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Closed 10 years ago.
We have been asked to do 5 or 6 iterations of particle swarm optimisation by hand for homework, but i don't really understand how and we were given no examples.
Would it be possible for someone to do the first run through for me so I can see how it works?
Explanations as each step would be fantastic.
Consider an illustrative example of a particle swarm optimisation system composed of three particles and Vmax = 10. To facilitate calculation, we will ignore the fact that r1 and r2 are random numbers and fix them to 0.5 for this exercise. The space of solutions is the two dimensional real valued space R2 and the current state of the swarm is as follows:
Position of particles: x1 = (5,5); x2 = (8,3); x3 = (6,7);
Individual best positions: x∗1 = (5,5); x∗2 = (7,3); x∗3 = (5,6);
Social best position: x∗ = (5,5);
Velocities: v1 = (2,2); v2 = (3,3); v3 = (4,4).
"I don't really understand how and we were given no examples". Let me add a little bit of critique to this sentence. If you're not given any examples it probably means you should be looking for examples for yourself. Have you even put "particle swarm optimization" into Google and look at some of the results? Do you expect everything in your study to be given to you?
There are many resources that explain the working of particle swarm optimization such as wikipedia, Google Scholar, Scholarpedia, or a dedicated website to PSO. The original paper is from Kennedy and Eberhart 1995 and is the top result in the scholar search. Also there are frameworks where PSO is implemented and where you can look at how it works like HeuristicLab. It's an opportunity to explore this topic.
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Closed 9 years ago.
I have a set of points (x0...xn, y0...yn, z0....zn) and an ellipsoid given by the equation: x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. Is there an algorithm that could I use to project my points onto my ellipsoid? If so, what are the steps to accomplish this?
You also need a source point, the point that you are projecting from. Each point and the source point form a line, and you can find the intersection of that line and your ellipsoid. There will typically be either two or zero projection points, depending on whether the line intersects the ellipsoid or not. You might try solving the 2d case first to see if you understand it.
David Eberly's book on geometrical methods is usually a good source for such algorithms. You can get some insight from chapter 3 in this pdf. It is about point to ellipsoid distance evaluation but a lot of theory is the same.
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Closed 10 years ago.
Say, you have a Newton Method algorithms with 2 parameters of interest(a,b).
And I would like to plot their domain of convergence with x-axis = a, y-axis = b. Is there a really fast and simple to do this??? Any suggestions?
My algorithm will basically converge for some values of a & b. If I input (a,b), it will return (the number of iterations , value of a that it converge to, value of b that it converge to). Right now, I am thinking of setting up a for loop within another for loop, which run through all possible values of b first holding a fixed, and all possible values that a will converge holding b fixed.
However, my trouble is: how to identify whether a & b is converging or not. And is there a better way than using nested for loops????
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Closed 10 years ago.
I'm doing a homework on data mining. Now I have a data set which stands for acquaintance network in social network. I want to visualize this network. In this network, vertex stands for user and edge stands for acquaintance relationship. Now I use igraph package for R to achieve my goal. However, my data set is too large with more than 100,000 vertexes and more than 1000,000 edges, which causes the generated graph not clear. In fact, the graph is totally unrecognized. How can I get a clear graph using igraph package? Or, which software can complete this task?
ps: my data set likes that:
100 20
10 2
2 4
each line stands for a relationship between two people
Thank you in advance!
In addition to Cytoscape, you might want to check out Gephi.
Another (quite different) approach to visualizing networks is by using hive plots -- worth checking out, too!
If you want an answer on this forum, you will need to provide at least a small amount of the data that you want to analyse and many people will help you get off to a good start.
You may also want to consider using an application, such as Cytoscape, that is designed for the analysis of networks. It may be easier to start your visualisation and exploration of this large network.
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Closed 11 years ago.
i assume that we have 2 labeled graphs G and T and the algorithm determine if G a subgraph of T and the corresponding vertices in the main graphT and the subgraph G should have same label
That problem is called "subgraph isomorphism" and it is NP-complete (and so likely to be hard). Do you need a general solution for this, or just for a particular graph G? The second case is much easier. There is some general information about algorithms here. There is a version of one of the algorithms (actually, for a more general problem) in the Boost Graph Library (see documentation here).
A general answer for a general question: the problem you want to solve is known as 'subgraph isomorphism.' Have a look here for further references: http://en.wikipedia.org/wiki/Subgraph_isomorphism_problem .
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Closed 12 years ago.
I need an recursive algorithm to calculate determinant of n*n matrix.
The Standard Method for computing the determinant is LU decomposition. Use a library like LAPACK in production code. There is absolutely no point in using recursion, LU decomposition is usually implemented by solving M = LU in closed form, and takes O(n^3) operations.
Wikipedia has a formula for calculating determinants. It involves permutations, which can easily be generated recursively. Google has plenty of results on "permutation algorithm".
I don't see the point in recursiveness here.
This matrix operation can easily be implemented in a SIMD operation, can be divided into threads, can be very well calculated on the GPU.
Recursiveness consumes a lot of memory, and some systems have limits in recursion depths.
|a b c d ...|
det |...........|
|...........|
|...........|
= a * det(M1) - b * det(M2) + c * det(M3) - d * det(M4) + ... - ...
where Mn is the remaining Matrix if you drop the first row and the n-th column