# Geometric Data Analytics

## What we do

GDA develops and applies mathematical, statistical, and computational tools for the analysis of diverse challenges in tracking, logistics, modeling, optimization, agriculture, machine learning/artificial intelligence, and biology. Coupling our applied mathematics expertise with a strong background in software development, we provide solutions to real-world problems to drive informed, confident decisions.

###### 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

###### Confidence Estimation

Confidence estimation is the process of determining the level of confidence or certainty associated with a particular prediction or decision made by a machine learning model. In other words, it involves calculating a score or probability that reflects the model's level of confidence in its prediction or decision. By knowing the level of confidence associated with a prediction, users can make informed decisions about whether to rely on the model's output or seek additional information.

Confidence Estimation is an integral part of the GDA development process and our algorithms are built from the ground up to measure and track uncertainty at multiple levels throughout our processing pipelines.

###### Uncertainty Mitigation

Uncertainty mitigation is the process of reducing or managing the level of uncertainty or risk associated with a particular decision or situation. It involves identifying potential sources of uncertainty, assessing their potential impact, and taking measures to reduce or manage that impact.

GDA has strong expertise in understanding uncertainty in complex systems and provides tools to to minimize the underlying risks through quantitative analysis.

###### Validation and Verification

Validation and Verification ensures software meets its specifications and requirements as well as user needs and expectations. In Artificial Intelligence (AI) applications, verification involves checking whether the algorithms, data, and models used in the system are accurate and reliable while validations involves testing the system to ensure that it solves the problem it was designed for and that it meets the user's requirements.

GDA has developing proprietary techniques to verify the alignment between structure of training data, the underlying statistical model, and input data to identify blind spots in the system and ensure proper operation under dynamic and unforeseen conditions

###### Pipeline Processing

Pipeline processing refers to a software development approach in which a series of tasks or processing modules are executed in a sequential manner, with the output of one task serving as the input for the next task in the sequence. A well designed pipeline  can improve efficiency and reduce the overall processing time by allowing multiple tasks to be executed simultaneously, while also reducing the amount of memory and processing power needed for each individual task. Modular programming is a core design principle at GDA where our software is specifically designed to support pipeline architectures.

###### Data Management

Data management, or the process of organizing, storing, protecting, and maintaining data is an important component of any big data application. GDA has significant expertises in data management technologies including databases,

## Information Analysis

#### Topological Data Analysis

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#### Machine Learning

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#### Data Assimilation

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#### Graph Theory

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#### Statistical Analysis

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## Confidence Management

#### risk mitigation

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#### Validation and Verification

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#### Confidence Estimation

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## Software Development

#### Pipeline Processing

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