t-SNE on principal component scores: standardization needed? I have a huge dataset (1.5 million obs and 70 features). I want to visualize the data in 2D, to look for naturally occurring clusters. Analogous to Van der Maaten's approach 1, I first reduce the dimensions to 10 using PCA. Then I apply t-SNE to the dataset where now each obs is represented as a vector of 10 PCA scores.
My question is, while applying t-SNE, do I need to standardize each of the 10 score columns? In MATLAB, the suggestion is :"When features in X are on different scales, set 'Standardize' to true. Do this because the learning process is based on nearest neighbors, so features with large scales can override the contribution of features with small scales." 
I am not sure if PC scores are on different scales or not. I know that the PC scores, on average fall in value with the PC.
 A: The PC scores are in inherently on different scales; we can actually find the scale of each one by checking its corresponding eigenvalue. That said, no, do not normalise the PC scores. The suggestion you read relates to original input data prior to PCA. Given that your current input data are already valid PCA scores (i.e. created using a normalised sample as input) there is no reason to renormalise them again. If anything that will distort their importance. 
Usual t-SNE implementations perform a PCA step internally to bring the dimensionality of the input data to a reasonable number. In R, the Rtsne::Rtsne() function by default uses $50$ dimensions as a "reasonable number of dimensions", in the 2008 and 2014 JMLR papers by van der Maaten this number is $30$. In any case though, we already provide PC scores as input we can skip that step. Performing PCA on PC scores will result to identical outputs (up to the sign).
A: Here's a different perspective on the problem:
Both PCA and t-SNE are algorithms that can be used to reduce the number of dimensions of your data in order to aid in its visualization. However, t-SNE produces a low-dimensional projection of your data by preserving more of the local (small-scale pairwise Euclidean distances) manifold structure of the data than its global structure (at reasonable or recommended values of perplexity), unlike PCA which mostly preserves data's manifold structure on a global level.

When doing t-SNE:
Hence, if you have non-standardized data as input to t-SNE, then it is possible that substructures/dimensions/subspaces in your data with a larger variance may dominate, leading to a loss of information on the local structure (cluster) of your data. Therefore, as a rule of thumb, one should always use standardized data (at least not having a substantially uneven balance of variance) as input to t-SNE!

When doing PCA:
Now, as far as PCA is concerned (which is also generally suggested to be used prior to t-SNE), standardization of data prior to application could be either  desirable or undesirable. If the data has a 1000 dimensions, out of which let's say 50 dimensions have disproportionately huge variance in their values, then performing PCA reduction on this data may lead to almost all the variance being retained in just 50-100 components. This may be desirable since you have managed to bring down the number of dimensions (say, for subsequent t-SNE application) while retaining most of the information in the data.
However, it is possible that some of the local structure –– that was crucial in deciding clustering of these points in the lower two-dimensional space by t-SNE –– may have also gotten lost.
So now, assume that you do standardize or normalize your data before performing PCA: Obviously, now that all the different features (dimensions) of your data are on a similar scale, you'll need more components to retain the same level of variance as before in your reduced data. This consequently makes convergence and run-time poor at the subsequent t-SNE step but you may now be able to reproduce several local structures in your high-dimensional data reliably in the lower two-dimensional space.

In conclusion, from my experience, I have applied standardization after PCA (and before the subsequent t-SNE reduction) than prior to PCA on average, unless there was some disproportionately huge distortion in my high dimensional data to begin with.
