Related papers: Minimal and minimum unit circular-arc models

Canonical correlation analysis (CCA) is a multivariate statistical technique for finding the linear relationship between two sets of variables. The kernel generalization of CCA named kernel CCA has been proposed to find nonlinear relations…

Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding…

Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

The $k$-mismatch problem consists in computing the Hamming distance between a pattern $P$ of length $m$ and every length-$m$ substring of a text $T$ of length $n$, if this distance is no more than $k$. In many real-world applications, any…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale parallel computation frameworks and has recently gained a lot of importance, especially in the context of classic graph problems.…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Let $M$ be any compact four-dimensional PL-manifold with or without boundary (e.g. the four-dimensional sphere or ball). Consider the space $T(M)$ of all simplicial isomorphism classes of triangulations of $M$ endowed with the metric…

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…

We present a new algorithm for clustering points in R^n. The key property of the algorithm is that it is affine-invariant, i.e., it produces the same partition for any affine transformation of the input. It has strong guarantees when the…

Integrated principal components analysis, or iPCA, is an unsupervised learning technique for grouped vector data recently defined by Tang and Allen. Like PCA, iPCA computes new axes that best explain the variance of the data, but iPCA is…

We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact}…

The Kasner metrics are among the simplest solutions of the vacuum Einstein equations, and we use them here to examine the conformal method of finding solutions of the Einstein constraint equations. After describing the conformal method's…

Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…

We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between…

The Circle Packing Theorem states that every planar graph can be represented as the tangency graph of a family of internally-disjoint circles. A well-known generalization is the Primal-Dual Circle Packing Theorem for 3-connected planar…

Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks…

Let $\mathcal A$ be a simple, $\sigma$-unital, non-unital, non-elementary C*-algebra and let $I_{min}$ be the intersection of all the ideals of $\mathcal M(\mathcal A)$ that properly contain $\mathcal A$. $I_{min}$ coincides with the ideal…