相关论文: Efficient Algorithms for Large-scale Generalized E…

Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem…

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…

Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we…

In this paper linear canonical correlation analysis (LCCA) is generalized by applying a structured transform to the joint probability distribution of the considered pair of random vectors, i.e., a transformation of the joint probability…

We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few non-zero…

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…

Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

Canonical Correlation Analysis (CCA) models are powerful for studying the associations between two sets of variables. The canonically correlated representations, termed \textit{canonical variates} are widely used in unsupervised learning to…

Given an input $x$, and a search problem $F$, local computation algorithms (LCAs) implement access to specified locations of $y$ in a legal output $y \in F(x)$, using polylogarithmic time and space. Mansour et al., (2012), had previously…

We consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and…

Incorporating prior knowledge into a data-driven modeling problem can drastically improve performance, reliability, and generalization outside of the training sample. The stronger the structural properties, the more effective these…

Linking between two data sources is a basic building block in numerous computer vision problems. In this paper, we set to answer a fundamental cognitive question: are prior correspondences necessary for linking between different domains?…

This article critically assesses the utility of the classical statistical technique of Canonical Correlation Analysis (CCA) for studying spatial associations and proposes a new approach to enhance it. Unlike bivariate correlation analysis,…

Tensor canonical correlation analysis (TCCA) has garnered significant attention due to its effectiveness in capturing high-order correlations in multi-view learning. However, existing TCCA methods often underemphasize the characterization…

Learning representations of two views of data such that the resulting representations are highly linearly correlated is appealing in machine learning. In this paper, we present a canonical correlation guided learning framework, which allows…

For over a century canonical correlations, variables, and related concepts have been studied across various fields, with contributions dating back to Jordan [1875] and Hotelling [1936]. This text surveys the evolution of canonical…

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but…

This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in…

Canonical correlation analysis (CCA) is a popular technique for learning representations that are maximally correlated across multiple views in data. In this paper, we extend the CCA based framework for learning a multiview mixture model.…