Related papers: Complexity reduction of C-algorithm

In this contribution, the clustering procedure based on K-Means algorithm is studied as an inverse problem, which is a special case of the illposed problems. The attempts to improve the quality of the clustering inverse problem drive to…

Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…

This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the…

Causal structure discovery from observational data is fundamental to the causal understanding of autonomous systems such as medical decision support systems, advertising campaigns and self-driving cars. This is essential to solve well-known…

We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or…

This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody…

We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those…

Recent trends see a move away from a fixed-resource server-centric datacenter model to a more adaptable "disaggregated" datacenter model. These disaggregated datacenters can then dynamically group resources to the specific requirements of…

In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012--4024, with respect to the convergence of the accelerated Riccati iteration method for solving the…

Finding informative low-dimensional representations that can be computed efficiently in large datasets is an important problem in data analysis. Recently, contrastive Principal Component Analysis (cPCA) was proposed as a more informative…

A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…

The iterative rational Krylov algorithm (\textsf{IRKA}) is a popular approach for producing locally optimal reduced-order $\mathcal{H}_2$-approximations to linear time-invariant (LTI) dynamical systems. Overall, \textsf{IRKA} has seen…

As a judicious correspondence to the classical maxcut, the anti-Cheeger cut has more balanced structure, but few numerical results on it have been reported so far. In this paper, we propose a continuous iterative algorithm (CIA) for the…

We develop a generic reduction procedure for active learning problems. Our approach is inspired by a recent polynomial-time reduction of the exact learning problem for weighted automata over integers to that for weighted automata over…

Reversible Cellular Automata (RCA) are a physics-like model of computation consisting of an array of identical cells, evolving in discrete time steps by iterating a global evolution G. Further, G is required to be shift-invariant (it acts…

This paper presents the design of a novel distributed algorithm d-IRA for the reachability analysis of linear hybrid automata. Recent work on iterative relaxation abstraction (IRA) is leveraged to distribute the computational problem among…

Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

Let $S\subset R^n$ be a compact basic semi-algebraic set defined as the real solution set of multivariate polynomial inequalities with rational coefficients. We design an algorithm which takes as input a polynomial system defining $S$ and…

When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier…