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In the past few days i was thinking of a solution for an AI problem. The problem sounds like this:
I want to determine an arrangement for a few given geometric forms(that do not exceed the given board size) on a square board of given size, in such a way that the board will be uniform covered and the forms will
not overlap.
I want to apply Depth first search / Greedy best first search, but it feels difficult to find a proper representation of the forms and the actual board in order to traverse it. I'm new to python so that makes it a bit more difficult. Any suggestions?
Visual example:
What you are describing is a variation on rectangle/square fitting. Versions of the problem exist where unused cells have to be minimised for an optimal placement of the figures, whereas other versions, like the one you are describing, require for the whole board to be covered uniformly. These are called 'perfect square/rectangle placement' problems.
Typical ways to solve these problems involve the usage of finite integer domains representing the variables of the rectangles and a set of constraints making sure the geometrical placements are valid ones (i.e. don't cross the board borders, don't overlap with each other mutually, ..).
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I recently bought a toy train for my kid. And when assembling it I wondered if I could create an app where you put in what peaces and how much of them you have and the result is track diagram, with at leased one closed circuit. So, my input will be how much peaces I have from each type, this is the types:
And the output will be something like this:
What algorithm can I use for implementing this, and if you have any suggestion or pointers please tell me.
You could use a brute force approach where you start with piece one and then try all the remaining pieces for piece two and then all the remaining ones for piece three and so on. You'd build up lots of layouts in parallel, for example
Piece1-Piece2-Piece3-...
Piece1-Piece3-Piece4-...
Piece1-Piece4-Piece5-...
...
(Where - indicates a join).
When you get to a point that the layout becomes invalid you could stop and cross it off your list.
An advantage of this approach is that it will find a solution if there is one. A disadvantage is that it could take a long time.
If you're after a single layout the question is how to determine which is "best". One way to do this might be to assign different weightings to different pieces and then you could assess your layout using these scores.
You could optimize this by categorizing your pieces, for example into straight ones and curved ones, and then making some deductions based on how many of each you have. For example, if you have 4 curved pieces and 16 straight pieces you could conclude that you've got 4 corners and the others must be the sides. So from this starting point you would come up with several layouts in parallel and when you get to a point that the layout becomes invalid you could stop and cross it off your list.
Another optimization might be to create a list of sample layouts and build on those. For example, if you had a sample loop layout as a starting point you could try replacing one of your straight pieces with a set of points and then building from there.
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Is it possible to provide a high-level, but specific explanation of how SVM algorithms work?
By high-level I mean it does not need to dig into the specifics of all the different types of SVM, parameters, none of that. By specific I mean an answer that explains the algebra, versus solely a geometric interpretation.
I understand it will find a decision boundary that separates the data points from your training set into two pre-labeled categories. I also understand it will seek to do so by finding the widest possible gap between the categories and drawing the separation boundary through it. What I would like to know is how it makes that determination. I am not looking for code, rather an explanation of the calculations performed and the logic.
I know it has something to do with orthogonality, but the specific steps are very "fuzzy" everywhere I could find an explanation.
Here's a video that covers one seminal algorithm quite nicely. The big revelations for me are (1) optimize the square of the critical metric, giving us a value that's always positive, so that minimizing the square (still easily differentiable) gives us the optimum; (2) Using a simple, but not-quite-obvious "kernel trick" to make the vector classifications compute easily.
Watch carefully at how unwanted terms disappear, leaving N+1 vectors to define the gap space in N dimensions.
I'll give you a very small details that will help you to continue understanding how SVM works.
make everything simple, 2 dimensions and linearly seperable data. The general idea in SVM is to find a hyperplan that maximize the margine between two classes. each of your data is a vector from the center. One you suggest a hyperplan, you project you data vector into the vector defining the hyperplan and then you see if the length of you projected vector is before or after the hyperplan and this is how you define your two classes.
This is very simple way of seeing it, and then you can go into more details by following some papers or videos.
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What is the optimal and usual value of selective pressure in tournament selection? What percent of the best members of the current generation should propagate to the next generation?
Unfortunately, there isn't a great answer to this question. The optimal parameters will vary from problem to problem, and people use a wide range of them. Selecting the right tournament selection parameters is currently more of an art than a science. Stronger selective pressure (a larger tournament) will generally result in the population converging on a solution faster, at the cost of that solution potentially not being as good. This is called the exploration vs. exploitation tradeoff, and it underlies most algorithms for searching a large space of possible solutions - you're not going to get away from it.
I know that's not very helpful, though - you want a starting place, and that's completely reasonable. So here's the best one I know of (and I know a number of others who use it as a go-to default tournament configuration as well): a tournament size of two. Basically, this means you just keep picking random pairs of solutions, choosing the best one, and sending it to the next generation (with mutation and crossover as desired), until the next generation is the desired size. This has the nice property that any member of the population besides the absolute worst has a chance of getting to the next generation, but better ones have a better chance.
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As many, I am interested in machine learning. I have taken a class on this topic, and have been reading some papers. I am interested in finding out what makes a problem difficult to solve with machine learning. Ideally, I want to learn about how the complexity of a problem regarding machine learning can be quantified or expressed.
Obviously, if a pattern is very noisy,one can look at the update techniques of different algorithms and observe that some particular machine learning algorithm incorrectly updates itself into the wrong direction due to a noisy label, but this is very qualitative arguing instead of some analytical / quantifiable reasoning.
So, how can the complexity of a problem or pattern be quantified to reflect the difficulty a machine learning algorithm faces? Maybe something from information theory or so, I really do not have an idea.
In thery of machine learning, the VC dimension of the domain is usually used to classify "How hard it is to learn it"
A domain said to have VC dimension of k if there is a set of k samples, such that regardless their label, the suggested model can "shatter them" (split them perfectly using some configuration of the model).
The wikipedia page offers the 2D example as a domain, with a linear seperator as a model:
The above tries to demonstrate that there is a setup of points in 2D, such that one can fit a linear seperator to split them, whatever the labels are. However, for every 4 points in 2D, there is some assignment of labels such that a linear seperator cannot split them:
Thus, the VC Dimension of 2D space with linear seperator is 3.
Also, if VC dimension of a domain and a model is infinty, it is said that the problem is not learnable
If you have strong enough mathematical background, and interested in the theory of machine learning, you can try following the lecture of Amnon Shashua about PAC
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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.