Prediction Learning Models Using TDA for Data Relationship Discovery
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Solution Overview
Problem
Existing methods for analyzing large multidimensional datasets are insufficient in identifying important relationships, are computationally inefficient, and require sophisticated experts to interpret, often losing detail due to sensitivity to large scale distances and lacking interactive and exploratory data analysis capabilities.
Innovation Solution
A system and method that uses Topological Data Analysis (TDA) to group data points into subsets, create transformation datasets, and apply machine learning models to generate prediction models, allowing for interactive visualization and exploration of data relationships.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional clustering methods are used to analyze large multidimensional datasets, then data points can be grouped, but important relationships are lost due to the blunt grouping approach
Solution Approach 1:
The patent segments the dataset into multiple subsets based on topological features and relationships, rather than using single blunt clusters. This segmentation preserves important relationships by creating finer-grained groups that maintain the structural integrity of the data while enabling more precise relationship identification.
Solution Approach 2:
The patent introduces topological dimensions to the analysis by computing persistence diagrams and barcode representations that capture the shape and structure of data relationships. This adds new analytical dimensions beyond traditional clustering, enabling precise identification of relationships while maintaining manageable complexity through mathematical abstraction.
2Measurement precision
If traditional linear algebraic and analytic methods are used, then data can be processed, but detail is lost due to sensitivity to large scale distances
Solution Approach 1:
The patent introduces persistence diagrams and barcode representations as intermediary structures that mediate between the raw data and final analysis. These intermediaries transform distance-sensitive data into topological features that are invariant to scale, preserving detail while eliminating sensitivity to large scale distances through the intermediary transformation.
Solution Approach 2:
The patent changes the parameters of analysis from Euclidean distances to topological persistence values. By computing birth and death parameters of topological features across multiple scales, the method transforms scale-sensitive distance measurements into scale-invariant persistence parameters, preserving detail while removing harmful sensitivity.
3Ease of operation
If sophisticated experts interpret the output of previous methods, then relationships can be understood, but considerable time is required
Solution Approach 1:
The patent creates visual copies of complex topological data in the form of persistence diagrams and barcode plots. These visual representations copy the essential relationship structure into an easily interpretable graphical format, making the data understandable without requiring sophisticated expert interpretation while preserving the full relationship information.
4Adaptability or versatility
If previous methods are used for data analysis, then some relationships can be depicted in graphs, but the graphs are not interactive and exploratory analysis cannot be quickly modified
Solution Approach 1:
The patent implements dynamic, interactive visualizations where users can modify parameters, filter data, and explore relationships in real-time. The system dynamically updates persistence diagrams and barcode representations based on user interactions, enabling exploratory analysis to be quickly modified without requiring complex static graph systems.
Data Source
AI summary
A method comprises receiving a network of a plurality of nodes and a plurality of edges, each of the nodes comprising members representative of at least one subset of training data points, each of the edges connecting nodes that share at least one data point, grouping the data points into a plurality of groups, each data point being a member of at least one group, creating a first transformation data set, the first transformation data set including the training data set as well as a plurality of feature subsets associated with at least one group, values of a particular data point for a particular feature subset for a particular group being based on values of the particular data point if the particular data point is a member of the particular group, and applying a machine learning model to the first transformation data set to generate a prediction model.