The last decade has seen a flurry of research on all-pairs-similarity-search (or, self-join) for text, DNA, and a handful of other datatypes, and these systems have been applied to many diverse data mining problems. Surprisingly, however, little progress has been made on addressing this problem for time series subseque…
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48 results for “matrix time series”
High-dimensional time series prediction is needed in applications as diverse as demand forecasting and climatology. Often, such applications require methods that are both highly scalable, and deal with noisy data in terms of corruptions or missing values. Classical time series methods usually fall short of handling bot…
Paper introduces SMM for forecasting multiple time series with missing values.
problem Forecasting multiple time series with missing and noisy values.
method Sliding Mask Method (SMM) using Non-negative Matrix Factorization (NMF).
result The method outperforms state-of-the-art methods in time series forecasting.
We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which st…
Deformation of semi-circle law for the correlated time series and Phase transitioncond-mat.stat-mech
Study on eigenvalue distribution of correlated time series deforming the semi-circle law.
problem Eigenvalue distribution of correlated time series differs from the semi-circle law.
method Analysis of Wigner random matrix with temporal correlation.
result Eigenvalue distribution converges to a deformed semi-circle law with longer tail and higher peak.
New method models matrix time series using tensor CP-decomposition.
problem Modeling matrix time series with reduced complexity.
method One-pass estimation via generalized eigenanalysis and refined projection.
result Component coefficient vectors estimated consistently with certain rates.
Split-and-Conquer: Distributed Factor Modeling for High-Dimensional Matrix-Variate Time Seriesstat.ML
A distributed framework for reducing high-dimensional matrix-variate time series data.
problem Reducing dimensionality of high-dimensional, heterogeneous matrix-variate time series data.
method Data partitioning, distributed two-dimensional tensor PCA, aggregation, final PCA, factor matrix computation.
result Preserves latent matrix structure, improves computational efficiency and information utilization.
A new method is proposed to compute connectivity measures on multivariate time series with gaps. Rather than removing or filling the gaps, the rows of the joint data matrix containing empty entries are removed and the calculations are done on the remainder matrix. The method, called measure adapted gap removal (MAGR), …
A method for inferring graph from multivariate time series using ADMM.
problem Inferring conditional independence graph from multivariate Gaussian time series.
method Formulated as multi-attribute graph estimation, used ADMM to minimize penalized negative log-likelihood.
result Proposed method outperforms existing frequency-domain approaches in graph edge detection.
Proposes a GNN for multivariate time-series prediction with filtering.
problem Low signal-to-noise ratio in complex systems data.
method Integrates a spatial-temporal GNN with a matrix filtering module to generate filtered graphs.
result Proposed model outperforms baseline approaches in multivariate time-series prediction.
In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand the structural evolution of the financial networks with time. For a set of time-v…
Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual serie…
Improved deep probabilistic time series forecasting by learning error autocorrelation.
problem Simplification of time-independent error process and lack of serial correlation in existing models.
method Proposes a training method that incorporates error autocorrelation to enhance probabilistic forecasting accuracy.
result Improves predictive accuracy and uncertainty quantification across multiple datasets.
Novel estimation methods improve MAR model accuracy for high-dimensional time series.
problem Limited estimation techniques for Matrix Autoregressive (MAR) models.
method Adapted Yule-Walker equations and Burg's method.
result Proposed methods achieve comparable model fit to VAR models.
Optimal model selection for forecasting large collections of short time series using latent space.
problem Challenges in choosing among multiple forecasting methods for large, high-dimensional time series with limited data.
method Combining low-rank temporal matrix factorization with optimal model selection using cross-validation.
result Forecasting latent factors leads to significant performance gains compared to direct uni-variate model application.
In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices an…
Graphical models improve portfolio optimization for financial time series.
problem Optimizing portfolios with time-varying covariance patterns.
method Various graphical models (PCA-KMeans, autoencoders, dynamic clustering, structural learning) to capture covariance matrix patterns.
result Graphical models outperform baseline methods in generating steady returns with low risk.
MPSTime uses matrix-product states for efficient time-series ML.
problem Learning complex correlations in time-series data.
method Developed an MPS-based algorithm for joint probability distribution learning.
result MPSTime efficiently learns time-series probability distributions.
Online graph learning from matrix-valued time series data.
problem Identifying dependency structure among sensors in a network.
method Extends VAR models to matrix-variate models, proposes online procedures for graph learning, and introduces Lasso-type approaches.
result Demonstrates effectiveness of online graph learning methods in both synthetic and real data.
Non-parametric Determination of Real-Time Lag Structure between Two Time Series: the "Optimal Thermal Causal Path" Methodcond-mat.stat-mech
We introduce a novel non-parametric methodology to test for the dynamical time evolution of the lag-lead structure between two arbitrary time series. The method consists in constructing a distance matrix based on the matching of all sample data pairs between the two time series. Then, the lag-lead structure is searched…
Reservoir computing's success depends on mapping different input time series to separable states.
problem Quantifying the ability of random linear reservoirs to map different input time series.
method Mathematical framework using spectral properties of the connectivity matrix.
result Separation capacity is fully characterized by the spectral properties of the connectivity matrix.
Overview of high-dimensional time series regression methods.
problem Estimation and inference with high-dimensional time series data.
method Limit theory for high-dimensional dependent data, asymptotic theory for time series regression, statistical learning methods.
result Main limit theory results and asymptotic theory for high-dimensional time series regression.
FLANDERS detects and blocks extreme model poisoning in federated learning.
problem Resilience against large-scale model poisoning attacks in federated learning.
method FLANDERS treats client updates as matrix-valued time series and identifies outliers using autoregressive forecasting.
result FLANDERS significantly improves robustness in federated learning across various attacks.
Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecastingstat.ML
The paper uses random matrix theory for multi-task regression, improving time series forecasting.
problem Improving time series forecasting using multi-task regression.
method Applying random matrix theory to multi-task regression problems, deriving closed-form solutions for optimization.
result Provides a robust foundation for hyperparameter optimization in multi-task regression scenarios.
This article investigates the correlation structure of the global crude oil market using the daily returns of 71 oil price time series across the world from 1992 to 2012. We identify from the correlation matrix six clusters of time series exhibiting evident geographical traits, which supports Weiner's (1991) regionaliz…
OLinear forecasts time series more efficiently by transforming data orthogonally.
problem Efficiently forecasting time series with entangled dependencies.
method OLinear uses OrthoTrans to transform data orthogonally, then applies NormLin for linear layer.
result OLinear achieves state-of-the-art performance with high efficiency.
Random, but not so much: A parameterization for the returns and correlation matrix of financial time seriesphysics.soc-ph
A parameterization that is a modified version of a previous work is proposed for the returns and correlation matrix of financial time series and its properties are studied. This parameterization allows easy introduction of non-stationarity and it shows several of the characteristics of the true, observed realizations, …
Noise-cleaning the precision matrix of fMRI time seriescond-mat.stat-mech
Noise-cleaning fMRI brain activity matrices for better precision estimation.
problem Denoise precision matrices of fMRI time series to estimate true matrices.
method Comparison of various noise-cleaning algorithms on synthetic and real fMRI data.
result Optimal Rotationally Invariant Estimator outperforms others in fMRI data.
We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension to scale with the series length . We treat the transition matrix of time series as a nuisance parameter and directly apply sparse principal component…
The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis, the extracted dynamic modes are a generalization of global stability modes. We a…
We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_θ(x) of different parameters θin the VAR model as features to descr…
Paper proposes LATC for multivariate time series prediction and missing data imputation.
problem Large-scale, incomplete, and corrupted multivariate time series data.
method Transforms multivariate time series into a tensor structure, models global and local trends, and uses autoregressive norm.
result Integration of global and local trends improves missing data imputation and rolling prediction.
We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space models where sequential approximate inference results in the factorization of a data…
Proposes RBLDA for multivariate time series data classification.
problem Classifying multivariate time series data.
method Regularized Bilinear Discriminant Analysis (RBLDA) for multivariate time series data.
result RBLDA achieves the best overall recognition performance on real MTS data sets.
Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and time-varying community detection in time-evolving graph sequences. The matrix factori…
We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and relate result to the corresponding ensemble of Wishart random matrices. It turns …
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may not be able to model the complexities of a time series, while a large number of …
The cohomology theory for financial market can allow us to deform Kolmogorov space of time series data over time period with the explicit definition of eight market states in grand unified theory. The anti-de Sitter space induced from a coupling behavior field among traders in case of a financial market crash acts like…
System uses TDA for user segmentation and demand forecasting.
problem User loyalty and demand forecasting challenges.
method TDA-based clustering of time series data with matrix factorization.
result Significantly higher accuracy in clustering and demand forecasting.
New method infers graph from dependent matrix data.
problem Inferring graph from dependent matrix data.
method Sparse-group lasso-based frequency-domain formulation with ADMM approach.
result Local convergence of inverse PSD estimators to true value.
This paper presents a novel time series clustering method, the self-organising eigenspace map (SOEM), based on a generalisation of the well-known self-organising feature map (SOFM). The SOEM operates on the eigenspaces of the embedded covariance structures of time series which are related directly to modes in those tim…
Hankel low-rank approximation and completion in time series analysis and forecasting: a brief reviewmath.NA
The paper reviews Hankel low-rank methods for time series analysis and forecasting.
problem Developing efficient methods for time series analysis and forecasting.
method Hankel low-rank approximation and completion techniques.
result Discussion of methods and challenges in obtaining optimal solutions.
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among brain regions. In this paper, we develop a non-asymptotic theory for regularize…
TMTF improves time series visualization by separating dynamic regimes.
problem Misleading global transition matrix in time series analysis.
method Temporal chunking, local transition matrices, and image assembly.
result Temporal segmentation reveals distinct transition dynamics.
Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updatescs.LG
Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extends classic nonnegative matrix factorization (NMF) to extract short-lived temporal motifs from a long …
Identification of cross and autocorrelations in time series within an approach based on Wigner eigenspectrum of random matricesphysics.data-an
We present an original and novel method based on random matrix approach that enables to distinguish the respective role of temporal autocorrelations inside given time series and cross correlations between various time series. The proposed algorithm is based on properties of Wigner eigenspectrum of random matrices inste…
Enhances Transformer models for multivariate time series with dataset-specific channel masks.
problem Capturing channel dependency in multivariate time series models.
method Introduces partial channel dependence and channel masks to refine channel dependency in Transformers.
result Improves model performance across diverse tasks and datasets.
Sparse Tucker Decomposition and Graph Regularization for High-Dimensional Time Series Forecastingmath.ST
Sparse Tucker decomposition with graph regularization improves time series forecasting accuracy.
problem High-dimensional time series forecasting with over-parameterization issue.
method Sparse Tucker decomposition and graph regularization for tensor-based model.
result Non-asymptotic error bound and superior performance in numerical experiments.