Statistical analysis usually requires a vector representation of categorical variables, using for instance \emph{one-hot encoding}. This encoding strategy is not practical when the number of different categories grows, as it creates high-dimensional feature vectors. Additionally, the corresponding entries in the raw data are often represented as strings, that have additional information not captured by one-hot encoding. Here, we seek low-dimensional vectorial encoding of string categorical variables with high-cardinality. Ideally, these should (i) be scalable to a very large number of categories, (ii) be interpretable to the end user, and (iii) facilitate statistical analysis. We introduce two new encoding approaches for string categories: a Gamma-Poisson matrix factorization on character-level substring counts, and a min-hash encoder, based on min-wise random permutations for fast approximation of the Jaccard similarity between strings. Beyond the well-known properties of min-hash collisions, we establish properties of these representations showing that they are useful to capture inclusions. Both approaches are scalable and are suitable for streaming settings. Extensive experiments on real and simulated data show that these encoding methods improve prediction performance for real-life supervised-learning problems with high-cardinality string categorical variables and works as well as standard approaches with clean, low-cardinality ones. We recommend the following: (i) if scalability is the main concern, the min-hash encoder is the best option as it does not require any fitting to the data; (ii) if interpretability is important, the Gamma-Poisson factorization is a good alternative, as it can be interpreted as one-hot encoding, giving each encoding dimension a feature name that summarizes the substrings captured. Both models remove the need for hand-crafting features and data cleaning of string columns in databases and can be used for feature engineering in online autoML settings.