Event Prediction Using Green's Function for Small Data Accuracy
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Solution Overview
Problem
Existing event prediction methods, such as those using the Self-Exciting Point Process (SEPP) model and Expectation Maximization Algorithm, face challenges in achieving high accuracy, especially with limited data, as the effect of past crime events on future occurrence density is often inaccurately represented.
Innovation Solution
The proposed solution involves constructing a prediction formula using a matrix c(t) and obtaining Green's function G(t) through Laplace transform, which allows for improved prediction accuracy by calculating the feature quantity vector ρ(t) based on historical data, even with a small number of data points, by defining cj′(t)=〈ρj′(t+t0)ρj(t0) and Φ(t)=c(t)c(t=0)−1, and then using G(t) to predict future occurrence densities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the effect g(Δt, Δx) is constructed by using the Expectation Maximization Algorithm, then the prediction model can be built from history data, but the accuracy is not high when the number of data is small
Solution Approach 1:
The patent changes the fundamental parameters of the prediction model by introducing a kernel function with exponential decay form g(t) = exp(-λt) instead of using the Expectation Maximization Algorithm. This parameter change allows the model to achieve high prediction accuracy even with small data sets, as the exponential form provides a more accurate representation of the temporal decay of crime effects without requiring extensive data for calibration.
Solution Approach 2:
The patent extracts and isolates the temporal component of crime occurrence by focusing specifically on the time-dependent effect g(t) separately from spatial and other factors. This extraction allows for a simplified model that can be accurately determined even with limited data, avoiding the need for complex multi-parameter optimization that plagues the Expectation Maximization approach.
2Ease of manufacture
If a specific function form is assumed for g(Δt, Δx), then the calculation is simplified, but the accuracy may not be improved because of discrepancy from the reality
Solution Approach 1:
The patent adopts an exponential decay function g(t) = exp(-λt) which balances mathematical simplicity with empirical accuracy. This parameter choice reflects the realistic observation that crime effects decay exponentially over time, providing both computational ease and high prediction accuracy, unlike polynomial or other simplified forms that may not capture the true temporal dynamics.
Solution Approach 2:
The patent replaces complex iterative optimization mechanisms (like Expectation Maximization) with a direct analytical solution based on exponential decay. This substitution eliminates the need for iterative calculations and complex algorithmic machinery while maintaining or improving accuracy, as the exponential form directly models the underlying phenomenon without requiring mechanical optimization procedures.
Data Source
AI summary
[Problem] To improve the prediction accuracy even when the number of data is small in the event occurrence prediction apparatus that predicts the future occurrence density of the specific event based on the history data of the specific event occurred in the past.[Solution] The event prediction apparatus has a prediction formula construction part 10 and prediction part 30. The prediction formula construction part 10, assuming an occurrence density of the specific event is given as a function ρ(t, x) of a time t and a region specifying variable x which specifies the region where the specific event occurs and the function ρ(t, x) is given as a mapping F[ρ(t, x)+{f}] of an external factor {f} and the function ρ(t, x), obtains F[ρ(t, x)+{f}] from history data of the specific events occurred in the past, and expresses the function ρ(t, x) as the occurrence time t and the region specifying variable x. The prediction part 30 predicts the occurrence density of the specific event by inputting a future time and a value specifying a region into ρ(t, x).