ATD: Anomaly detection and functional data analysis with applications to threat detection for multimodal satellite data

Trustees Of Boston University, Boston

Investigators

Abstract

The combination of massive data analysis and advancements in Artificial Intelligence (AI) is causing major changes in society. One area where this is crucial is the integration of remote sensing and Geographic Information System (GIS), like satellite data, which is important for understanding the impact of human activities on the environment and climate. Deforestation is a key factor in climate change, causing negative effects on ecosystems, biodiversity, and human populations. Fortunately, there are now extensive satellite datasets that can help detect deforestation, especially in critical forests like the Amazon. However, tracking deforestation, degradation, and forest regrowth is challenging due to factors like clouds and shadows. To address these challenges, the investigators will develop an innovative approach based on a new mathematical framework. This research is relevant to various fields such as human migration, climate change, transportation logistics, and epidemic disease diffusion. The findings will be valuable for intelligence gathering and will contribute to understanding security conditions, informing assessments and decisions, including those with military and political implications. Moreover, the investigators are committed to training and nurturing students' expertise in these areas, providing them with valuable learning opportunities. The investigators will develop an innovative and distinct approach to change-point and anomaly detection within the framework of mathematical functional analysis, utilizing representations like the Karhunen-Loeve (KL) expansion. This approach deviates from previous methods in several significant ways. KL expansions are ideal for representing random processes, providing optimal representations. They exhibit a remarkable level of generality, enabling accurate representation of various processes and fields over complex geometrical domains. Detection is achieved by constructing and matching nested eigenspaces tailored to truncated KL expansions. Unlike current statistical approaches, the proposed approach is rooted in functional analysis and offers several advantages for detecting hidden phenomena in complex domains: 1) Principled detection of anomalous global and local signals. 2) Development of reliable hypothesis tests using robust concentration inequalities without making assumptions about data distributions (essential) e.g. robust statistical significance for detection. 3) Precise anomaly quantification. 4) Applicability to diverse geometries, including geo-spatial, spatio-temporal, surfaces, networks, etc. The construction of nested subspaces involves efficient algorithms derived from computational applied mathematics and high-performance computing. 5) Integration of multilevel filters capable of processing massive volumes of data with near-optimal performance. Overall, this approach, rooted in functional analysis, presents a new perspective on change and anomaly detection. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.