I want to distribute the work from PCA among a set of workers.
So let samples $x_1,... , x_d\in \mathbb{R}^n$ be samples. Then to find a dimension reduction subspace we need
- covariance matrix $cov(\overrightarrow{x_i},\overrightarrow{x_j}) = \frac{1}{n} \sum_{k=1}^{n}(x_{ik} - \mu_{\overrightarrow{x_i}})(x_{jk} - \mu_{\overrightarrow{x_j}})$ where $\mu = \frac{1}{n}\sum_{i=1}^{n}x_i$
- Eigenvektor and -values
- Feature vector matrix which are the eigenvektor as as columns
My question is where can I distribute the work. I assume it is only the during the covariance matrix. Do have some book recommendation that cover distributed PCA.