Boolean Decomposition of Spatiotemporal Tensors

This technical note TN discusses Boolean decompositions of binary tensors containing spatiotemporal data. The increase in data collection technology has led to a proliferation of data containing information on human movement. Effectively managing and gaining insights from this influx of data is presenting a significant challenge to the Army geospatial community. This information can extend beyond just time and position coordinates to include features such as weather, social interactions, etc. The addition of these extra variables can provide new insight into human behavior and patterns of life. The capability to geocomputationally manipulate these related datasets will provide additional insight into human behavior and patterns of life, thereby enhancing the Army GEOINT- HUMINT spectrum of operations. Since spatiotemporal data is often binary, new theory is needed to fully exploit this information and draw conclusions. A uniform framework is needed to combine the spatiotemporal moving object information, along with other contextual data, before a holistic data analysis can be applied. A tensor is a data structure that is a natural representation for many multi-modal datasets. To extract patterns and find correlations in the data, various decompositions of the tensor can be studied. A commonly used method is the CANDECOMPPARAFAC CP decomposition, which expresses a tensor as a minimum-length linear combination of rank-one tensors Kolda and Bader 2009. This decomposition always exists, but is computationally difficult to determine. Thus an approximate decomposition is used. In addition to being computationally efficient, an approximation can serve to separate noise from signal by preserving the most important features of a tensor. This idea has been applied to fields such as signal processing, acoustics, and chemometrics Kolda and Bader 2009. Thus far, most tensor analysis, both in theory and in applications, has been done using real or complex numbers.