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I searched to learn Backpropagation algorithm with adaptive learning rate, and find a lot of resources but it was hard for me to understand, because I'm new in neural network. I know how standard backpropagation algorithm works, very well. Is anybody here to explain me how these two algorithms are different from each other?
I think the core difference is the update function, as you could see from here
For classic EBP
w(k+1) <- w(k) - a * gradient
For adaptive learning:
w(k+1) <- w(k) - eta * gradient
where:
eta =
(w(k) - w(k-1)) / (gradient(k) - gradient(k-1)) if eta < etamax
etamax otherwise
So you only need to change the weight update function part. The above is just a simplified version, for implementation, you would have to adjust eta according to the error(k) and error(k-1). And there are many ways to do that.
The basic idea of adaptive is that
if you get a smaller error, you want to try increasing learning rate
if you get a larger error, you want to decrease learning rate to that it converges
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I have problems with certain algorithmic terms.
What is a robust algorithm ?
What is a resistant algorithm ?
What is a resilient algorithms ?
Thank you in advance.
These attributes have no exact definition. So it depends on your topic/problem what they mean.
They are all used to describe algorithms that can cope with some kind of errors (e.g. outlier or noise) in the input-data and still deliver a useful / the expected result.
So in general you define the kind of errors the algorithm is expected to handle in a defined way.
E.g 'This algorithm returns for an input with less than 5% outlier a result with an accuracy of 99%.'
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I am trying to compare the performance of couple of sorting algorithms. Are there any existing benchmarks that can make my task easy? If not I want create my own benchmark. How would I achieve this?
Couple of things I need to consider:
Test on different possible input permutation
Test on different scale of input size
Keep hardware configuration consistent across all the algorithms
Major challenge is in implementing sorting algorithm. Because if I implement one and if that happens to be the non-efficient way of implementation it will generate inaccurate result. How would I tackle this?
Tomorrow if someone comes up with his/her own sorting algorithms how would he/she compare with other sorting algorithm?
Though I am flexible with any programming language but would really appreciate if someone can suggest me some functions available in python.
Well, i think you are having trouble what a doubling ratio test is. I know only basics of python so i got this code from here
#!/usr/bin/python
import time
# measure wall time
t0 = time.time()
procedure() // call from here the main function of your sorting class and as
the (sorting)process ends then it will automatically print
the time taken by a sorting algorithm
print time.time() - t0, "seconds wall time"
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Does anybody know the examples of indefinite or definite integral that can be done in the terms of elementary functions manually by a good first-year or second-year student, but which Wolfram Alpha (or Mathematica) evaluate not correctly?
In other words, I want to find some tasks for mathematical test, where students cannot easily find the answer using wolfram and just rewrite it in their papers.
Thanks in advance.
It is probably impossible. Set of functions known by 1-2 years students is constrained. Mathematica uses symbolic algebra system to transform integrals, and big repository with properties of functions.
http://functions.wolfram.com/
For example for Hypergeometric Functions you have (218,254 formulas)!
Methods of calculations of integrals are explained on wolframalpha.com as step by step solutions for pro users. ($4.75/mo billed annually or $6 billed monthly)
Calculating integrals by computers is nowadays on level comparable to chess games. You have to talk with student individually.
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What is the usage of mandelbrot set and julia set in programming? Is there any sample competitive problems that use these set?
To the best of my knowledge, the Mandelbrot set (and Julia set alike) is computed to produce beautiful fractal pictures and animations, and there aren't any other good reasons to compute it.
Designing algorithms to compute Mandelbrot efficiently requires skills in complex analysis, bigint arithmetic, and low-level assembly code optimization.
Using Mandelbrot for competitive problems would be problematic due to floating-point round-off errors, which can make it hard to compare results and tell which one is correct. Though depending on what you mean by competitive, you could consider that making Mandelbrot deep zoom videos to be competitive (with bigger and bigger magnification factors) - you can see YouTube for examples.
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Does any have an algorithm for creating infinite terrain/landscape/surface?
Constraints
The algorithm should start by a random seed
The algorithm should be one to one, (the same seed gives the same result)
Other input parameter are allowed as long as 2 is fulfilled
The algorithm may output a 2d map
It suppose to create only surface with varying height (mountains), not three, ocean etc.
I’m looking for an algorithm and not a software.
It should be fast
None of other related questions in here answers this question.
If anything is unclear please let me know!
I would suggest something like Perlin noise, I've used it before for something like you're describing above, and it fits the bill. Check out this Example and you can see the sort of output you would expect from the noise generator.Here is a link to algorithm p-code too.
http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
As others already said perlin noise is a possibility. Gpugems 3 has a nice capter about procedual generation using (IIRC, it has been some time since I read this) 3D Perlin noise.
Of course there are other methods too, e.g. Vterrain.org might be worth a look.