dimensionality reductionhigh-dimensionalnormalizationtsne
Some of my data's features have large values, while other features have much smaller values.
Is it necessary to center+scale data before applying t-SNE to prevent bias towards the larger values?
I use Python's sklearn.manifold.TSNE implementation with the default euclidean distance metric.
Question 1: Let's say you have observed a data matrix $X \in \mathbb R^{n \times p}$. From this you can compute the eigendecomposition $X^T X = Q \Lambda Q^T$. The question now is: if we get new data coming from the same population, perhaps collected into a matrix $Z \in \mathbb R^{m \times p}$, will $ZQ$ be close to the ideal orthogonal rotation of $Z$? This kind of question is addressed by the Davis-Kahan theorem, and matrix perturbation theory in general (if you can get ahold of a copy, Stewart and Sun's 1990 textbook is the standard reference).
Question 2: you definitely can speed things up if you know you only need the top $k$ eigenvectors. In R I use rARPACK for this; I'm sure there's a Java equivalent since they're all fortran wrappers anyway.
Question 3: I don't know anything about Java implementations, but this thread discusses speeding up PCA as does this CV thread. There's a ton of research on this sort of thing and there are tons of methods out there using things like low rank approximations or randomization.
Determine the smallest number in your time series , say -10. for example . The constant you would need is then 10.0000000001 or larger in order to make all the adjusted values positive. It doesn't make make any difference as the reverse transformation needed to obtain forecasts will use the same adjustment factor.
Please see https://www.ime.usp.br/~abe/lista/pdfm9cJKUmFZp.pdf where Box & Cox suggested an alternative to deal with negative numbers without adding a constant .
EDITED after OP's question re logs ...
From the above reference ...perhaps this helps ... ..logs are used
Best Answer
Centering shouldn't matter since the algorithm only operates on distances between points, however rescaling is necessary if you want the different dimensions to be treated with equal importance, since the 2-norm will be more heavily influenced by dimensions with large variance.