Finding the reduced-dimensional structure is critical to understanding complex networks. Existing approaches such as spectral clustering are applicable only when the full network is explicitly observed. In this paper, we focus on the online factorization and partition of implicit large lumpable networks based on observations from an associated random walk. We formulate this into a nonconvex stochastic factorization problem and propose an efficient and scalable stochastic generalized Hebbian algorithm (GHA). The algorithm is able to process random walk data in a streaming fashion and learn a low-dimensional representation for each vertex. By applying a diffusion approximation analysis, we show that the continuous-time limiting process of the stochastic algorithm converges globally to the “principal components” of the Markov chain. We also establish a finite-sample error bound that matches the nonimprovable state-of-art result for online factorization. Once learned the low-dimensional state representations, we further apply clustering techniques to recover the network partition. We show that when the associated Markov process is lumpable, one can recover the partition exactly with high probability given sufficient data. We apply the proposed approach to model the traffic flow of Manhattan as city-wide random walks. By using our algorithm to analyze the taxi trip data, we discover a latent partition of the Manhattan city that closely matches the traffic dynamics.
more »
« less
Seasonal Disorder in Urban Traffic Patterns: A Low Rank Analysis
Abstract This article proposes several advances to sparse nonnegative matrix factorization (SNMF) as a way to identify large-scale patterns in urban traffic data. The input to our model is traffic counts organized by time and location. Nonnegative matrix factorization additively decomposes this information, organized as a matrix, into a linear sum of temporal signatures. Penalty terms encourage this factorization to concentrate on only a few temporal signatures, with weights which are not too large. Our interest here is to quantify and compare the regularity of traffic behavior, particularly across different broad temporal windows. In addition to the rank and error, we adapt a measure introduced by Hoyer to quantify sparsity in the representation. Combining these, we construct several curves which quantify error as a function of rank (the number of possible signatures) and sparsity; as rank goes up and sparsity goes down, the approximation can be better and the error should decreases. Plots of several such curves corresponding to different time windows leads to a way to compare disorder/order at different time scalewindows. In this paper, we apply our algorithms and procedures to study a taxi traffic dataset from New York City. In this dataset, we find weekly periodicity in the signatures, which allows us an extra framework for identifying outliers as significant deviations from weekly medians. We then apply our seasonal disorder analysis to the New York City traffic data and seasonal (spring, summer, winter, fall) time windows. We do find seasonal differences in traffic order.
more »
« less
- Award ID(s):
- 1727785
- NSF-PAR ID:
- 10243516
- Date Published:
- Journal Name:
- Journal of Big Data Analytics in Transportation
- Volume:
- 3
- Issue:
- 1
- ISSN:
- 2523-3556
- Page Range / eLocation ID:
- 43 to 60
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Imputing missing data is a critical task in data-driven intelligent transportation systems. During recent decades there has been a considerable investment in developing various types of sensors and smart systems, including stationary devices (e.g., loop detectors) and floating vehicles equipped with global positioning system (GPS) trackers to collect large-scale traffic data. However, collected data may not include observations from all road segments in a traffic network for different reasons, including sensor failure, transmission error, and because GPS-equipped vehicles may not always travel through all road segments. The first step toward developing real-time traffic monitoring and disruption prediction models is to estimate missing values through a systematic data imputation process. Many of the existing data imputation methods are based on matrix completion techniques that utilize the inherent spatiotemporal characteristics of traffic data. However, these methods may not fully capture the clustered structure of the data. This paper addresses this issue by developing a novel data imputation method using PARATUCK2 decomposition. The proposed method captures both spatial and temporal information of traffic data and constructs a low-dimensional and clustered representation of traffic patterns. The identified spatiotemporal clusters are used to recover network traffic profiles and estimate missing values. The proposed method is implemented using traffic data in the road network of Manhattan in New York City. The performance of the proposed method is evaluated in comparison with two state-of-the-art benchmark methods. The outcomes indicate that the proposed method outperforms the existing state-of-the-art imputation methods in complex and large-scale traffic networks.
-
An effective real-time estimation of the travel time for vehicles, using AVL (Automatic Vehicle Locators) has added a new dimension to the smart city planning. In this paper, the authors used data collected over several months from a transit agency and show how this data can be potentially used to learn patterns of travel time during specially planned events like NFL (National Football League) games and music award ceremonies. The impact of NFL games along with consideration of other factors like weather, traffic condition, distance is discussed with their relative importance to the prediction of travel time. Statistical learning models are used to predict travel time and subsequently assess the cascading effects of delay. The model performance is determined based on its predictive accuracy according to the out-of-sample error. In addition, the models help identify the most significant variables that influence the delay in the transit system. In order to compare the actual and predicted travel time for days having special events, heat maps are generated showing the delay impacts in different time windows between two timepoint-segments in comparison to a non-game day. This work focuses on the prediction and visualization of the delay in the public transit system and the analysis of its cascading effects on the entire transportation network. According to the study results, the authors are able to explain more than 80% of the variance in the bus travel time at each segment and can make future travel predictions during planned events with an out-of-sample error of 2.0 minutes using information on the bus schedule, traffic, weather, and scheduled events. According to the variable importance analysis, traffic information is most significant in predicting the delay in the transit system.more » « less
-
Congested traffic wastes billions of liters of fuel and is a significant contributor to Green House Gas (GHG) emissions. Although convenient, ride sharing services such as Uber and Lyft are becoming a significant contributor to these emissions not only because of added traffic but by spending time on the road while waiting for passengers. To help improve the impact of ride sharing, we propose an algorithm to optimize the efficiency of drivers searching for customers. In our model, the main goal is to direct drivers represented as idle agents, i.e., not currently assigned a customer or resource, to locations where we predict new resources to appear. Our approach uses non-negative matrix factorization (NMF) to model and predict the spatio-temporal distributions of resources. To choose destinations for idle agents, we employ a greedy heuristic that strikes a balance between distance greed, i.e., to avoid long trips without resources and resource greed, i.e., to move to a location where resources are expected to appear following the NMF model. To ensure that agents do not oversupply areas for which resources are predicted and under supply other areas, we randomize the destinations of agents using the predicted resource distribution within the local neighborhood of an agent. Our experimental evaluation shows that our approach reduces the search time of agents and the wait time of resources using real-world data from Manhattan, New York, USA.more » « less
-
more » « less
Abstract Nonnegative matrix factorization (NMF) is widely used to analyze high-dimensional count data because, in contrast to real-valued alternatives such as factor analysis, it produces an interpretable parts-based representation. However, in applications such as spatial transcriptomics, NMF fails to incorporate known structure between observations. Here, we present nonnegative spatial factorization (NSF), a spatially-aware probabilistic dimension reduction model based on transformed Gaussian processes that naturally encourages sparsity and scales to tens of thousands of observations. NSF recovers ground truth factors more accurately than real-valued alternatives such as MEFISTO in simulations, and has lower out-of-sample prediction error than probabilistic NMF on three spatial transcriptomics datasets from mouse brain and liver. Since not all patterns of gene expression have spatial correlations, we also propose a hybrid extension of NSF that combines spatial and nonspatial components, enabling quantification of spatial importance for both observations and features. A TensorFlow implementation of NSF is available from
https://github.com/willtownes/nsf-paper .
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s42421-021-00033-4
