RAFisher2cda

Canonical Discriminant Analysis is a dimension-reduction technique related to PCA and CCA.

Description

Canonical discriminant analysis is a dimension-reduction technique related to principal component analysis and canonical correlation called canonical discriminant analysis. It derives the canonical coefficients parallels that of one-way MANOVA and it finds linear combinations of the quantitative variables that provide maximal separation between the classes or groups in much the same way that principal components summarize total variation.

The output produced are the canonical coefficients and the scored canonical variables. The canonical coefficients are rotated. The ellipse confidence bounds. Also, it proceeds with a Bartlett's approximate chi-squared statistic for testing the canonical correlation coefficients.

In summary, the canonical discriminant analysis:
- Transform the variables so that the pooled within-group covariance matrix is
an identity matrix.
- Compute group means on the transformed variables.
- Performs a principal component analysis on the means, weighting each mean by the number of observations in the group. The eigenvalues are equal to the ratio of between-group variation to the within-group variation in the direction of each principal component. Here, the principal component analysis is runned by the singular value decomposition.
- Back-transform the principal components into the space of the original variables, obtaining the canonical variables.

File gives you the option to get an unbiased or maximum-likelihood parameter estimation.

• MATLAB release: MATLAB 5.3 (R11)

[Renze luo]

perfect!

[Thilo Pfau]

The function did not work for my dataset. The problem seemed to be that data (feature vectors) were not sorted by group. Easily fixable.
Ellipse plots seem to be all over the place.

[anil rohilla]

 

[Bryan Prazen]

Great contribution. Note that the data must be sorted according to class and the first column of the data containes the class infromation.

[Simon Eickhoff]

Crashed...

??? Error using ==> inv
Matrix must be square.

Error in ==> RAFisher2cda at 290
S = S*inv(triu(qr(s*v')));

[Francisco Rodrigues]

Very good... Who needs canonical analysis, I recomend.

[Ji Cling]

Shame on you.
Self downloading 1000ths of times to get to the top of the rank.

[Michael Hamman]

My Dear Ji Cling,
 
Regularly I visit this FEX site in which excellent contributions for the fast solution of diverse types of problems in several disciplines have been given. The accusation that you are causing is very delicate. I do not know you. Neither the authors. We known them only by the references given in their author page. Only what I believe is in the quality of ethics of each one of them and ours. We are serious people dedicated to our work in the most diverse specialties. To be certain what you say. Then not alone this author does cheating but also all the others. Even you, that in principle, I think you are not signing with your true name. Finally, or really the community are honestly dawnloaded the m-files or finally someone are doing a very bad play. This because there exists a lack of control on this.

Best Wishes.

Mike

[Asim Ban]

awesome

[Gerardo Aragon]

Good for my reserach

[dafna hirschfeld]

Eval
I also don't see a good reason to use 'eval' when there is no need to.

[Mike Alonzo]

Just used this and it seems to work well. I have two questions:
1. Like Simon noted this crashed if I tried to run more than 20 columns of data (my actual matrix is 761 by 36). "Matrix must be square..."
2. Interpretation: I'd like to feed the results into LDA classifier. I've done this before with the PCA scores matrix since that has the same dimensions as my original data. Can't figure out how to do that with the CDA output though. Any thoughts?

Thanks,
Mike