ST-SiameseNet: Validating Trajectory Authenticity

When we modify a trajectory, how do we know the result still looks like a real taxi trip? FAMAIL uses a Siamese LSTM neural network — called ST-SiameseNet — that has been trained to determine whether two trajectory sequences were generated by the same driver.

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Architecture Overview

The discriminator takes two trajectories as input and outputs a similarity score between 0 and 1:

                          ┌──────────────┐
Original Trajectory τ  ──→│              │
                          │   Shared     │
                          │   LSTM       │──→  Compare  ──→  Similarity
                          │   Encoder    │        ↑          Score ∈ [0, 1]
Modified Trajectory τ′ ──→│              │        │
                          └──────────────┘        │
                          (shared weights)    MLP + Sigmoid

Input

Each trajectory is a sequence of spatiotemporal states: grid coordinates, time of day, and day of week.

Encoding

A bidirectional LSTM with shared weights processes both trajectories into fixed-length vector representations. Sharing weights ensures that both trajectories are embedded into the same feature space, enabling meaningful comparison.

Comparison

The two representations are compared via a multi-layer perceptron (MLP) that outputs \(P(\text{same driver})\).

Output

• Score \(\approx 1.0\): The modified trajectory is indistinguishable from the original — the edit preserves the driver's behavioral signature.
• Score \(\approx 0.0\): The modification has altered the trajectory so much that it no longer resembles the original driver's behavior.

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Role in the Optimization

During trajectory modification, the discriminator is frozen — its parameters are not updated. However, gradients flow through the discriminator back to the modified trajectory, allowing the optimizer to learn which modifications preserve driver-consistent behavior.

The fidelity score acts as a regularization term in the objective function:

\[\mathcal{L} = \alpha_1 \cdot F_{\text{spatial}} + \alpha_2 \cdot F_{\text{causal}} + \alpha_3 \cdot F_{\text{fidelity}}\]

This prevents the optimizer from making unrealistically large location shifts just to improve fairness metrics. The discriminator anchors the modifications to behavioral reality.

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Why a Siamese Architecture?

Traditional classifiers answer "is this trajectory real?" — a question that requires defining what "real" means in absolute terms. The Siamese architecture instead answers a relative question: "do these two trajectories look like they came from the same driver?"

This relative framing is ideal for FAMAIL because:

• We always have the original trajectory as a reference point
• We care about the degree of change, not absolute quality
• The shared encoder naturally learns driver-invariant features

Pre-trained and frozen

ST-SiameseNet is trained once on the full trajectory dataset, then frozen during the optimization loop. Only the trajectory pickup locations are modified — the discriminator provides gradient signal but is never updated.

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