Geometric Data Analytics

Topological Data Analysis

Topological Data Analysis (TDA) is a branch of data analysis that uses tools from topology to study the shape and structure of complex datasets. In TDA, the dataset is represented as a topological space, and various topological features, such as the number of connected components, loops, and holes, are extracted and analyzed to gain insights into the underlying structure and patterns of the data. These features are then used for tasks such as clustering, classification, and visualization. TDA is particularly useful for analyzing complex datasets that cannot be easily represented or analyzed using traditional statistical methods.
Solutions: Root Image Segmentation, AI Safety Guardrails, Ridgeline Extraction

Machine Learning

Machine learning is a field of artificial intelligence (AI) that focuses on developing computer programs that can learn from and make predictions or decisions based on data. It involves creating algorithms and models that enable computers to identify patterns and relationships within large datasets, and use this information to make predictions or take actions without being explicitly programmed to do so.

GDA applies TDA approaches to machine learning problems to reduce the computational demands and to analyze the structure of the training data, measured data, and underlying network topology. This structural analysis identifies mismatches in the system to predict network performance.

Solutions: Root Image Segmentation, AI Safety Guardrails

Data Assimilation

Data assimilation is a process used in science, engineering, and other fields to combine observations with model predictions or simulations, in order to obtain an optimal estimate of the true state of a system. 

GDA applies data assimilation techniques to Earth Systems Data to generate hyperlocal forecasts of weather phenomena by combining data from multiple sources and integrating location specific measurements. 

Solutions: Localized Wind Forecasts, Overspray Prediction, Flight Time optimization, Ocean Drift Prediction

Graph Theory

Graph theory is a branch of mathematics that deals with the study of graphs, which are used to model and analyze complex systems, networks, and relationships between objects generally.

GDA uses graph theory techniques for spatial optimization problems and  as a data reduction technique to reduce the search complexity for.

Solutions: Flight Time Optimization, Multi-agent Orchestration, Latent Scheduling

Bayesian Inference

Bayesian inference is a statistical approach to modeling and analyzing data that is based on the principles of Bayesian probability theory. In Bayesian inference, prior knowledge or beliefs about the parameters of a model are combined with data to produce a posterior distribution, which represents updated knowledge or beliefs about the parameters.

GDA Uses bayesian inference techniques to incorporate prior knowledge into estimation problems to improve forecast accuracy. 

Solutions: Localized Wind Forecasts, Over Spray Prediction, Communication Coverage, Dynamic Detection Probability