I am trying to understand this paper called High Dimensionality Reduction Using CUR Matrix Decomposition and Auto-encoder for Web Image Classification. I have understood the method proposed for dimension reduction using CUR decomposition. Only thing i have not understood is this paragraph from point 3.2 :

In our application, as to reduce the dimension of image feature space, we just need to sample matrix $R$ from the column feature space using $ColumnSelect$ Algorithm and project the origin feature vector on the subspace spanned by the columns of $R$, that is $$A_{reduced} = A × R^T$$ where $A_{reduced}$ is the data matrix in reduced space.

Does this paragraph means, that after applying CUR decomposition on matrix $A$, we can directly reduced the dimension using matrix $R$ by projecting matrix $A$ on matrix $R$?


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