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Related papers: Isotropic PCA and Affine-Invariant Clustering

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We introduce a mini-batch stochastic variance-reduced algorithm to solve finite-sum scale invariant problems which cover several examples in machine learning and statistics such as principal component analysis (PCA) and estimation of…

Optimization and Control · Mathematics 2023-04-25 Cheolmin Kim , Youngseok Kim , Diego Klabjan

In the context of unsupervised learning, effective clustering plays a vital role in revealing patterns and insights from unlabeled data. However, the success of clustering algorithms often depends on the relevance and contribution of…

Machine Learning · Computer Science 2025-03-18 Fabian Galis , Darian Onchis

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

Computer Vision and Pattern Recognition · Computer Science 2020-07-07 Wei Lian , WangMeng Zuo , Lei Zhang

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

Optimization and Control · Mathematics 2022-02-22 Dimitris Bertsimas , Ryan Cory-Wright , Jean Pauphilet

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Computation · Statistics 2023-11-06 Olga Dorabiala , Aleksandr Aravkin , J. Nathan Kutz

Particle swarm optimization is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The approach of particle swarms is an example for…

Artificial Intelligence · Computer Science 2014-07-24 Deepak Kumar , A G Ramakrishnan

Unsupervised disentangled representation learning is a long-standing problem in computer vision. This work proposes a novel framework for performing image clustering from deep embeddings by combining instance-level contrastive learning with…

Machine Learning · Computer Science 2021-10-05 Ramakrishnan Sundareswaran , Jansel Herrera-Gerena , John Just , Ali Jannesari

Clustering is one of the fundamental tasks in computer vision and pattern recognition. Recently, deep clustering methods (algorithms based on deep learning) have attracted wide attention with their impressive performance. Most of these…

Computer Vision and Pattern Recognition · Computer Science 2021-06-14 Yanhai Gan , Xinghui Dong , Huiyu Zhou , Feng Gao , Junyu Dong

In this paper we address the problem of building a class of robust factorization algorithms that solve for the shape and motion parameters with both affine (weak perspective) and perspective camera models. We introduce a Gaussian/uniform…

Computer Vision and Pattern Recognition · Computer Science 2020-12-16 Andrei Zaharescu , Radu Horaud

Subspace clustering methods based on expressing each data point as a linear combination of other data points have achieved great success in computer vision applications such as motion segmentation, face and digit clustering. In face…

Machine Learning · Computer Science 2020-05-11 Chong You , Chun-Guang Li , Daniel P. Robinson , Rene Vidal

It is well-known that box filters can be efficiently computed using pre-integrations and local finite-differences [Crow1984,Heckbert1986,Viola2001]. By generalizing this idea and by combining it with a non-standard variant of the Central…

Computer Vision and Pattern Recognition · Computer Science 2015-05-30 Kunal N. Chaudhury , Sebanti Sanyal

Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However,…

Computer Vision and Pattern Recognition · Computer Science 2021-06-21 Zhengrui Ma , Zhao Kang , Guangchun Luo , Ling Tian

It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…

Machine Learning · Statistics 2015-06-02 Anastasia Podosinnikova , Simon Setzer , Matthias Hein

Unsupervised learning techniques in computer vision often require learning latent representations, such as low-dimensional linear and non-linear subspaces. Noise and outliers in the data can frustrate these approaches by obscuring the…

This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose…

Computer Vision and Pattern Recognition · Computer Science 2012-02-20 Rene Vidal , Yi Ma , Shankar Sastry

The paper presents the algorithm for clustering a dataset by grouping the optimal, from the point of view of the BIC criterion, number of Gaussian clusters into the optimal, from the point of view of their statistical separability,…

Machine Learning · Computer Science 2023-10-31 Oleg I. Berngardt

We propose a general method for deep learning based point cloud analysis, which is invariant to rotation on the inputs. Classical methods are vulnerable to rotation, as they usually take aligned point clouds as input. Principle Component…

Computer Vision and Pattern Recognition · Computer Science 2024-02-05 Shuqing Luo , Wei Gao

This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Nicolas Paul , Luc Fety , Michel Terre

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Computation · Statistics 2010-06-04 Vladimir Rokhlin , Arthur Szlam , Mark Tygert

Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We give an algorithm for this problem that has a running time, and data requirement polynomial in the dimension and…

Machine Learning · Computer Science 2010-04-27 Ankur Moitra , Gregory Valiant