I would like to find a correlation in the dataset represented by three dimensional vector field (35x observed displacement vector field). I thought about the PCA analysis, but I am not sure how I can properly construct the covariance / correlation matrix on the given dataset. Please, is PCA a good way to start? I appreciate any suggestion. Thank you, .
Petr Henyš
That depends on what you mean by finding correlations. Assume you have N dimensions and M samples. if you are interested in the pairwise correlations, what you need is an MxM kernel-gram matrix where each entry is the correlation of a pair. If you want to observe the correlations between the space dimensions, not the specific pairs, then the dual NxN "covariance "matrix will estimate you the dimension relations (1/M times A x transpose(A), where each column of the matrix A contains an N dimensional sample minus the mean vector of all samples).
Firstly, thank you for your reponses.
To Ozkan: Thus, if I would like to measure the correlation (or rather similarity) of different vector shapes, the "dual covariance matrix" may I use?
Petr,
1) If you believe your data have certain classes of behaviors, and each behavior is followed by some subset of vectors, maybe a clustering algorithm (e.g. k-means) would work better, first to categorizing them and then measuring & studying the similarity vector shapes within each cluster might work.
2) If you are not sure that there are obviously distinct trends in the data, and just want to see how those vectors follow a more general shape, then PCA based on "correlation" (not covariance) matrix can be employed to observe a general trend. However, if you need to understand how different coordinates are correlated the PCA matrix should be a "covariance" matrix (i.e. mean removed correlation).
I think Canonical Correlation Analysis, which is inherently related to PCA and LDA, will your help you to find a pair of linear projections that maximizes the correlation between two sets of variates. You can use CCA between features and the target variable. In case of regression, you can directly provide the response vector. In case of classification, you can provide the labels as 1-of-C coded label matrix (similar to that given to a Neural Network). This scheme reduces CCA to LDA!
In MATLAB the built-in function is canoncorr(). You may also find Magnus Borga's code online.
Dear friend,
Greetings.
I would like to add a little spice to the above answers.
You can start with correlation analysis. Even you can think of different types of correlation analysis.
You can also think of Independent component analysis (ICA).
You can also perform some association rules or clustering method to see the relation between different features.
All the best
Best regards
Dr.Indrajit Mandal,Ph.D.
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