A new neural approach for generating origin-destination matrices in ABMs.
problem Challenges in generating origin-destination matrices for ABMs, including discretisation errors and inability to explore multimodal distributions.
method A computationally efficient framework that learns trip intensity through a neural differential equation, operating directly on the discrete combinatorial space.
result Outperforms prior art in terms of reconstruction error and ground truth matrix coverage, at a fraction of the computational cost.
Predicts fine-grained OD matrices for ridesharing platforms to optimize supply-demand balance.
problem Accurately predicting spatial-temporal OD demands for ridesharing platforms.
method OD-CED model combining unsupervised space coarsening and encoder-decoder architecture.
result Significant improvement in prediction accuracy (45% RMSE reduction, 60% WAPE reduction).
Modern intelligent transportation systems provide data that allow real-time dynamic demand prediction, which is essential for planning and operations. The main challenge of prediction of dynamic Origin-Destination (O-D) demand matrices is that demands cannot be directly measured by traffic sensors; instead, they have t…
Origin-destination (OD) matrices are often used in urban planning, where a city is partitioned into regions and an element (i, j) in an OD matrix records the cost (e.g., travel time, fuel consumption, or travel speed) from region i to region j. In this paper, we partition a day into multiple intervals, e.g., 96 15-min …
Proposes a new model to predict travel demand with zero-inflated and long-tail characteristics.
problem Sparse and long-tailed travel demand data with many zeros.
method Spatial-Temporal Tweedie Graph Neural Network (STTD) using Tweedie distribution.
result STTD provides accurate predictions and precise confidence intervals.
The study introduces measures of collective mobility from aggregated OD data.
problem Understanding large-scale mobility patterns from aggregated data.
method Developed a framework using synthetic and real data to interpret network-level mobility.
result Aggregated mobility measures reveal network structure and flow constraints.
Study uses neural networks to predict travel times for public transportation.
problem Inaccurate travel time predictions due to road traffic irregularities.
method Developed two neural network models (MLP and LSTM) using OD travel time matrix.
result Both models can make near-accurate predictions, but LSTM is more susceptible to noise.
Due to the significance of transportation planning, traffic management, and dispatch optimization, predicting passenger origin-destination has emerged as a crucial requirement for intelligent transportation systems management. In this study, we present a model designed to forecast the origin and destination of travels …
Taxi demand prediction has recently attracted increasing research interest due to its huge potential application in large-scale intelligent transportation systems. However, most of the previous methods only considered the taxi demand prediction in origin regions, but neglected the modeling of the specific situation of …
In this study, we present a machine learning approach to infer the worker and student mobility flows on daily basis from static censuses. The rapid urbanization has made the estimation of the human mobility flows a critical task for transportation and urban planners. The primary objective of this paper is to complete i…
New model predicts travel demand uncertainty with high accuracy.
problem Uncertainty and sparsity in sparse travel demand prediction.
method Spatial-Temporal Zero-Inflated Negative Binomial Graph Neural Network (STZINB-GNN).
result STZINB-GNN outperforms benchmarks in predicting travel demand uncertainty.
Paper predicts in-situ metro passenger density using smart card data.
problem Crowd management in metro systems.
method Statistical models and EM algorithm for time-dependent OD matrix and travel time cost estimation.
result Accurate prediction of in-situ passenger density for future time points.
AI helps Vancouver identify where off-street parking saves time and space.
problem On-street parking inefficiencies and associated costs in Vancouver.
method Developed AI models for on-street and off-street parking, comparing time costs.
result Many areas off-street parking saves time and space, aligning with city goals.
OpFlow predicts robust OD flows by learning choice potentials conditioned on spatial exposures.
problem Deep models trained on raw counts are vulnerable to distribution shift.
method OpFlow learns row-centered choice potentials and reconstructs flows by combining them with a calibrated origin scale.
result OpFlow improves robustness under environment shifts, as shown by controlled synthetic shifts and a real-world experiment.
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
Minimal submanifolds in matrix spaces proven for specific ranks.
problem Minimal submanifolds in matrix spaces.
method Proving semialgebraic sets of matrices are minimal.
result Rectangular, skew-symmetric, and symmetric matrices with prescribed eigenvalues are minimal.
Computes isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
problem Computing isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
method Algorithm for solving a matrix equation to compute isotropy subgroups.
result Computed isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
Study on random matrices in deep neural networks with IID entries.
problem Distribution of singular values in product of random matrices for deep neural networks.
method Random matrix theory with a streamlined approach for non-Gaussian data.
result Generalization of macroscopic universality property to non-Gaussian data.
Financial markets analyzed by reducing correlation matrix complexity.
problem Understanding complex financial market correlations.
method Coarse graining Pearson correlation matrices into Guhr matrices by market sectors.
result Significant reduction in the number of relevant variables.
Study isotropy groups for complex orthogonal and skew-symmetric matrices.
problem Understanding isotropy subgroups of orthogonal similarity transformations.
method Analysis of group structure of nonsingular block matrices.
result Group structure of isotropy subgroups related to block Toeplitz matrices.
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important difference is that the population covariance matrices, which are assumed to be non-random…
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a s…
Study of strictly accretive matrices using Finsler geometry.
problem Characterize the set of strictly accretive matrices.
method Introduced Finsler metrics and characterized geodesics and distance.
result Geodesic distance applied to matrix approximation problem.
Minimal spectral radii found for specific matrix types.
problem Finding smallest spectral radii for certain matrix classes.
method Analyzing skew-reciprocal integer matrices of fixed even dimensions.
result Most classes of matrices have smaller spectral radii than their reciprocal counterparts.
Researchers develop geodesics for a new metric on correlation matrices.
problem Lack of intrinsic tools for statistical analyses of correlation matrices.
method Developed geodesics for the quotient-affine metric on full-rank correlation matrices.
result Provided fundamental Riemannian operations for the quotient-affine metric.
We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.
New methods for sketching non-PSD matrices improve regression and optimization tasks.
problem Efficiently handling non-PSD matrices in computations.
method Developed novel matrix sketching techniques for non-PSD and complex matrices.
result Improved performance in convex and non-convex optimization, regression, and vector-matrix-vector queries.
Improved method for computing Fréchet means on SPD matrices.
problem Computing Fréchet means on the manifold of SPD matrices.
method Random matrix theory-based approach for estimating Fréchet means.
result Significantly outperforms state-of-the-art methods in experiments.
Algorithm finds isotropy subgroups of orthogonal similarity on symmetric matrices.
problem Computing isotropy subgroups of orthogonal similarity on symmetric matrices.
method Algorithmic procedure solving a Toeplitz matrix equation.
result Structure of isotropy subgroups described.
We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…
Method estimates M-matrices in graphical models with improved accuracy.
problem Estimating M-matrices as precision matrices in Gaussian graphical models.
method Adaptive multiple-stage estimation method solving weighted ℓ1-regularized problems.
result Method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification.
Algorithm calculates Seifert matrices for colored links.
problem Computing Seifert matrices for colored links.
method Developed an algorithm implemented in Clasper software.
result Computes Seifert matrices, potential function, and signatures.
A framework estimates multiple precision matrices with shared structures.
problem Estimating multiple precision matrices with shared structures.
method Penalized likelihood framework with iterative algorithm alternating between convex and clustering problems.
result The method outperforms competitors and performs similarly to methods using prior information.
In this paper we extend DDVV-type inequalities involving the Frobenius norm of commutators from real symmetric and skew-symmetric matrices to Hermitian and skew-Hermitian matrices.
Proposes a new Sliced-Wasserstein distance for covariance matrices in M/EEG signals.
problem Efficiently dealing with distributions of covariance matrices in M/EEG multivariate time series.
method Defines a Sliced-Wasserstein distance for symmetric positive definite matrices and applies it to brain-age prediction and Brain Computer Interface applications.
result Demonstrates computational efficiency and strong theoretical guarantees for the proposed distance.
Study extends bounds on sample covariance matrices with general dependence.
problem Quantitative bounds on sample covariance matrices with i.i.d. columns.
method Extends previous work on deterministic equivalent to rectangular random matrices with general dependence structure.
result Proves quantitative bounds involving dimensions and spectral parameter, including closer proximity to real positive semi-line.
New k-means method clusters radar image sequences using SPD matrices.
problem Clustering radar image sequences efficiently.
method Developed k-means on SPD matrices for non-Euclidean data. result Effective clustering of radar image sequences via SPD matrices.
Kaleidoscope matrices improve model quality and inference speed.
problem Choosing structured linear transformations for efficiency and accuracy.
method Introduce kaleidoscope matrices that can capture any structured matrix with near-optimal space and time complexity. Learn these matrices automatically within end-to-end pipelines.
result Kaleidoscope matrices can improve model quality and inference speed.
Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such matrices have long been leveraged for algorithmic purposes, little is known about their impact on statistical estimation. In this work, we …
A method learns matrix factorization from diverse matrices and applies the knowledge to unseen matrices.
problem Matrix factorization without shared rows or columns.
method Neural network meta-learned to minimize expected imputation error using MAP estimation.
result The method can impute missing values from unseen matrices efficiently.
The paper identifies and critiques problems with risk matrices using ordinal scales.
problem Problems with risk matrices using ordinal scales.
method Overview of risk assessment process, explanation of fallacies, and suggestions for improvement.
result The paper proposes avoiding risk matrices and using fully quantitative methods instead.
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of activity that are reproducible with statistically significant frequency compared…
Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computation…
In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erdős-Mordell inequality, we establish the DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system …
In this paper, we study the problem of compressed sensing using binary measurement matrices and ℓ1-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to achieve robust sparse recovery with binary matrices. We establish sufficient conditi…
Study of J-Hermitian matrices and geometric mean definition.
problem Understanding the cone of J-Hermitian matrices and its geometric mean.
method Analysis of the cone structure, Riemannian structure, and definition of J-geometric mean.
result Uniquely characterized J-geometric mean defined as a solution to a Riccati-type equation.
Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.
problem Matching vertices in two correlated Erdős-Rényi graphs.
method Iterative matching algorithm for correlated Gaussian Wigner matrices.
result First polynomial time algorithm for graph matching with arbitrarily small constant correlation.
We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we describe the full group of isometries