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In this note we discuss a common misconception, namely that embeddings arealways used to reduce the dimensionality of the item space. We show that whenwe measure dimensionality in terms of information entropy then the embedding ofsparse probability distributions, that can be used to represent sparse featuresor data, may or not reduce the dimensionality of the item space. However, theembeddings do provide a different and often more meaningful representation ofthe items for a particular task at hand. Also, we give upper bounds and moreprecise guidelines for choosing the embedding dimension.

On the Dimensionality of Embeddings for Sparse Features and Data