  Machine learning and data mining techniques have been used extensively in
order to detect credit card frauds. However, most studies consider credit card
transactions as isolated events and not as a sequence of transactions. In this
framework, we model a sequence of credit card transactions from three different
perspectives, namely (i) The sequence contains or doesn't contain a fraud (ii)
The sequence is obtained by fixing the card-holder or the payment terminal
(iii) It is a sequence of spent amount or of elapsed time between the current
and previous transactions. Combinations of the three binary perspectives give
eight sets of sequences from the (training) set of transactions. Each one of
these sequences is modelled with a Hidden Markov Model (HMM). Each HMM
associates a likelihood to a transaction given its sequence of previous
transactions. These likelihoods are used as additional features in a Random
Forest classifier for fraud detection. Our multiple perspectives HMM-based
approach offers automated feature engineering to model temporal correlations so
as to improve the effectiveness of the classification task and allows for an
increase in the detection of fraudulent transactions when combined with the
state of the art expert based feature engineering strategy for credit card
fraud detection. In extension to previous works, we show that this approach
goes beyond ecommerce transactions and provides a robust feature engineering
over different datasets, hyperparameters and classifiers. Moreover, we compare
strategies to deal with structural missing values.
