Nested Categorization Using Unique Factorization Domain Elements
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Solution Overview
Problem
Existing information categorization systems face challenges in handling nested categorizations and dynamic changes efficiently, particularly in applications like email message categorization, where previous methods are resource-intensive and complex.
Innovation Solution
A method using Unique Factorization Domain (UFD) elements to assign numbers to nodes in a hierarchical structure, allowing for efficient querying and re-parenting of nodes by manipulating these numbers, enabling nested categorizations and handling dynamic changes without increasing complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If transitive closure calculation is used to handle nested categorization, then reachability between categories is achieved, but resource consumption increases significantly for dynamic applications
Solution Approach 1:
The patent segments the categorization problem by introducing intermediate summary records that store pre-computed reachability information. Instead of calculating transitive closure for the entire category hierarchy each time, the system divides the hierarchy into manageable segments (summary records) that can be independently maintained and updated, significantly reducing computational resources for dynamic applications
Solution Approach 2:
The patent applies preliminary action by pre-computing and storing reachability information in summary records before queries are executed. These summary records are maintained and updated in advance through background processes, so when a categorization query occurs, the system can quickly retrieve pre-computed results rather than performing expensive transitive closure calculations at query time
2Ease of operation
If relational database approach is used to store category links, then leaf-node changes are easy to handle, but non-leaf node changes become difficult and query complexity increases
Solution Approach 1:
The patent introduces summary records as intermediary structures between the category hierarchy and the actual categorization data. These summary records act as mediators that simplify operations: leaf-node changes only require updating the leaf node itself, while non-leaf node changes are handled by updating the intermediate summary records that aggregate information from multiple sources, reducing query complexity
3Adaptability or versatility
If traditional folder hierarchy is used for categorization, then nested categories are supported, but cycles are not permitted and re-parenting is complex
Solution Approach 1:
The patent replaces the mechanical folder hierarchy system with a mathematical approach using Unique Factorization Domain (UFD) elements. Each category is assigned a UFD element, and category relationships are represented through mathematical operations on these elements. This substitution allows cycles to be permitted (unlike traditional folder hierarchies) and simplifies re-parenting operations to straightforward mathematical computations rather than complex structural reorganizations
Data Source
AI summary
A method for information item categorization in which each non-leaf node in a hierarchical organization of nodes represents a category, and each leaf node represents an information item. A number P is associated with each node. For non-leaf nodes, the associated number P is selected from a subset of relatively prime elements chosen from an appropriate Unique Factorization Domain (UFD), such as a set of relatively prime numbers which are a subset of the familiar set of integers. For leaf nodes, P is set to 1. A number M is also associated with each node. For each root node, M is set to the value of P for that node. For each non-root node, M is set to the product of the M's of all parent nodes of the node and the P of that node.