- Edited
I am trying to convert some matlab/octave code that implements a Support Vector Machine (SVM) into PHP. This code was distributed with homework assignments as part of Andrew Ng's 'Supervised Machine Learning: Regression and Classification' class on the Coursera website. Don't worry, I have already completed the class, and converting it to PHP is not part of the assignment.
NOTE: I've looked into FANN, but this requires the installation of another php extension. My goal here is ultimately to make lightweight, dependency-free PHP code that doesn't require exec or evocations of other languages.
For starters, I'll need to perform some matrix operations: multiply, transpose, subtract, exponentiation, etc. Here's an example matlab/octave routine. The supplied parameters x1 and x2 are row vectors:
function sim = gaussianKernel(x1, x2, sigma)
%RBFKERNEL returns a radial basis function kernel between x1 and x2
% sim = gaussianKernel(x1, x2) returns a gaussian kernel between x1 and x2
% and returns the value in sim
% Ensure that x1 and x2 are column vectors
x1 = x1(:); x2 = x2(:);
% You need to return the following variables correctly.
sim = 0;
% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return the similarity between x1
% and x2 computed using a Gaussian kernel with bandwidth
% sigma
%
%
sim = exp(-sum((x1 - x2) .^ 2) / (2 * sigma^2));
% =============================================================
endI've googled 'PHP matrix operations' and the PHP libs that appear in the results are disappointing for various reasons. Is there no orthodox/canonical way of performing matrix operations in PHP?
PHP-ML is pretty impressive, and actually implements a Support Vector Classifier. However, installing it brings in 150 PHP files, and the SVM is implemented by calling exec on an executable. Installing gives you linux, windows, and macos executables.
MarkBaker's PHPMatrix kinda works but its constructor seems to convert row vectors to column vectors and vice versa. This:
$matrix = new Matrix\Matrix([1,2,3,4]);
print_r($matrix);appears to construct a column vector:
Matrix\Matrix Object
(
[rows:protected] => 4
[columns:protected] => 1
[grid:protected] => Array
(
[0] => Array
(
[0] => 1
)
[1] => Array
(
[0] => 2
)
[2] => Array
(
[0] => 3
)
[3] => Array
(
[0] => 4
)
)
)This code creates the exact same column vector, with 4 rows and one column:
$matrix = new Matrix\Matrix([[1],[2],[3],[4]]);It gets even more confusing because matrix multiplication is not a symmetric operation. Consider this matlab code:
m1 = [1,1,1,1]
m2 = [1,3,5,7]
m1' * m2
ans =
1 3 5 7
1 3 5 7
1 3 5 7
1 3 5 7
m2 * m1'
ans = 16You'd think this code using the MarkBaker lib would yield that first 4x4 matrix, but it does not:
$m1 = new Matrix\Matrix([1,1,1,1]);
$m2 = new Matrix\Matrix([1,3,5,7]);
$v = $m1->transpose()->multiply($m2);
print_r($v->toArray());The result:
Array
(
[0] => Array
(
[0] => 16
)
)While one might rationalize the order of operations to say that $m1 is being applied as a multiplication operation to $m2, it's just confusing.
And then there's NumPHP. The documentation for extremely sparse and not especially helpful. No details are given about transposition, for instance. I also can't seem to find any way to perform matrix multiplication -- the documentation mentions only the dot product. Unless I'm mistaken, matrix multiplication and dot products are not the same thing.
Any suggestions for a canonical/orthodox/intuitive approach to matrix operations would be much appreciated.
.