I'm quite surprised not to find one in standard library. Is there some reason it is missing or I just need to use a specific toolbox?
Implementing it myself would be very problematic because of the complexity of algorithm involved.
Related
I am programming a machine learning algorithm in Scala. For that one I don't think I will need matrices, but I will need vectors. However, the vectors won't even need a dot product, but just element-wise operations. I see two options:
use a linear algebra library like Breeze
implement my vectors as Scala collections like List or Vector and work on them in a functional manner
The advantage of using a linear algebra library might mean less programming for me... will it though, considering learning? I already started learning and using it and it seems not that straight forward (documentation is so-so). (Another) disadvantage is having a extra dependency. I don't have much experience in writing my own projects (so far I programmed in the job, where libraries usage was dictated).
So, is a linear algebra library - e.g. Breeze - worth the learning and dependency compared to programming needed functionality myself, in my particular case?
I'm considering to learn Scala for my algorithm development, but first need to know if the language has implemented (or is implementing) complex inverse and pseudo-inverse functions. I looked at the documentation (here, here), and although it states these functions are for real matrices, in the code, I don't see why it wouldn't accept complex matrices.
There's also the following comment left in the code:
pinv for anything that can be transposed, multiplied with that transposed, and then solved
Is this just my wishful thinking, or will it not accept complex matrices?
Breeze implementer here:
I haven't implemented inv etc. for complex numbers yet, because I haven't figured out a good way to store complex numbers unboxed in a way that is compatible with blas and lapack and doesn't break the current API. You can set the call up yourself using netlib java following a similar recipe to the code you linked.
What algorithm is used by the matlab function linopt::minimize ? I have to write the source code for solving a Mixed Integer Linear Programming problem. Please tell me the algorithms I can work upon.
It is not specified in the documentation of Mathlab (c.f. http://www.mathworks.fr/fr/help/symbolic/mupad_ref/linopt-minimize.html). However, they do provide some references at the end of the page (you should have a look there).
My guesses are the following (based on my humble knowledge regarding state-of-the-art methods for solving LP/MILP) :
1-If the problem is not MILP, we usually use the simplex algorithm (http://en.wikipedia.org/wiki/Simplex_algorithm).
2-If the problem is MILP (i.e. there is some integer variables), one usually use a Branch and Bound algorithm in which we might use simplex for improving the search (we call it Branch and Cut)
P.S. This is not an exhaustive response since other methods can be used but the above are the most known ones.
I have been recently trying to use svm for feature classification. While i was doing so, a question came to my mind.
Which would be a better method to use, LIBSVM or svmclassify? What I mean by svmclassify is to use in-built functions in MATLAB such as svmtrain and svmclassify. In that sense, I was interested to know which method would be more accurate and which would be easier to use.
Since MATLAB has already the Bioinformatics toolbox already, why would you use LIBSVM? Aren't the functions like svmtrain and svmclassify already built in.. what additional benefits does LIBSVM bring about?
I would like to hear some of your opinions. Please Pardon me if the question is stupid..
I expect you would get very similar result using each library.
They are both very easy to use. The only big difference is that one comes with the MATLAB Bioinformatics toolbox and the other one you need to obtain from the authors web site and install by hand. If to you this is an issue I would recommend you stick to what is already installed in your computer. If not consider using LIBSVM, as it is a very well tested and well regarded library.
Also, from personal experience on playing with both, libSVM is much faster than MATLAB svm routines for obvious reasons. Last but not the least, libSVM has MATLAB plugins which can be called from MATLAB if you are more comfortable within a MATLAB environment.
I have also the same question, but I think that Libsvm is very useful and very easy in the case of multi-classes classification , but the matlab toolbox is designed for only two classes classification.
In my experience the libsvm performed giving cross validaion results as 45% where matlab code did 90%. So I looked up the explanation of matlab function for svm where they had such options related with perceptrones, I wonder if they are using pure svm or not but will write again in my case matlab was much better. (multiclass svm)
I have to solve a multiobjective problem but I don't know if I should use CPLEX or Matlab. Can you explain the advantage and disadvantage of both tools.
Thank you very much!
This is really a question about choosing the most suitable modeling approach in the presence of multiple objectives, rather than deciding between CPLEX or MATLAB.
Multi-criteria Decision making is a whole sub-field in itself. Take a look at: http://en.wikipedia.org/wiki/Multi-objective_optimization.
Once you have decided on the approach and formulated your problem (either by collapsing your multiple objectives into a weighted one, or as series of linear programs) either tool will do the job for you.
Since you are familiar with MATLAB, you can start by using it to solve a series of linear programs (a goal programming approach). This page by Mathworks has a few examples with step-by-step details: http://www.mathworks.com/discovery/multiobjective-optimization.html to get you started.
Probably this question is not a matter of your current concern. However my answer is rather universal, so let me post it here.
If solving a multiobjective problem means deriving a specific Pareto optimal solution, then you need to solve a single-objective problem obtained by scalarizing (aggregating) the objectives. The type of scalarization and values of its parameters (if any) depend on decision maker's preferences, e.g. how he/she/you want(s) to prioritize different objectives when they conflict with each other. Weighted sum, achievement scalarization (a.k.a. weighted Chebyshev), and lexicographic optimization are the most widespread types. They have different advantages and disadvantages, so there is no universal recommendation here.
CPLEX is preferred in the case, where (A) your scalarized problem belongs to the class solved by CPLEX (obviously), e.g. it is a [mixed integer] linear/quadratic problem, and (B) the problem is complex enough for computational time to be essential. CPLEX is specialized in the narrow class of problems, and should be much faster than Matlab in complex cases.
You do not have to limit the choice of multiobjective methods to the ones offered by Matlab/CPLEX or other solvers (which are usually narrow). It is easy to formulate a scalarized problem by yourself, and then run appropriate single-objective optimization (source: it is one of my main research fields, see e.g. implementation for the class of knapsack problems). The issue boils down to finding a suitable single-objective solver.
If you want to obtain some general information about the whole Pareto optimal set, I recommend to start with deriving the nadir and the ideal objective vectors.
If you want to derive a representation of the Pareto optimal set, besides the mentioned population based-heuristics such as GAs, there are exact methods developed for specific classes of problems. Examples: a library implemented in Julia, a recently published method.
All concepts mentioned here are described in the comprehensive book by Miettinen (1999).
Can cplex solve a pareto type multiobjective one? All i know is that it can solve a simple goal programming by defining the lexicographical objs, or it uses the weighted sum to change weights gradually with sensitivity information and "enumerate" the pareto front, which highly depends on the weights and looks very subjective.
You can refer here as how cplex solves the bi-objetive one, which seems not good.
For a true pareto way which includes the ranking, i only know some GA variants can do like NSGA-II.
A different approach would be to use a domain-specific modeling language for mathematical optimization like YALMIP (or JUMP.jl if you like to give Julia a try). There you can write your optimization problem with Matlab with some extra YALMIP functionalities and use CPLEX (or any other supported solver as a backend) without restricting to one solver.