VCI-LSTM: Vector Choquet Integral-Based Long Short-Term Memory

Choquet integral is a widely used aggregation operator on 1-D and interval-valued information, since it is able to take into account the possible interaction among data. However, there are many cases where the information taken into account is vectorial, such as long short-term memories (LSTM). LSTM units are a kind of recurrent neural networks that have become one of the most powerful tools to deal with sequential information since they have the power of controlling the information flow. In this article, we first generalize the standard Choquet integral to admit an input composed by n-dimensional vectors, which produces an n-dimensional vector output. We study several properties and construction methods of vector Choquet integrals (VCIs). Then, we use this integral in the place of the summation operator, introducing in this way the new VCI-LSTM architecture. Finally, we use the proposed VCI-LSTM to deal with two problems: 1) sequential image classification; 2) text classification.