DOC Fix three typos in manifold documentation
@@ -533,7 +533,7 @@ the quality of the resulting embedding:
* maximum number of iterations
* angle (not used in the exact method)
-The perplexity is defined as :math:`k=2^(S)` where :math:`S` is the Shannon
+The perplexity is defined as :math:`k=2^{(S)}` where :math:`S` is the Shannon
entropy of the conditional probability distribution. The perplexity of a
:math:`k`-sided die is :math:`k`, so that :math:`k` is effectively the number of
nearest neighbors t-SNE considers when generating the conditional probabilities.
@@ -598,8 +598,8 @@ where label regions largely overlap. This is a strong clue that this data can
be well separated by non linear methods that focus on the local structure (e.g.
an SVM with a Gaussian RBF kernel). However, failing to visualize well
separated homogeneously labeled groups with t-SNE in 2D does not necessarily
-implie that the data cannot be correctly classified by a supervised model. It
-might be the case that 2 dimensions are not enough low to accurately represents
+imply that the data cannot be correctly classified by a supervised model. It
+might be the case that 2 dimensions are not low enough to accurately represents
the internal structure of the data.
