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The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

The explosive growth of IoT-enabled sensors is producing enormous amounts of time series data across many domains, offering valuable opportunities to extract insights through temporal pattern mining. Among these patterns, an important class…

Time series forecasting plays a crucial role in various applications, particularly in healthcare, where accurate predictions of future health trajectories can significantly impact clinical decision-making. Ensuring transparency and…

Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…

Multivariate time series data come as a collection of time series describing different aspects of a certain temporal phenomenon. Anomaly detection in this type of data constitutes a challenging problem yet with numerous applications in…

In this paper, we aim to improve multivariate anomaly detection (AD) by modeling the \textit{time-varying non-linear spatio-temporal correlations} found in multivariate time series data . In multivariate time series data, an anomaly may be…

Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…

This paper presents an extensive empirical study on the integration of dimensionality reduction techniques with advanced unsupervised time series anomaly detection models, focusing on the MUTANT and Anomaly-Transformer models. The study…

Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications, including video surveillance, medical imaging data, and urban traffic monitoring. Existing anomaly detection methods focus mainly on…

Time series data appears in a variety of applications such as smart transportation and environmental monitoring. One of the fundamental problems for time series analysis is time series forecasting. Despite the success of recent deep time…

Empirical mode decomposition (EMD) has developed into a prominent tool for adaptive, scale-based signal analysis in various fields like robotics, security and biomedical engineering. Since the dramatic increase in amount of data puts…

Modeling matrix-valued time series is an interesting and important research topic. In this paper, we extend the method of Chang et al. (2017) to matrix-valued time series. For any given $p\times q$ matrix-valued time series, we look for…

Current time-series forecasting problems use short-term weather attributes as exogenous inputs. However, in specific time-series forecasting solutions (e.g., demand prediction in the supply chain), seasonal climate predictions are crucial…

Time series anomaly detection is important in modern large-scale systems and is applied in a variety of domains to analyze and monitor the operation of diverse systems. Unsupervised approaches have received widespread interest, as they do…

Robust anomaly detection is a requirement for monitoring complex modern systems with applications such as cyber-security, fraud prevention, and maintenance. These systems generate multiple correlated time series that are highly seasonal and…

Real-world phenomena that can be formulated as signals are often affected by a number of factors and appear as multi-component modes. To understand and process such phenomena, "divide-and-conquer" is probably the most common strategy to…

We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are…

The paper suggests a method of recovering missing values for sequences, including sequences with a multidimensional index, based on optimal approximation by processes featuring spectrum degeneracy. The problem is considered in the pathwise…

In this paper we propose a novel machine-learning method for anomaly detection applicable to data with periodic characteristics where randomly varying period lengths are explicitly allowed. A multi-dimensional time series analysis is…

The performance of transformers for time-series forecasting has improved significantly. Recent architectures learn complex temporal patterns by segmenting a time-series into patches and using the patches as tokens. The patch size controls…