I have symmetrical sparse matrices. Some of the elements would form "blocks" or "components" .
Please look at the output of spy on example matrix.
I want to efficiently find those clusters in MATLAB.
This problem is equivalent to finding connected components of a graph, however I have a feeling that relevant functionality should be available as a (combination of) fast MATLAB built-in functions that operate on sparse matrices.
Can you suggest such combination?
OK, found graphconncomp function in bioinformatics toolbox. It uses some mex routines internally.
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I have computed colour descriptors of a dataset of images and generated a 152×320 matrix (152 samples and 320 features). I would like to use PCA to reduce the dimensionality of my image descriptors space. I know that I could implement this using Matlab PCA built-in function but as I have just started learning about this concept I would like to implement the Matlab code without the built-in function so I can have a clear understanding how the function works. I tried to find how to do that online but all I could find is the either the general concept of PCA or the implementation of it with the built-in functions without explaining clearly how it works. Anyone could help me with a step by step instructions or a link that could explain a simple way on how to implement PCA for dimensionality reduction. The reason why I'm so confused is because there are so many uses for PCA and methods to implement it and the more I read about it the more confused I get.
PCA is basically taking the dominant eigen vectors of the data (Or better yet their projection of the dominant Eigen Vectors of the covariance matrix).
What you can do is use the SVD (Singular Value Decomposition).
To imitate MATLAB's pca() function here what you should do:
Center all features (Each column of your data should have zero mean).
Apply the svd() function on your data.
Use the V Matrix (Its columns) as your vectors to project your data on. Chose the number of columns to use according to the dimension of the data you'd like to have.
The projected data is now you new dimensionality reduction data.
I am trying to implement bayesian optimization using gauss process regression, and I want to try the multiple output GP firstly.
There are many softwares that implemented GP, like the fitrgp function in MATLAB and the ooDACE toolbox.
But I didn't find any available softwares that implementd the so called multiple output GP, that is, the Gauss Process Model that predict vector valued functions.
So, Are there any softwares that implemented the multiple output gauss process that I can use directly?
I am not sure my answer will help you as you seem to search matlab libraries.
However, you can do co-kriging in R with gstat. See http://www.css.cornell.edu/faculty/dgr2/teach/R/R_ck.pdf or https://github.com/cran/gstat/blob/master/demo/cokriging.R for more details about usage.
The lack of tools to do cokriging is partly due to the relative difficulty to use it. You need more assumptions than for simple kriging: in particular, modelling the dependence between in of the cokriged outputs via a cross-covariance function (https://stsda.kaust.edu.sa/Documents/2012.AGS.JASA.pdf). The covariance matrix is much bigger and you still need to make sure that it is positive definite, which can become quite hard depending on your covariance functions...
I have a linear program with order N^4 variables and order N^4 constraints. If I want to solve this in AMPL, I define the constraints one by one without having to bother about the exact coefficient matrices. No memory issues arises. When using the standard LP-solver in Matlab however, I need to define the matrices explicitly.
When I have variables with four subscripts, this will lead to a massively sparse matrix of dimension order N^4 x N^4. This matrix won't even fit in memory for non trivial problem sizes.
Is there a way to get around this problem using Matlab, apart from various column generation/cutting plane techniques? Since AMPL manages to solve it, I suppose they're either automating some kind of decomposition, or they somehow solve the LP without explicitly working with this sparse monster matrix.
Apart from sparse mentioned by m.s. you can also use AMPL API for MATLAB. It is especially useful if you already have an AMPL model and want to work with it from MATLAB.
Converting my comment into an answer:
MATLAB supports sparse matrices using the sparse command which allows you to build your constraint matrix without exceeding memory limits.
Does Matlab support efficient operations on large sparse tensors?
More specifically:
Is there an elegant way, similar to sparse, of loading and storing a sparse tensor? As far as I can understand, sparse can only load matrices.
Are operations like tensor product implemented efficiently over sparse tensors?
I realize I can always store a tensor as a combination of cell arrays of matrices, but that would require using loops, and I'm hoping to avoid that.
Since the data I'm working with is very large, I cannot consider a non-sparse representation.
Out of the box, I believe MATLAB only handles sparse matrices, as you say.
But you might like to take a look at the Tensor Toolbox and the N-way Toolbox to see if they meet your needs. Both are freely available, and I've heard good things about both (although I've used neither myself). The Tensor Toolbox in particular seems to have at least some support for sparse multidimensional arrays.
You can use the Tensor Toolbox for working with tensors. you can use the sptensor() to create the sparse tensor in this Toolbox.
If you're looking for a truly scalable solution, take a look at SPLATT: http://glaros.dtc.umn.edu/gkhome/splatt/overview
I have a matrix of size 200000 X 200000 .I need to find the eigen values for this .I was using matlab till now but as the size of the matrix is unhandleable by matlab i have shifted to perl and now even perl is unable to handle this huge matrix it is saying out of memory.I would like to know if i can find out the eigen values of this matrix using some other programming language which can handle such huge data. The elements are not zeros mostly so no option of going for sparse matrix. Please help me in solving this.
I think you may still have luck with MATLAB. Take a look into their distributed computing toolbox. You'd need some kind of parallel environment, a computing cluster.
If you don't have a computational cluster, you might look into distributed eigenvalue/vector calculation methods that could be employed on Amazon EC2 or similar.
There is also a discussion of parallel eigenvalue calculation methods here, which may direct you to better libraries and programming approaches than Perl.