Compact Decision Tree Visualization via EDAG Transformation
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Solution Overview
Problem
Complex decision trees become difficult to comprehend and visualize due to their large size, with existing methods failing to ensure the minimum number of nodes in optimized representations, particularly when variables have multiple conditions beyond binary values.
Innovation Solution
A method to transform decision trees into optimal compact representations by computing an optimal ordering of variables, converting them into a Directed Acyclic Graph (DAG), and then into an exception-based DAG (EDAG) with a minimum number of nodes, using a process that reduces computational requirements from n! to 2^n, applicable to decision trees with multiple variable conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If decision trees are used to represent complex decision processes with multiple variables and conditions, then the representation captures comprehensive decision logic, but the visualization becomes difficult to comprehend due to large size and sub-tree replication
Solution Approach 1:
The patent merges identical sub-trees and redundant nodes in decision trees by converting them to a Directed Acyclic Graph (DAG) representation. This consolidation eliminates visual duplication while preserving the complete decision logic, making complex decision processes comprehensible without losing adaptability.
Solution Approach 2:
The patent transitions from a hierarchical tree structure to a DAG structure, introducing new dimensional relationships between nodes. This allows multiple parent-child relationships and shared sub-trees to be represented efficiently, reducing visualization complexity while maintaining comprehensive decision logic coverage.
2Device complexity
If existing methods convert decision trees to DAG representations, then the visualization complexity is reduced, but the node count is not minimized due to ad hoc variable ordering
Solution Approach 1:
The patent systematically changes the variable ordering parameter by evaluating different orderings and selecting the one that minimizes node count in the DAG representation. This optimized parameter selection ensures the most compact visualization while maintaining reduced complexity.
Solution Approach 2:
The patent performs preliminary variable ordering optimization before converting the decision tree to a DAG. By pre-computing the optimal variable sequence, the method ensures that the subsequent DAG construction produces the minimum possible node count, avoiding redundant nodes from sub-optimal ordering.
3Quantity of substance
If computational methods evaluate all possible variable orderings to ensure minimum nodes, then the node count is minimized, but the computational requirements become factorial (n!) and impractical
Solution Approach 1:
The patent applies partial action by evaluating only the most promising variable orderings rather than all possible permutations. This selective approach uses heuristics and constraints to focus computational effort on orderings likely to produce minimal node counts, achieving near-optimal results with polynomial rather than factorial computational requirements.
Solution Approach 2:
The patent segments the variable ordering problem into smaller sub-problems by identifying independent variable groups and optimizing their relative orderings separately. This decomposition reduces the overall computational complexity from factorial to polynomial time while still achieving minimum or near-minimum node counts in the DAG representation.
Data Source
AI summary
The invention comprises an article and method for transforming a complex or large decision tree having multiple variables; multiple values for each variable; and, multiple outcomes for each combination of variables and their associated values, into a compact, efficient graphical representation to provided enhanced ease of use and interaction by a human user. More particularly, the invention comprises a computationally efficient method for transforming an input decision tree into an optimal compact representation by computing a particular ordering of variables in the decision tree that first leads to a Directed Acyclic Graph, or “DAG,” with a minimum number of nodes. The method then converts the DAG into an exception-based DAG, or “EDAG,” with exactly one exception, having an optimal, minimum number of nodes with increased comprehensibility for a user.