More docs

Author: rezazadeh

docs/mllib-dimensionality-reduction.md

@@ -43,16 +43,16 @@ If we keep the top $k$ singular values, then the dimensions of the resulting low
 We assume $n$ is smaller than $m$. The singular values and the right singular vectors are derived
 from the eigenvalues and the eigenvectors of the Gramian matrix $A^T A$. The matrix
 storing the right singular vectors $U$, is computed via matrix multiplication as
-$U = A (V S^{-1})$, if requested by user via the computeU parameter. 
+$U = A (V S^{-1})$, if requested by the user via the computeU parameter. 
 The actual method to use is determined automatically based on the computational cost:
 
-* If n is small ($n < 100$) or $k$ is large compared with $n$ ($k > n / 2$), we compute the Gramian matrix
+* If $n$ is small ($n < 100$) or $k$ is large compared with $n$ ($k > n / 2$), we compute the Gramian matrix
 first and then compute its top eigenvalues and eigenvectors locally on the driver.
 This requires a single pass with $O(n^2)$ storage on each executor and on the driver, and
 $O(n^2 k)$ time on the driver.
 * Otherwise, we compute $(A^T A) v$ in a distributive way and send it to
 <a href="http://www.caam.rice.edu/software/ARPACK/">ARPACK</a> to
-compute $(A^T^ A)$'s top eigenvalues and eigenvectors on the driver node. This requires $O(k)$
+compute $(A^T A)$'s top eigenvalues and eigenvectors on the driver node. This requires $O(k)$
 passes, $O(n)$ storage on each executor, and $O(n k)$ storage on the driver.
 
 ## SVD Example