Topological Time-Window Forecasting for Multiscale Sales Data
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Solution Overview
Problem
Existing methods for analyzing large multidimensional datasets are insufficient in identifying important relationships, often losing detail due to sensitivity to large-scale distances and creating noise, making it difficult to derive meaningful insights.
Innovation Solution
A method involving topological hierarchical decomposition of sales and purchase data into historical and future time windows, generating directed graph adjacency arrays, and performing matrix multiplications to create customer attention matrices, which are used to generate forecasts and provide dashboards for inventory management.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If traditional clustering or linear regression methods are used to analyze large multidimensional datasets, then the analysis process is simplified, but important relationships are lost or noise is created
Solution Approach 1:
The patent segments the dataset into multiple subsets using topological hierarchical decomposition, organizing data at different levels of granularity. This segmentation preserves important relationships by analyzing data at appropriate scales rather than treating the entire dataset uniformly, thus resolving the contradiction between simplifying analysis and preserving information.
2Productivity
If existing linear algebraic and analytic methods are applied to large-scale datasets, then computational efficiency is improved, but detail is lost due to sensitivity to large-scale distances
Solution Approach 1:
The patent introduces a topological hierarchical dimension to the data analysis, organizing data points in a multi-level hierarchical structure rather than flat Euclidean space. This dimensional transformation allows efficient computation while preserving local details by capturing relationships at multiple scales, thus resolving the contradiction between computational efficiency and measurement precision.
3Measurement precision
If comprehensive data analysis is performed to identify all relationships, then insight accuracy is improved, but analysis time and computational resources increase
Solution Approach 1:
The patent performs preliminary organization of data into topological hierarchical structures and pre-computes distance metrics at different hierarchical levels. This preliminary action enables faster subsequent analysis by having data ready in an optimized structure, thus resolving the contradiction between insight accuracy and analysis time.
Data Source
AI summary
An example computer-implemented method for temporal data analysis and forecasting utilizes topological hierarchical decompositions to process historical and future time windows. The method receives sales data and purchase data for at least one item and generates multiple sets of historical time subsets with varying lengths, where information in shorter subsets is duplicated in longer ones. Future time windows are also generated in a similar manner. Future time windows are chronologically after a given initial time. The method creates past and future topological hierarchical decompositions and directed graph adjacency arrays. Customer attention matrices are generated for past and future windows, and matrix multiplications are performed to create self-attention arrays. These arrays are then multiplied together. The method culminates in providing a dashboard for forecasting after an initial time point, enabling comprehensive temporal data analysis and prediction.