Trajectory Similarity Estimation Using Siamese 1D CNN Fréchet Distance
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Solution Overview
Problem
Existing methods for calculating the Fréchet distance between trajectories are computationally expensive and require significant resources, making them unsuitable for processing large volumes of data, and existing deep learning approaches are limited by image resolution and computing resources.
Innovation Solution
A method using a Siamese architecture of a one-dimensional convolutional neural network to determine the Fréchet distance, which involves training on discretized positioning data and optimizing the mean squared error, reducing the computational burden and enabling rapid implementation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional dynamic programming or discrete Fréchet distance methods are used to calculate similarity between trajectories, then measurement precision is improved, but computing time and resource consumption increase significantly
Solution Approach 1:
The patent replaces traditional mechanical computation methods (dynamic programming algorithms) with a neural network-based system. The Fréchet distance calculation is transformed into a machine learning prediction task, where the neural network learns the distance metric during training and performs rapid inference during operation, substituting computationally intensive algorithmic processing with trained model evaluation.
Solution Approach 2:
The patent performs preliminary training of the neural network offline using trajectory data pairs and their corresponding Fréchet distances. During this training phase, the model learns the complex patterns and relationships in trajectory data. Once trained, the model can rapidly compute similarities for new trajectories without requiring intensive online computation, effectively performing the heavy lifting beforehand.
2Reliability
If traditional Fréchet distance calculation methods are used, then reliability is improved, but device complexity and resource requirements increase
Solution Approach 1:
The patent replaces complex algorithmic computation with a trained neural network model. The Fréchet distance calculation is transformed into a machine learning prediction task, where the neural network learns the distance metric during training and performs rapid inference during operation, substituting computationally intensive algorithmic processing with trained model evaluation.
Solution Approach 2:
The patent changes the computational parameters by representing trajectories as sequences of discrete points and using a neural network architecture that processes these sequences. The continuous Fréchet distance calculation is approximated through discrete point sampling and neural network prediction, changing the mathematical parameters while maintaining acceptable accuracy.
3Productivity
If deep learning approaches with image-based representations are used, then productivity is improved, but manufacturing precision and resource efficiency deteriorate due to image resolution limitations
Solution Approach 1:
The patent transitions from two-dimensional image-based representations to one-dimensional sequence-based representations of trajectories. By treating trajectories as ordered sequences of points rather than rasterized images, the method preserves the temporal and spatial relationships along the path while reducing dimensional complexity, avoiding the resolution loss inherent in image-based approaches.
Solution Approach 2:
The patent replaces image processing mechanisms with sequence processing mechanisms. Instead of converting trajectories to images and using convolutional neural networks for image analysis, the method directly processes trajectory point sequences, preserving the inherent sequential structure and avoiding information loss from discretization and resampling required for image representation.
Data Source
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AI summary
The present invention relates to a method for determining similarity by means of a Fréchet distance (DF) between two paths (TRAi, TRAj), in which a Fréchet distance model (MOD) is built by machine learning (APP) implementing a Siamese architecture of one-dimensional convolutional neural networks.