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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.

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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.

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