Sparse principal component analysis (PCA) is a popular unsupervised method used in dimension reduction and feature selection. The main advantage of Sparse PCA over standard PCA is the added interpretibility obtained by imposing a zero-enforcing constraint on the elements of the loading vectors (i.e., weights). Sparse loading vectors allow for a better understanding of the feature selection process of PCA.
Consider a zero-mean data matrix X of size pxn, where n is the number of samples. Let's denote the first principal loading vector obtained by PCA as w. This loading vector contains p weights that together produce the first principal component w'X, which contains 1-dimensional variables corresponding to each sample. In PCA, w is non-sparse and therefore no information can be readily obtained to determine the most important features.
Several studies use Sparse PCA to enforce zero weights in w. Using sparse PCA, one can interpret the importance/relevance of a feature in the dimension reduction process. However, let's say we want to reduce the dimension p to an arbitrary integer q, such 1<q<=p. In this case, conventional sparse PCA methods do not guarantee that all q loading vectors w_i, for i=1,...,q, will select the same features; in other words, they won't have the same sparsity pattern. The table below shows an example for simulated data.
Our proposed method calculates principal loadings while preserving sparsity patterns.
Please cite the following paper
Seghouane,Shokouhi, Koch, "Sparse Principal Component Analysis with Preserved Sparsity Pattern," IEEE Transactions on Image Processing.
The main function is Sparse_PCA.m, which depends on the function sparse_rank_1.m.
The code is in Matlab and our Matlab version at the time of publishing this code was 2017b.
There is a dependency on fsvd.m from this link. If you don't want to use fsvd, simply replace
it with the built-in Matlab function svds.
Feel free to reach out for help on integrating the code into your project.
NS