Singular Value Decomposition (SVD) in PHP

Question

Hello!

I would like to implement Singular Value Decomposition (SVD) in PHP. I know that there are several external libraries which could do this for me. But I have two questions concerning PHP, though: 1) Do you think it's possible and/or reasonable to code the SVD in PHP? 2) If (1) is yes: Can you help me to code it in PHP?

I've already coded some parts of SVD by myself. Here's the code which I made comments to the course of action in. Some parts of this code aren't completely correct.

It would be great if you could help me. Thank you very much in advance!

Answer 1

Regarding question 1: It definitely is possible. Whether it's reasonable depends on your scenario: How big are your matrices? How often do you intend to run the code? Is it run in a web site or from the command line? If you do care about speed, I would suggest writing a simple extension that wraps calls to the GNU Scientific Library.

Answer 2

1) Yes. this is perfectly possible to be implemented in PHP. I don't know what the reasonable time frame for execution and how large it can compute. I would probably have to implement the algorithm to get a rought idea.

2) Yes I can help you code it. Buy why do you need help? Doesn't the code you wrote work?

Just as an aside question. What version of PHP do you use?

Answer 3

Be careful when you say "I don't care what the time limits are". SVD is an O(N^3) operation (or O(MN^2) if it's a rectangular m*n matrix) which means that you could very easily be in a situation where your problem can take a very long time. If the 100*100 case takes one minute, the 1000*1000 case would 10^3 minutes, or nearly 17 hours (and probably worse, realistically, as you're likely to be out of cache). With something like PHP, the prefactor -- the number multiplying the N^3 in order to calculate the required FLOP count, could be very, very large.

Having said that, of course it's possible to code it in PHP -- the language has the required data structures and operations.

Answer 4

Yes it's posible, but implementing SVD in php ins't the optimal approach. As you can see here PHP is slower than C and also slower than C++, so maybe it was better if you could do it in one of this languages and call them as a function to get your results. You can find an implementation of the algorithm here, so you can guide yourself trough it.

About the function calling can use:

• The exec() Function

The system function is quite useful and powerful, but one of the biggest problems with it is that all resulting text from the program goes directly to the output stream. There will be situations where you might like to format the resulting text and display it in some different way, or not display it at all.

• The system() Function

The system function in PHP takes a string argument with the command to execute as well as any arguments you wish passed to that command. This function executes the specified command, and dumps any resulting text to the output stream (either the HTTP output in a web server situation, or the console if you are running PHP as a command line tool). The return of this function is the last line of output from the program, if it emits text output.

• The passthru() Function

One fascinating function that PHP provides similar to those we have seen so far is the passthru function. This function, like the others, executes the program you tell it to. However, it then proceeds to immediately send the raw output from this program to the output stream with which PHP is currently working (i.e. either HTTP in a web server scenario, or the shell in a command line version of PHP).

Answer 5

SVD-python Is a very clear, parsimonious implementation of the SVD. It's practically psuedocode and should be fairly easy to understand and compare/draw on for your php implementation, even if you don't know much python.

SVD-python

That said, as others have mentioned I wouldn't expect to be able to do very heavy-duty LSA with php implementation what sounds like a pretty limited web-host.

Cheers

Edit: The module above doesn't do anything all by itself, but there is an example included in the opening comments. Assuming you downloaded the python module, and it was accessible (e.g. in the same folder), you could implement a trivial example as follow,

#!/usr/bin/python
import svd
import math

a = [[22.,10., 2.,  3., 7.],
     [14., 7.,10.,  0., 8.],
     [-1.,13.,-1.,-11., 3.],
     [-3.,-2.,13., -2., 4.],
     [ 9., 8., 1., -2., 4.],
     [ 9., 1.,-7.,  5.,-1.],
     [ 2.,-6., 6.,  5., 1.],
     [ 4., 5., 0., -2., 2.]]

u,w,vt = svd.svd(a)
print w

Here 'w' contains your list of singular values.
Of course this only gets you part of the way to latent semantic analysis and its relatives. You usually want to reduce the number of singular values, then employ some appropriate distance metric to measure the similarity between your documents, or words, or documents and words, etc. The cosine of the angle between your resultant vectors is pretty popular.

Latent Semantic Mapping (pdf)

is by far the clearest, most concise and informative paper I've read on the remaining steps you need to work out following the SVD.

Edit2: also note that if you're working with very large term-document matrices (I'm assuming this is what you are doing) it is almost certainly going to be far more efficient to perform the decomposition in an offline mode, and then perform only the comparisons in a live fashion in response to requests. while svd-python is great for learning, the svdlibc is more what you would want for such heavy computation.

finally as mentioned in the bellegarda paper above, remember that you don't have to recompute the svd every single time you get a new document or request. depending on what you are trying to do you could probably get away with performing the svd once every week or so, in an offline mode, a local machine, and then uploading the results (size/bandwidth concerns notwithstanding).

anyway good luck!