Related papers: Data-driven pattern identification and outlier det…
We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…
Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…
Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…
Signal decomposition (SD) approaches aim to decompose non-stationary signals into their constituent amplitude- and frequency-modulated components. This represents an important preprocessing step in many practical signal processing…
The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank $k$ approximation of a matrix $A$ using matrix-vector products with standard Gaussian vectors. Here, we generalize the…
Time series data occurs widely, and outlier detection is a fundamental problem in data mining, which has numerous applications. Existing autoencoder-based approaches deliver state-of-the-art performance on challenging real-world data but…
To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…
Recent advances in digitization have led to the availability of multivariate time series data in various domains, enabling real-time monitoring of operations. Identifying abnormal data patterns and detecting potential failures in these…
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,…
We apply the truncated singular value decomposition (SVD) to extract the underlying 2D correlation functions from small-angle scattering patterns. We test the approach by transforming the simulated data of ellipsoidal particles and show…
Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared…
This paper presents a post-processing algorithm for training fair neural network regression models that satisfy statistical parity, utilizing an explainable singular value decomposition (SVD) of the weight matrix. We propose a linear…
Outlier detection aims to identify unusual data instances that deviate from expected patterns. The outlier detection is particularly challenging when outliers are context dependent and when they are defined by unusual combinations of…
In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we developed an incremental approach to compute the proper orthogonal decomposition (POD) of PDE simulation data. Specifically, we developed an…
The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
In order to allow machine learning algorithms to extract knowledge from raw data, these data must first be cleaned, transformed, and put into machine-appropriate form. These often very time-consuming phase is referred to as preprocessing.…
The development of the manufacturing systems has made it increasingly necessary to monitor the data generated by multiple interconnected subsystems with rapid incoming of samples. Based on incremental Singular Value Decomposition (ISVD), we…
We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with…
Randomized singular value decomposition (RSVD) is a class of computationally efficient algorithms for computing the truncated SVD of large data matrices. Given an $m \times n$ matrix $\widehat{{\mathbf M}}$, the prototypical RSVD algorithm…