just wondering if you have any suggestions here. I need a lot of sample maps/graphs to test my shortest path search solution (I was told I should have >100 of them). My code is supposed to work in a simulator, which uses OpenStreetMap maps of urban setting, limiting the total number of junctions to a few thousand. the problem is, there are only two or three maps provided with the simulator. The way I see it, I have a few choices here:
Write my own random graph generator. Possibly lots of work (do you think? --I've never done it before) and reinventing the wheel.
Use off-the-shelf solution. I'm not aware of any that would generate me map-like graphs (well, at least I didn't find it in JUNG :-) )
In some automated way grab them from OSM. I don't really intend to myself go and pick out a 100+ urban maps that would satisfy <15000 nodes requirement. I don't think that would be easy to automate either, though.
I would assume that 3 would be tough to do. Any advice on some off-the-shelf solution? or comments about writing my own? I'm not an experienced programmer by any measure, but given a few days.
The first thought:
You have a known problem and you need to test its solution. Generate lots of test data, find correct solutions with verified algorithm, then run your algorithm against generated data set and compare results. (or just download verified dijkstra algorithm implementation, I believe that implementing this algorithm is your task)
The second thought:
Random-generated data set is not the best way to test algorithms. You need to think about cases when your algorithm can fail and create correspondent tests. For example, graph with 1 node, graph with cycles, linear graph i.e. N1---N2---N3-...-Nn, complete graph with maximum nodes number. I think if you create these 4 tests and 2-3 small random tests it'll be enough to be sure that your algorithm is implemented correctly.
Related
I'm in the process of making a swimlane diagram but can't come up with a good algorithm to automatically lay out the lines that connect the nodes in the diagram. What I essentially want is this.
However, I don't have any protection against lines overlapping or intersecting right now and it sometimes gets very messy.
Does anyone know a way to detect if a line will intersect ANY of the lines already drawn?
One idea that I've come up with is to store the paths in an array or table and check the entire table every time a new line is slated to be drawn but that does not seem efficient.
I'm doing this in javascript and java through the use of GWT so maybe there is an easy way to solve this using one of the tools provided by these languages?
If your real issue is to minimize the line intersections, there are several algorithms that try to accomplish this in diagrams. Check this link for example, there are also more algorithms that are used in auto routing for electric design automation that are also used in this kind of diagrams, like Lee algorithm, or A* Algorithm.
I don't know if the tools that you are using have enough flexibility to implement this kind of algorithms, usually you need to implement your own heuristic according to the specific type of diagram, but I hope that this links are enough to give you good ideas.
Minimizing the line intersections in a graph is a difficult NP-Hard problem, check this link (about the crossing number) for more information.
Good luck.
Let's say I want to build a function that would properly schedule three bus drivers to drive in a week with the following constraints:
Each driver must not drive more than five times per week
There must be two drivers driving everyday
They will rest one day each week (will not clash with other drivers' rest day)
What kind of algorithm would be used to solve a problem like this?
I looked through several sites and I found these:
1) Backtracking algorithm (brute force)
2) Genetic algorithm
3) Constraint programming
Frankly, these are all "culture shock" for me as I have never learnt any kind of linear programming in the past. There are two things I want to know:
1) Which algorithm will best suit the case scenario above?
2) What would be the simplest algorithm to solve this problem?
3) Please suggest any other algorithms I can look into to solve the above problem.
1) I agree brute force is bad.
2) Your Problem is an Integer Problem. They can be solved with Linear Programming though.
3) You can distinquish 2 different approaches: heuristics and exact approaches.
Heuristics provide good solutions in reasonable computation time. They are used when there are strict requirements on the computation time or if the problem is too hard to calculate an optimal solution. Genetic Algorithms is a heuristic.
As your Problem is comparably simple, you would probably go with an exact approach.
4) The standard way to solve this exacly, is to embed a Linear Program in a Branch & Bound search tree. There is lots of literature on it. The procedure can be outlined as follows:
Solve the Linear Program with the Simplex-Algorithm
Find a fractional variable for branching. I.e. x=1.5
Create two new nodes and add the constraints x<=1 and x>=2 respectively
Go into one node (selected by some strategy)
Go to point 1
Additionally, at every node in the tree, after point 1, the algorithms checks, if a node can be pruned. That means to stop searching 'deeper' from this node on, because
a) the problem has become infeasible,
b) a better solution already exists,
c) an integer solution is found. This objective value of this solution is used to determine point b.
The procedure finishes when all nodes are pruned.
Luckily, as Nicolas stated, there are free implementations that do just this. All you have to do is to create your model. Code its objective and constraints in some tool and let it solve.
First of all this is a discrete optimization problem, so linear programming is probably not a good idea (since it is meant for continuous optimization). You can still solve this using linear programming (it will become an integer or mixed-integer program) but that is exponentially heard (if your input size is small then it is ok).
Now back to the comparison:
Brute force : worst.
Genetic: Can not guarantee optimality. The algorithm may not be able to solve the problem.
Constraint programming: definitely the best in this case (and in many discrete optimization problems). There is a super efficient implementation of it in IBM ILOG CPLEX solver (but is is not free, it is free for academia or for testing though).
I want to implement a OCR system. I need my program to not make any mistakes on the letters it does choose to recognize. It doesn't matter if it cannot recognize a lot of them (i.e high precision even with a low recall is Okay).
Can someone help me choose a suitable ML algorithm for this. I've been looking around and find some confusing things. For example, I found contradicting statements about SVM. In the scikits learn docs, it was mentioned that we cannot get probability estimates for SVM. Whereas, I found another post that says it is possible to do this in WEKA.
Anyway, I am looking for a machine learning algorithm that best suites this purpose. It would be great if you could suggest a library for the algorithm as well. I prefer Python based solutions, but I am OK to work with Java as well.
It is possible to get probability estimates from SVMs in scikit-learn by simply setting probability=True when constructing the SVC object. The docs only warn that the probability estimates might not be very good.
The quintessential probabilistic classifier is logistic regression, so you might give that a try. Note that LR is a linear model though, unlike SVMs which can learn complicated non-linear decision boundaries by using kernels.
I've seen people using neural networks with good results, but that was already a few years ago. I asked an expert colleague and he said that nowadays people use things like nearest-neighbor classifiers.
I don't know scikit or WEKA, but any half-decent classification package should have at least k-nearest neighbors implemented. Or you can implement it yourself, it's ridiculously easy. Give that one a try: it will probably have lower precision than you want, however you can make a slight modification where instead of taking a simple majority vote (i.e. the most frequent class among the neighbors wins) you require larger consensus among the neighbors to assign a class (for example, at least 50% of neighbors must be of the same class). The larger the consensus you require, the larger your precision will be, at the expense of recall.
For the last week I've been researching and experimenting with facial recognition. The intended application is for a person to be able to look up a person's information in a database (SQL) by simply taking a picture of their face. The initial expectation was to be able to compress a face down to a key or hash and use this as the database lokup. This need not be extremely accurate as the person looking up the information can and most likely will end up doing a final comparison between the original image on file and the person standing in front of them.
OpenCV/JavaCV seems to be the obvious starting point, and the facial detection that it provides works well, however the implementation of Eigenfaces for facial recognition isn't ideal because online training by recompiling hundreds of thousands of user faces every time a new face needs to be added to the training set wouldn't work.
I am experimenting with using SURF descriptors on a face extracted using OpenCV's Haar Cascade features, and this appears to get me closer to the intended result, however I am unable to think of a way to efficiently lookup and compare roughly 30 descriptors (which are either 64 or 128 dimensional vectors) in a database. I've done some reading about LSH and Spectral Hashing algorithms, however there are no implementations to be found for Java and my math isn't strong enough to implement them myself.
Does anyone have any thoughts or ideas on how this might be accomplished, or if it is even possible?
Hashing isn't complicated, nor do you need a degree in maths.
Assuming that any 2 images will result in a fairly similar number of 'descriptors' then it only requires that you get a reasonable match with enough of them to get to a high enough confidence factor.
How specific these descriptors are determines what level of collision you can accept in your hashing algorithm.
As you have several of them, I would suggest that you don't need anything too sophisticated - after all, you probably want a level of 'fuzziness' in your search?
Start with something simple - experiment and refine. You might even find that you'll need different hashing for different descriptors - i.e. some might be more specific than others?
Hopefully some food for thought.
I'm writing a biological evolution simulator. Currently, all of my code is written in Python. For the most part, this is great and everything works sufficiently well. However, there are two steps in the process which take a long time and which I'd like to rewrite in Scala.
The first problem area is sequence evolution. Imagine you're given a phylogenetic tree which relates a large set of proteins. The length of each branch represents the evolutionary distance between the parent and child. The root of the tree is seeded with a single sequence, and then an evolutionary model (e.g. http://en.wikipedia.org/wiki/Models_of_DNA_evolution) is used to evolve the sequence along the tree structure; taking into account the branch lengths. PyCogent takes a long time to perform this step, and I believe that a reasonable Java/Scala implementation would be significantly faster. Do you know of any libraries that implement this type of functionality. I want to write the application in Scala, so, due to interoperability, any Java library will suffice.
The second problem area is the comparison of the generated sequences. The problem is, given a set of sequences for the proteins in a number of different extant species, attempt to use the sequence to reconstruct the phylogenetic tree which relates the species. This problem is inherently computationally demanding, because one must basically do a pairwise comparison between all sequences in the extant species. Here again, however, I feel like a Java/Scala implementation would perform significantly faster than a Python one, if for nothing else than the unfortunately slow speed of looping in Python. This part I could write from scratch more easily than the sequence evolution part, but I'd be willing to use a library for it as well if a good one exists.
Thanks,
Rob
For the second problem, why not make use an existing program for comparing sequences and infering phylogenetic trees, like RAxML or MrBayes and call that? Maximum likelihood and Bayesian inference are very sophisticated models for these problems, and using them seems a far better idea than implementing it yourself - something like a maximum parsiomony or a neihbour-joining tree, which probably could be written from scratch for such a project, is not sufficient for evolutionary analysis. Unless you just want a very quick and dirty topology (and trees inferred via MP or NJ are really often quite false), where you can probably use something like this