Irregular Time Intervals Research Articles

Addressing local sparsity in massive agricultural machinery trajectories: A BiLSTM-GRU approach

Trajectory data acquired from GNSS (Global Navigation Satellite System) terminals on agricultural machinery are crucial for identifying agricultural machinery operation modes, evaluating agricultural machinery operational efficiency and exploring agricultural machinery trans-regional harvesting operation characteristics. However, GNSS terminals often experience signal delays due to factors such as weather conditions and environmental obstructions. These delays result in irregular time intervals between trajectory points, leading to local sparsity within the trajectory data, which subsequently reduces the accuracy of applications and analyses based on agricultural machinery trajectories. To address this issue, we propose a novel approach that leverages Bidirectional Long Short-Term Memory (BiLSTM) and Gated Recurrent Unit (GRU) networks, along with an attention mechanism, to mitigate the problem of local trajectory sparsity, and experiments were conducted using agricultural machinary trajectory data collected during the 2023 wheat harvest period. The results demonstrate the efficiency of our approach by successfully resolving the local sparsity of agricultural machinery trajectories. Moreover, each newly added trajectory point contains all original attributes (e.g., speed and direction). When integrated into state-of-the-art algorithms (e.g., DT, DBSCAN + rules, GCN) for identifying machinery operation modes, our method improves accuracies by 21.83 %, 26.86 %, and 1.17 %, respectively. Our approach effectively addresses the issue of local trajectory sparsity, thus providing assistance for applications and studies based on massive agricultural machinery trajectories.

ChronoVectors: Mapping Moments through Enhanced Temporal Representation

Time-series data are prevalent across various fields and present unique challenges for deep learning models due to irregular time intervals and missing records, which hinder the ability to capture temporal information effectively. This study proposes ChronoVectors, a novel temporal representation method that addresses these challenges by enabling a more specialized encoding of temporal relationships through the use of learnable parameters tailored to the dataset’s dynamics while maintaining consistent time intervals post-scaling. The theoretical demonstration shows that ChronoVectors allow the transformed encoding tensors to map moments in time to continuous spaces, accommodating potentially infinite extensions of the sequence and preserving temporal consistency. Experimental validation using the Parking Birmingham and Metro Interstate Traffic Volume datasets reveals that ChronoVectors enhanced the predictive capabilities of deep learning models by reducing prediction error for regression tasks compared to conventional time representations, such as vanilla timestamp encoding and Time2Vec. These findings underscore the potential of ChronoVectors in handling irregular time-series data and showcase its ability to improve deep learning model performance in understanding temporal dynamics.

TABLE: Time-aware Balanced Multi-view Learning for stock ranking

Stock ranking is a significant and challenging problem. In recent years, the use of multi-view data, such as price and tweet, for stock ranking has gained considerable attention in the research field. Most existing methods are performed in (some of) the 3 steps: 1) view-specific representation learning; 2) cross-view representation interaction; 3) multi-view representation fusion. Although these methods make breakthroughs in stock ranking, they often treat all views equally. This neglects the unbalanced phenomenon in multi-view stock data, i.e., the dimension of the text view may be extremely big compared with those of other views; the price view exhibits standard and high-quality data, whereas the text view contains noise and has irregular time intervals. To solve this, we propose a Time-Aware Balanced multi-view LEarning (TABLE) method. TABLE method consists of a view-specific learning stage and a multi-view fusion stage. In the first stage, we aim to improve the quality of the low-quality text view. We achieve this by attenuating the negative impact of irrelevant texts using a hierarchical temporal attention mechanism that captures text correlations. Additionally, we explicitly model the time irregularities between sequential texts. In the fusion stage, we address the dimensions unbalance problem by establishing a multi-view decision fusion paradigm by weighted averaging the view-specific stock predictions. These weights are dynamic and determined based on the quality discrepancy between the views. Finally, we obtain the optimal stock ranking list by optimizing the point-wise regression loss and the ranking-aware loss. We empirically compare TABLE method with state-of-the-art baselines using the publicly available dataset, S&P500. The experimental results demonstrate that TABLE method outperforms the baseline methods in terms of accuracy and investment revenue.

Multiple-Exposure PTV With Variable Time Steps

Recording multiple exposures of the tracer particles onto a single digital image has the potential to simplify the hardware needed for 3D PTV measurements. A sequence with equal time intervals leads to the well-known directional ambiguity problem. Instead, a sequence with irregular time-intervals (two or more) allows resolving the ambiguity. Two fundamental criteria are introduced that determine whether a set of particle samples corresponds to a physical trace for a given neighborhood: the kinematic similarity criterion imposes similarity (i.e. proportionality) between the length travelled by the particle and time elapsed. Additionally, the trace regularity criterion favors sets with minimum fluctuations of the velocity vector. A numerical algorithm, based on combinatorial analysis is presented, whereby all possible sets are scrutinized and the set of particles yielding the minimum disparity from the above criteria corresponds to the physical trace. The algorithm is demonstrated using 3D experimental data and results are benchmarked against the state-of-the-art time-resolved analysis Shakethe-Box (single-frame, single-exposure).

TA-RNN: an attention-based time-aware recurrent neural network architecture for electronic health records.

Electronic health records (EHRs) represent a comprehensive resource of a patient's medical history. EHRs are essential for utilizing advanced technologies such as deep learning (DL), enabling healthcare providers to analyze extensive data, extract valuable insights, and make precise and data-driven clinical decisions. DL methods such as recurrent neural networks (RNN) have been utilized to analyze EHR to model disease progression and predict diagnosis. However, these methods do not address some inherent irregularities in EHR data such as irregular time intervals between clinical visits. Furthermore, most DL models are not interpretable. In this study, we propose two interpretable DL architectures based on RNN, namely time-aware RNN (TA-RNN) and TA-RNN-autoencoder (TA-RNN-AE) to predict patient's clinical outcome in EHR at the next visit and multiple visits ahead, respectively. To mitigate the impact of irregular time intervals, we propose incorporating time embedding of the elapsed times between visits. For interpretability, we propose employing a dual-level attention mechanism that operates between visits and features within each visit. The results of the experiments conducted on Alzheimer's Disease Neuroimaging Initiative (ADNI) and National Alzheimer's Coordinating Center (NACC) datasets indicated the superior performance of proposed models for predicting Alzheimer's Disease (AD) compared to state-of-the-art and baseline approaches based on F2 and sensitivity. Additionally, TA-RNN showed superior performance on the Medical Information Mart for Intensive Care (MIMIC-III) dataset for mortality prediction. In our ablation study, we observed enhanced predictive performance by incorporating time embedding and attention mechanisms. Finally, investigating attention weights helped identify influential visits and features in predictions. https://github.com/bozdaglab/TA-RNN.

Prediction of steelmaking process variables using K-medoids and a time-aware LSTM network

A new method is required to address the challenge of predicting process parameters in high-temperature, high-pressure industrial processes. This study proposes a multi-model Long Short-Term Memory (LSTM) network prediction algorithm with irregular time interval sequences to predict the silicon yield in converter steelmaking. The experimental results demonstrate that this algorithm performs better than comparable neural network models in classifying high-dimensional, redundant industrial production data with noise and outliers. The algorithm is evaluated using data from a steel plant. The proposed algorithm has lower errors for predicting the alloy yield than other neural network models. An average mean absolute error (MAE) of less than 0.01 confirms the algorithm's feasibility and practicality.

DCNeT: A disease comorbidity network-based temporal deep learning framework to predict cardiovascular risk in patients with mental disorders

Patients with mental disorders (MDs) are at higher subsequent risk of developing cardiovascular diseases (CVDs) than the general population. Early identification of cardiovascular risk in patients with MDs is beneficial for timely intervention and reducing disease burden. Recently, deep learning approaches have been increasingly applied in CVDs risk prediction. However, these methods have three major issues: 1) mostly relying on multiple types of clinical data, 2) not sufficiently mining and utilizing comorbidity patterns hidden in complex correlations among various diseases, and 3) not fully leveraging the time information, including the irregular intervals. To address these issues, we propose a disease comorbidity network-based temporal deep learning framework (DCNeT) to predict the subsequent CVDs risk for patients with MDs based on routinely collected administrative health data. Firstly, to identify the comorbidity patterns of MDs, we construct a disease comorbidity network (DCN) for MDs and apply graph embedding method to generate disease embeddings for each disease in the DCN. Then, a code attention mechanism is proposed to obtain the weight of each disease which is embedded into dense vectors based on the structure of DCN. We present a view attention mechanism to compute the attention weights of different types of features including disease embeddings, basic features, and disease indicators for generating the final representations of patients’ hospitalizations. Furthermore, to fully utilize the information on the irregular time intervals between hospitalizations, a time encoding module is designed, and the time-aware LSTM is adopted to model the irregular time intervals and capture the temporal patterns of patients’ hospitalizations. The experimental results show that DCNeT outperforms the state-of-the-art methods, with the area under the receiver operating characteristic curve of 0.7658, 0.8143, 0.8110, and 0.7839 on four datasets, respectively. The ablation experiments further demonstrate that each module of DCNeT, including the code attention, view attention, and time encoding module, contributes to its superior performance, with average improvements of 1.20 %, 1.65 %, and 1.13 % in accuracy, respectively. Our DCNeT could be utilized as an efficient framework for identifying high-risk groups of CVDs among patients with MDs that may benefit from screening and preventive strategies.

TSOANet: Time-Sensitive Orthogonal Attention Network for medical event prediction

Medical Event Prediction (MEP) based on Electronic Medical Records (EMR) is an essential and valuable task for healthcare. For a patient, information in the EMR can be organized into a structured sequence, consisting of multiple visits each with details about visit time and various types of medical events. As the time intervals between neighboring visits are irregular and the medical events at different visits can vary significantly, MEP based on EMR is still challenging. Many studies have been proposed to model the irregular time intervals, relations among different types of medical events within each visit and relations among medical events across visits, and reported exciting results. However, most of these studies focus on two out of the three aspects mentioned above, with only a few addressing all the three aspects simultaneously. In this study, we propose a novel network, the Time-Sensitive Orthogonal Attention Network (TSOANet), which can fully utilize the irregular time intervals, relations among different types of medical events within and across visits. In particular, we design two key components: (1) Time-Sensitive Block, used to model the time intervals at both local and global levels to determine the impact of each visit in EMR; (2) Orthogonal Attention Block, used to model relations among different types of medical events within each visit and across visits in two axes, that is, event axis and time axis. Extensive experiments on two public real-world EMR datasets demonstrate that TSOANet outperforms the state-of-the-art models for various prediction tasks, thereby verifying the effectiveness of our approach. The source code of TSOANet is released at https://github.com/chh13502/TSOANet.

SNN-PDE: Learning Dynamic PDEs from Data with Simplicial Neural Networks

Dynamics of many complex systems, from weather and climate to spread of infectious diseases, can be described by partial differential equations (PDEs). Such PDEs involve unknown function(s), partial derivatives, and typically multiple independent variables. The traditional numerical methods for solving PDEs assume that the data are observed on a regular grid. However, in many applications, for example, weather and air pollution monitoring delivered by the arbitrary located weather stations of the National Weather Services, data records are irregularly spaced. Furthermore, in problems involving prediction analytics such as forecasting wildfire smoke plumes, the primary focus may be on a set of irregular locations associated with urban development. In recent years, deep learning (DL) methods and, in particular, graph neural networks (GNNs) have emerged as a new promising tool that can complement traditional PDE solvers in scenarios of the irregular spaced data, contributing to the newest research trend of physics informed machine learning (PIML). However, most existing PIML methods tend to be limited in their ability to describe higher dimensional structural properties exhibited by real world phenomena, especially, ones that live on manifolds. To address this fundamental challenge, we bring the elements of the Hodge theory and, in particular, simplicial convolution defined on the Hodge Laplacian to the emerging nexus of DL and PDEs. In contrast to conventional Laplacian and the associated convolution operation, the simplicial convolution allows us to rigorously describe diffusion across higher order structures and to better approximate the complex underlying topology and geometry of the data. The new approach, Simplicial Neural Networks for Partial Differential Equations (SNN PDE) offers a computationally efficient yet effective solution for time dependent PDEs. Our studies of a broad range of synthetic data and wildfire processes demonstrate that SNN PDE improves upon state of the art baselines in handling unstructured grids and irregular time intervals of complex physical systems and offers competitive forecasting capabilities for weather and air quality forecasting.

Modeling high-frequency financial data using R and Stan: A bayesian autoregressive conditional duration approach

In econometrics, Autoregressive Conditional Duration (ACD) models use high-frequency economic or financial duration data, which mostly exhibit irregular time intervals. The ACD model is widely used to examine the duration of transaction volume and duration of price variations in stock markets. In this work, our goal is to devise testing that will aid in the identification of the best potential duration model among a set of four models using Bayesian approach. We test three models that rely on conditional mean duration (Weibull ACD, Log Weibull ACD, Generalized Gamma ACD) and one conditional median duration model (Birnbaum-Saunders ACD), and are being compared each other. The study was done in Rstan, a programming language for statistical inference, and the simulation uses the Hamiltonian Monte Carlo (HMC) algorithm of Markov Chain Monte Carlo (MCMC) to sample from the posterior distribution. Our findings show that Log Weibull ACD (second-generation model) as best among the four models followed by Birnbaum-Saunders ACD (third-generation model). The result offers methodological implications for algorithmic trading (algo-trading), high-frequency trading and risk management.

Irregular longitudinal data analysis with statistical and machine learning methods for hazardous asteroids

Observations of the asteroids have been performed as long as it has been feasible by the available observational equipment. Recorded data, going back to 18th century, allowed a classification of these celestial objects’ hazardous status. Unfortunately, previous studies used methods that ignore subject dependency in Near-Earth Asteroids (NEA) data. This study aims to perform hazard classification of asteroids by proposing various statistical and machine learning methods on NEA data to overcome these shortcomings. We analyze data from 751 asteroids observed at irregular time intervals through the NASA. We compare algorithms suitable for longitudinal data structure, such as the Generalized Linear Mixed Models (GLMM), marginal model, GLMM-Tree, Historical Random Forest, GPBoost, and Spline. To the best of our knowledge and based on a comprehensive review of the existing literature, our study stands as the pioneering in the utilization of these advanced methodologies for the in-depth analysis of Near-Earth Asteroid (NEA) data. According to the findings, the accuracies of the models range from 0.89 to 0.99. The GPBoost model has the highest performance, while the marginal model has the poorest one.

Multifractal and chaotic characteristics of geomagnetic inter-storm interval over eight solar cycles

The structure and characteristics of geomagnetic inter-storm intervals, the sequence of time differences between two successive storm events, can provide information about the origin and drivers of the storms compared to analyzing the entire data set. In this study, the inter-storm event was investigated using the Kp index over 8 solar cycles (17–24). Three nonlinear approaches were considered: burstiness, multifractal detrended fluctuation analysis, and chaos analysis. The burstiness analysis reveals that the inter-storm intervals are heterogeneous events with irregular time intervals. The multifractal strength of inter-storm intervals ranges from 0.23 to 0.65 for each of the solar cycles, compared to 0.38 for the entire period. Long-range correlations largely drove the multifractality across most solar cycles. Chaos analysis confirmed the low predictability of inter-storm intervals across each solar cycle. The results will be relevant to the prediction and understanding of drivers of storm events across different solar cycles.

Rayleigh step-selection functions and connections to continuous-time mechanistic movement models

BackgroundThe process known as ecological diffusion emerges from a first principles view of animal movement, but ecological diffusion and other partial differential equation models can be difficult to fit to data. Step-selection functions (SSFs), on the other hand, have emerged as powerful practical tools for ecologists studying the movement and habitat selection of animals.MethodsSSFs typically involve comparing resources between a set of used and available points at each step in a sequence of observed positions. We use change of variables to show that ecological diffusion implies certain distributions for available steps that are more flexible than others commonly used. We then demonstrate advantages of these distributions with SSF models fit to data collected for a mountain lion in Colorado, USA.ResultsWe show that connections between ecological diffusion and SSFs imply a Rayleigh step-length distribution and uniform turning angle distribution, which can accommodate data collected at irregular time intervals. The results of fitting an SSF model with these distributions compared to a set of commonly used distributions revealed how precision and inference can vary between the two approaches.ConclusionsOur new continuous-time step-length distribution can be integrated into various forms of SSFs, making them applicable to data sets with irregular time intervals between successive animal locations.

ATIN: Attention-embedded time-aware imputation networks for production data anomaly detection

Effective identification of anomalous data from production time series in the oilfield affects future analysis and forecasting. Such time series is often characterized by irregular time intervals due to uneven manual sampling, and missing values caused by incomplete measurements. Therefore, the identification task becomes more challenging. In this paper, an Attention-Embedded Time-Aware Imputation Network (ATIN) with two sub-networks is proposed for this task. First, Time-Aware Imputation LSTM (TI-LSTM) is designed for modeling irregular time intervals and incomplete measurements. It decays the long-term memory component as the producing well conditions may be varied during the water cut stage. Second, Attention-Embedding LSTM (ATEM) is designed to improve the effectiveness of anomaly detection. It focuses on the correlation between the last and historical measurements in a given sequence. Comparison experiments with several state-of-the-art methods, including mTAN, GRU-D, T-LSTM, ATTAIN, and BRITS are conducted. Results show that the proposed ATIN performs better in accuracy, F1-score, and area under curve (AUC).

TERI: An Effective Framework for Trajectory Recovery with Irregular Time Intervals

The proliferation of trajectory data has facilitated various applications in urban spaces, such as travel time estimation, traffic monitoring, and flow prediction. These applications require a substantial volume of high-quality trajectories as the prerequisite to achieve effective performance. Unfortunately, a large number of real-world trajectories are inevitably collected in unsatisfactory quality due to device constraints. To address this issue, previous studies have proposed numerous trajectory recovery methods to augment the quality of such trajectories, thereby ensuring the performance of related applications. However, these methods all assume the awareness of the recovery positions in advance, which is a condition not always available in practice. In this paper, we discard this strong assumption and focus on trajectory recovery with irregular time intervals as a more prevalent setting in downstream scenarios. We propose a novel framework, called TERI, to tackle trajectory recovery without prior information in a two-stage process, where recovery positions are first detected, followed by the imputation of the missing data points. In each stage, TERI framework deploys a model named RETE, which is based on Transformer encoder architecture enhanced by novel designs to boost the performance for the new problem setting. Specifically, RETE features a learnable Fourier encoding module to better model spatial and temporal correlations, and integrates collective transition pattern learning and trajectory contrastive learning to effectively capture sequential transition patterns. Extensive experiments on three real-world datasets demonstrate that TERI consistently outperforms all the baselines by a significant large margin.

Post-pandemic modeling of COVID-19: Waning immunity determines recurrence frequency

There are many factors in the current phase of the COVID-19 pandemic that signal the need for new modeling ideas. In fact, most traditional infectious disease models do not address adequately the waning immunity, in particular as new emerging variants have been able to break the immune shield acquired either by previous infection by a different strain of the virus, or by inoculation of vaccines not effective for the current variant. Furthermore, in a post-pandemic landscape in which reporting is no longer a default, it is impossible to have reliable quantitative data at the population level. Our contribution to COVID-19 post-pandemic modeling is a simple mathematical predictive model along the age-distributed population framework, that can take into account the waning immunity in a transparent and easily controllable manner. Numerical simulations show that under static conditions, the model produces periodic solutions that are qualitatively similar to the reported data, with the period determined by the immunity waning profile. Evidence from the mathematical model indicates that the immunity dynamics is the main factor in the recurrence of infection spikes, however, irregular perturbation of the transmission rate, due to either mutations of the pathogen or human behavior, may result in suppression of recurrent spikes, and irregular time intervals between consecutive peaks. The spike amplitudes are sensitive to the transmission rate and vaccination strategies, but also to the skewness of the profile describing the waning immunity, suggesting that these factors should be taken into consideration when making predictions about future outbreaks.

PPAD: a deep learning architecture to predict progression of Alzheimer's disease.

Alzheimer's disease (AD) is a neurodegenerative disease that affects millions of people worldwide. Mild cognitive impairment (MCI) is an intermediary stage between cognitively normal state and AD. Not all people who have MCI convert to AD. The diagnosis of AD is made after significant symptoms of dementia such as short-term memory loss are already present. Since AD is currently an irreversible disease, diagnosis at the onset of the disease brings a huge burden on patients, their caregivers, and the healthcare sector. Thus, there is a crucial need to develop methods for the early prediction AD for patients who have MCI. Recurrent neural networks (RNN) have been successfully used to handle electronic health records (EHR) for predicting conversion from MCI to AD. However, RNN ignores irregular time intervals between successive events which occurs common in electronic health record data. In this study, we propose two deep learning architectures based on RNN, namely Predicting Progression of Alzheimer's Disease (PPAD) and PPAD-Autoencoder. PPAD and PPAD-Autoencoder are designed for early predicting conversion from MCI to AD at the next visit and multiple visits ahead for patients, respectively. To minimize the effect of the irregular time intervals between visits, we propose using age in each visit as an indicator of time change between successive visits. Our experimental results conducted on Alzheimer's Disease Neuroimaging Initiative and National Alzheimer's Coordinating Center datasets showed that our proposed models outperformed all baseline models for most prediction scenarios in terms of F2 and sensitivity. We also observed that the age feature was one of top features and was able to address irregular time interval problem. https://github.com/bozdaglab/PPAD.

A self-supervised learning-based approach to clustering multivariate time-series data with missing values (SLAC-Time): An application to TBI phenotyping

Self-supervised learning approaches provide a promising direction for clustering multivariate time-series data. However, real-world time-series data often include missing values, and the existing approaches require imputing missing values before clustering, which may cause extensive computations and noise and result in invalid interpretations. To address these challenges, we present a Self-supervised Learning-based Approach to Clustering multivariate Time-series data with missing values (SLAC-Time). SLAC-Time is a Transformer-based clustering method that uses time-series forecasting as a proxy task for leveraging unlabeled data and learning more robust time-series representations. This method jointly learns the neural network parameters and the cluster assignments of the learned representations. It iteratively clusters the learned representations with the K-means method and then utilizes the subsequent cluster assignments as pseudo-labels to update the model parameters. To evaluate our proposed approach, we applied it to clustering and phenotyping Traumatic Brain Injury (TBI) patients in the Transforming Research and Clinical Knowledge in Traumatic Brain Injury (TRACK-TBI) study. Clinical data associated with TBI patients are often measured over time and represented as time-series variables characterized by missing values and irregular time intervals. Our experiments demonstrate that SLAC-Time outperforms the baseline K-means clustering algorithm in terms of silhouette coefficient, Calinski Harabasz index, Dunn index, and Davies Bouldin index. We identified three TBI phenotypes that are distinct from one another in terms of clinically significant variables as well as clinical outcomes, including the Extended Glasgow Outcome Scale (GOSE) score, Intensive Care Unit (ICU) length of stay, and mortality rate. The experiments show that the TBI phenotypes identified by SLAC-Time can be potentially used for developing targeted clinical trials and therapeutic strategies.

Predicting chaotic dynamics from incomplete input via reservoir computing with (D+1)-dimension input and output.

Predicting future evolution based on incomplete information of the past is still a challenge even though data-driven machine learning approaches have been successfully applied to forecast complex nonlinear dynamics. The widely adopted reservoir computing (RC) can hardly deal with this since it usually requires complete observations of the past. In this paper, a scheme of RC with (D+1)-dimension input and output (I/O) vectors is proposed to solve this problem, i.e., the incomplete input time series or dynamical trajectories of a system, in which certain portion of states are randomly removed. In this scheme, the I/O vectors coupled to the reservoir are changed to (D+1)-dimension, where the first D dimensions store the state vector as in the conventional RC, and the additional dimension is the corresponding time interval. We have successfully applied this approach to predict the future evolution of the logistic map and Lorenz, Rössler, and Kuramoto-Sivashinsky systems, where the inputs are the dynamical trajectories with missing data. The dropoff rate dependence of the valid prediction time (VPT) is analyzed. The results show that it can make forecasting with much longer VPT when the dropoff rate θ is lower. The reason for the failure at high θ is analyzed. The predictability of our RC is determined by the complexity of the dynamical systems involved. The more complex they are, the more difficult they are to predict. Perfect reconstructions of chaotic attractors are observed. This scheme is a pretty good generalization to RC and can treat input time series with regular and irregular time intervals. It is easy to use since it does not change the basic architecture of conventional RC. Furthermore, it can make multistep-ahead prediction just by changing the time interval in the output vector into a desired value, which is superior to conventional RC that can only do one-step-ahead forecasting based on complete regular input data.

Time-distance vision transformers in lung cancer diagnosis from longitudinal computed tomography.

Features learned from single radiologic images are unable to provide information about whether and how much a lesion may be changing over time. Time-dependent features computed from repeated images can capture those changes and help identify malignant lesions by their temporal behavior. However, longitudinal medical imaging presents the unique challenge of sparse, irregular time intervals in data acquisition. While self-attention has been shown to be a versatile and efficient learning mechanism for time series and natural images, its potential for interpreting temporal distance between sparse, irregularly sampled spatial features has not been explored. In this work, we propose two interpretations of a time-distance vision transformer (ViT) by using (1) vector embeddings of continuous time and (2) a temporal emphasis model to scale self-attention weights. The two algorithms are evaluated based on benign versus malignant lung cancer discrimination of synthetic pulmonary nodules and lung screening computed tomography studies from the National Lung Screening Trial (NLST). Experiments evaluating the time-distance ViTs on synthetic nodules show a fundamental improvement in classifying irregularly sampled longitudinal images when compared to standard ViTs. In cross-validation on screening chest CTs from the NLST, our methods (0.785 and 0.786 AUC respectively) significantly outperform a cross-sectional approach (0.734 AUC) and match the discriminative performance of the leading longitudinal medical imaging algorithm (0.779 AUC) on benign versus malignant classification. This work represents the first self-attention-based framework for classifying longitudinal medical images. Our code is available at https://github.com/tom1193/time-distance-transformer.