arXiv subjects

Pedro Lencastre

Publications and source records attributed to Pedro Lencastre.

7 recordsLinked to original sources

arXiv2026

Identification of fixations and saccades in eye-tracking data using adaptive threshold-based method

Properties of ocular fixations and saccades are highly stochastic during many experimental tasks, and their statistics are often used as proxies for various aspects of cognition. Although distinguishing saccades from fixations is not trivial, experimentalists generally use common ad-hoc thresholds in detection algorithms. This neglects inter-task and inter-individual variability in oculomotor dynamics, and potentially biases the resulting statistics. In this article, we introduce and evaluate an adaptive method based on a Markovian approximation of eye-gaze dynamics, using saccades and fixations as states such that the optimal threshold minimizes state transitions. Applying this to three common threshold-based algorithms (velocity, angular velocity, and dispersion), we evaluate the overall accuracy against a multi-threshold benchmark as well as robustness to noise. We find that a velocity threshold achieves the highest baseline accuracy (90-93\%) across both free-viewing and visual search tasks. However, velocity-based methods degrade rapidly under noise when thresholds remain fixed, with accuracy falling below 20% at high noise levels. Adaptive threshold optimization via K-ratio minimization substantially improves performance under noisy conditions for all algorithms. Adaptive dispersion thresholds demonstrate superior noise robustness, maintaining accuracy above 81% even at extreme noise levels (σ = 50 px), though a precision-recall trade-off emerges that favors fixation detection at the expense of saccade identification. In addition to demonstrating our parsimonious adaptive thresholding method, these findings provide practical guidance for selecting and tuning classification algorithms based on data quality and analytical priorities.

cs.NE↗

arXiv2025

Saccade crossing avoidance as a visual search strategy

Although visual search appears largely random, several oculomotor biases exist such that the likelihoods of saccade directions and lengths depend on the previous scan path. Compared to the most recent fixations, the impact of the longer path history is more difficult to quantify. Using the step-selection framework commonly used in movement ecology, and analyzing data from 45-second viewings of "Where's Waldo?", we report a new memory-dependent effect that also varies significantly between individuals, which we term self-crossing avoidance. This is a tendency for saccades to avoid crossing those earlier in the scan path, and is most evident when both have small amplitudes. We show this by comparing real data to synthetic data generated from a memoryless approximation of the spatial statistics (i.e. a Markovian nonparametric model with a matching distribution of saccade lengths over time). Maximum likelihood fitting indicates that this effect is strongest when including the last $\approx 7$ seconds of a scan path. The effect size is comparable to well-known forms of history dependence such as inhibition of return. A parametric probabilistic model including a self-crossing penalty term was able to reproduce joint statistics of saccade lengths and self-crossings. We also quantified individual strategic differences, and their consistency over the six images viewed per participant, using mixed-effect regressions. Participants with a higher tendency to avoid crossings displayed smaller saccade lengths and shorter fixation durations on average, but did not display more horizontal, vertical, forward or reverse saccades. Together, these results indicate that the avoidance of crossings is a local orienting strategy that facilitates and complements inhibition of return, and hence exploration of visual scenes.

q-bio.NC↗

arXiv2025

IntLevPy: A Python library to classify and model intermittent and Lévy processes

IntLevPy provides a comprehensive description of the IntLevPy Package, a Python library designed for simulating and analyzing intermittent and Lévy processes. The package includes functionalities for process simulation, including full parameter estimation and fitting optimization for both families of processes, moment calculation, and classification methods. The classification methodology utilizes adjusted-$R^2$ and a noble performance measure Γ, enabling the distinction between intermittent and Lévy processes. IntLevPy integrates iterative parameter optimization with simulation-based validation. This paper provides an in-depth user guide covering IntLevPy software architecture, installation, validation workflows, and usage examples. In this way, IntLevPy facilitates systematic exploration of these two broad classes of stochastic processes, bridging theoretical models and practical applications.

cs.NE↗

arXiv2025

The dynamical law behind eye movements: distinguishing between Lévy and intermittent strategies

Foraging is a complex spatio-temporal process which is often described with stochastic models. Two particular ones, Lévy walks (LWs) and intermittent search (IS), became popular in this context. Researchers from the two communities, each advocating for either Lévy or intermittent approach, independently analyzed foraging patterns and reported agreement between empirical data and the model they used. We resolve this Lévy-intermittent dichotomy for eye-gaze trajectories collected in a series of experiments designed to stimulate free foraging for visual information. By combining analytical results, statistical quantifiers, and basic machine learning techniques, we devise a method to score the performance of the models when they are used to approximate an individual gaze trajectory. Our analysis indicates that the intermittent search model consistently yields higher scores and thus approximates the majority of the eye-gaze trajectories better.

cond-mat.stat-mech↗

arXiv2024

Modeling Eye Gaze Velocity Trajectories using GANs with Spectral Loss for Enhanced Fidelity

Accurate modeling of eye gaze dynamics is essential for advancement in human-computer interaction, neurological diagnostics, and cognitive research. Traditional generative models like Markov models often fail to capture the complex temporal dependencies and distributional nuance inherent in eye gaze trajectories data. This study introduces a GAN framework employing LSTM and CNN generators and discriminators to generate high-fidelity synthetic eye gaze velocity trajectories. We conducted a comprehensive evaluation of four GAN architectures: CNN-CNN, LSTM-CNN, CNN-LSTM, and LSTM-LSTM trained under two conditions: using only adversarial loss and using a weighted combination of adversarial and spectral losses. Our findings reveal that the LSTM-CNN architecture trained with this new loss function exhibits the closest alignment to the real data distribution, effectively capturing both the distribution tails and the intricate temporal dependencies. The inclusion of spectral regularization significantly enhances the GANs ability to replicate the spectral characteristics of eye gaze movements, leading to a more stable learning process and improved data fidelity. Comparative analysis with an HMM optimized to four hidden states further highlights the advantages of the LSTM-CNN GAN. Statistical metrics show that the HMM-generated data significantly diverges from the real data in terms of mean, standard deviation, skewness, and kurtosis. In contrast, the LSTM-CNN model closely matches the real data across these statistics, affirming its capacity to model the complexity of eye gaze dynamics effectively. These results position the spectrally regularized LSTM-CNN GAN as a robust tool for generating synthetic eye gaze velocity data with high fidelity.

cs.NE↗

arXiv2015

From empirical data to continuous Markov processes: a systematic approach

We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption that only time-homogeneous generators exist. Here, a systematic extension to time-inhomogeneity is presented, based in new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation. Our detection algorithm shows to be effective in more than $80\%$ of tested matrices, typically $90\%$ to $95\%$, and for those an estimate of the (non-homogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.

physics.data-an↗

arXiv2014

Are credit ratings time-homogeneous and Markov?

We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and show that the validity of these assumptions - existence of a homogeneous generator and Markovianity - is not always guaranteed. Our analysis is based on a comparison between empirical transition matrices aggregated over fixed time windows and candidate transition matrices generated from measurements taken over shorter periods. Ratings are widely used in credit risk, and are a key element in risk assessment; our results provide a tool for quantifying confidence in predictions extrapolated from these time series.

q-fin.RM↗