People Flow Estimation via Minimum-Cost Path Graph Inference
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Solution Overview
Problem
Existing estimation techniques for the number of people moving between areas based on spatiotemporal population data using a maximum a posteriori (MAP) estimation on a collective graphical model (CGM) are inaccurate due to Stirling's approximation when sample sizes are small and produce non-integer solutions by relaxing constraints.
Innovation Solution
The method constructs a CGM in a path graph, generates an instance of a minimum cost flow problem, and solves it using a shortest path iteration method to estimate the number of people moved, avoiding Stirling's approximation and continuous relaxation of the feasible region.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Stirling's approximation is applied to the factorial part of the objective function, then the computation is simplified, but the estimation accuracy deteriorates when the total number of samples is small
Solution Approach 1:
The patent extracts and removes the problematic Stirling's approximation component from the objective function, instead using the exact factorial computation. This eliminates the source of inaccuracy for small sample sizes while maintaining the overall MAP estimation framework.
Solution Approach 2:
The patent changes the computational parameter approach by not applying Stirling's approximation at all, instead computing factorials directly. This parameter change in the computational method resolves the accuracy issue for small samples while still allowing the optimization to proceed.
2Ease of operation
If the feasible region is continuously relaxed by removing the integer constraint, then the optimization becomes easier, but the solution becomes non-sparse and less accurate
Solution Approach 1:
The patent segments the optimization problem into two parts: first solving the relaxed continuous optimization problem, then applying a rounding procedure to obtain integer solutions. This segmentation allows the benefits of continuous optimization while recovering the sparsity and accuracy of integer solutions.
Solution Approach 2:
The patent performs preliminary relaxation of the integer constraints to make optimization easier, then applies a rounding step as a preliminary correction to restore integer properties. This preliminary action approach allows the optimization to proceed smoothly while maintaining solution quality.
3Adaptability or versatility
If MAP estimation on CGM is used to estimate people flow, then the method provides a systematic approach, but it produces inaccurate solutions when total number of samples is small
Solution Approach 1:
The patent applies local quality by treating small sample cases differently from large sample cases. Specifically, it avoids Stirling's approximation which is only valid for large numbers, and instead uses exact factorial computation for small samples, thereby adapting the method quality to the local data conditions.
Data Source
AI summary
An estimation apparatus includes a memory; and a processor configured to execute: receiving spatiotemporal population data and a probability of movement between areas as input; constructing a collective graphical model (CGM) in a path graph for estimating a number of people who have moved between areas from the spatiotemporal population data and the probability of movement between areas; generating an instance of a minimum cost flow problem for performing MAP estimation on the constructed CGM; solving the instance of the minimum cost flow problem to estimate the number of people who have moved between areas at individual time steps; and outputting the estimated number of people who have moved between the areas at the individual time steps.