Related papers: Polar $n$-Complex and $n$-Bicomplex Singular Value…
Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
A first order trace formula is obtained for a higher-order differential operator on a segment in the case where the perturbation is an operator of multiplication by a finite complex-valued measure. For the operators of even order $n\ge4$ a…
We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent Structures. Our approach differs from the usual Lagrangian Data Assimilation approach,…
The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…
In this paper, we revisit the problem of local optimization in RANSAC. Once a so-far-the-best model has been found, we refine it via Dual Principal Component Pursuit (DPCP), a robust subspace learning method with strong theoretical support…
Tensors are becoming increasingly common in data mining, and consequently, tensor factorizations are becoming more and more important tools for data miners. When the data is binary, it is natural to ask if we can factorize it into binary…
The best pair problem aims to find a pair of points that minimize the distance between two disjoint sets. In this paper, we formulate the classical robust principal component analysis (RPCA) as the best pair; which was not considered…
Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…
The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…
Recently, Ar{\i}kan introduced the method of channel polarization on which one can construct efficient capacity-achieving codes, called polar codes, for any binary discrete memoryless channel. In the thesis, we show that decoding algorithm…
Efficiently computing a subset of a correlation matrix consisting of values above a specified threshold is important to many practical applications. Real-world problems in genomics, machine learning, finance other applications can produce…
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…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…
We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over…
Independent component analysis (ICA) is a fundamental problem in the field of signal processing, and numerous algorithms have been developed to address this issue. The core principle of these algorithms is to find a transformation matrix…