of EM clustering in R. So far, what I can find seem to be specialized or 'some-assembly-required' versions of it. For example, the implementation from mclust defines a range of parameters that I'm not familiar with and doesn't take a parameter for k. What I am looking for is something closer to the kmeans implementation that comes with R, or ELKI's implementation of EM.
How about reading the documentation for mclust?
http://cran.r-project.org/web/packages/mclust/mclust.pdf
https://en.wikibooks.org/wiki/Data_Mining_Algorithms_In_R/Clustering/Expectation_Maximization_%28EM%29
Make sure to choose the desired model (probably VVV?), and if you want a fixed k, then set G to a single value instead of the default 1:9.
Try this:
library(mclust)
m <- Mclust(data, 4:4, c("VVV"), control=emControl(tol=e1-4))
I must say I don't use or like R much. It has tons of stuff, but it doesn't fit together. It's just random stuff written independently by random people and then uploaded to a central repository. But there is no QA at all, and nobody that makes libraries compatible.
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Closed 10 years ago.
What are some good libraries for handling mathematical functions. these types of things(Preferably Open Source).
In particular:
Derivative of a function.
Solving a function for a particular variable, not always for a real value, but in terms of other variables.
Ex. Solving x^2 + y^2 = y for y in terms of x.
Graphing functions.
Ability to handle piece-wise functions.
scipy or gsl
What I was looking for is symbolic mathmetatics.
Sympy is a very good python library for this with very little special syntax to learn.