Multi-feature matrix regression?

2 views (last 30 days)
ML
ML on 4 Oct 2015
Edited: Ahmet Cecen on 17 May 2016
Hi, can anyone help to get the following regression done?
X is the input multi-dimension matrix (e.g. 90 rows * 20 columns). Y is the target one dimension vector (e.g. 90 rows * 1 column).
How the polynomial regression e.g. polytool can be applied for inputs with more than one feature (I need to test the model by different poly degrees)? What about the K-fold cross validation? how it can be formulated?
Thanks.

Accepted Answer

Ahmet Cecen
Ahmet Cecen on 17 May 2016
Edited: Ahmet Cecen on 17 May 2016
Use the function I created expressly for this purpose. And you are in luck, a lightning fast Leave One Out Cross Validation is already embedded in to the core functionality: http://www.mathworks.com/matlabcentral/fileexchange/34918-multivariate-polynomial-regression
All you have to do is MultiPolyRegress(X(:,selectcolumnvectors),Y,POWEROFPOLYNOMIAL,'figure').
Keep in mind the number of polynomial terms follow a pascal triangle, so don't create billion term polynomials. The code wasn't written with memory in mind. Below is a start (blue is number of feature vectors/columns, red is power of polynomial).

More Answers (2)

Walter Roberson
Walter Roberson on 4 Oct 2015
It does not sound to me as if you are trying for a polynomial: it sounds to me as if you need a multinomial.
Construct a matrix of all of the various combinations you want, such as
A = [x(:,1), x(:,1).^2, x(:,1).^3, x(:,2), x(:,2).^2, x(:,1).*x(:,2), x(:,3), x(:,4), x(:,5).*x(:,6).*x(:,7) ..]
meaning (for example) c1*x1 + c2*x1^2 + c3*x1^3 + c4*x2 + c5*x2^2 + c5*x1*x2 + c6*x3 + c7*x4 + c8*x5*x6*x7 + ...
Then,
A\Y
will give the coefficients c1, c2, c3, ...
To use different degrees or a different mix of the various features, construct a different A matrix.

Walter Roberson
Walter Roberson on 17 May 2016
You have indicated that you accepted the answer by mistake. Please explain further why the above did not work for you.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by