  We investigate anomaly detection in an unsupervised framework and introduce
Long Short Term Memory (LSTM) neural network based algorithms. In particular,
given variable length data sequences, we first pass these sequences through our
LSTM based structure and obtain fixed length sequences. We then find a decision
function for our anomaly detectors based on the One Class Support Vector
Machines (OC-SVM) and Support Vector Data Description (SVDD) algorithms. As the
first time in the literature, we jointly train and optimize the parameters of
the LSTM architecture and the OC-SVM (or SVDD) algorithm using highly effective
gradient and quadratic programming based training methods. To apply the
gradient based training method, we modify the original objective criteria of
the OC-SVM and SVDD algorithms, where we prove the convergence of the modified
objective criteria to the original criteria. We also provide extensions of our
unsupervised formulation to the semi-supervised and fully supervised
frameworks. Thus, we obtain anomaly detection algorithms that can process
variable length data sequences while providing high performance, especially for
time series data. Our approach is generic so that we also apply this approach
to the Gated Recurrent Unit (GRU) architecture by directly replacing our LSTM
based structure with the GRU based structure. In our experiments, we illustrate
significant performance gains achieved by our algorithms with respect to the
conventional methods.
