Related papers: Scalable Iterative Algorithm for Robust Subspace C…

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…

Spectral clustering became a popular choice for data clustering for its ability of uncovering clusters of different shapes. However, it is not always preferable over other clustering methods due to its computational demands. One of the…

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Tensor clustering, which seeks to extract underlying cluster structures from noisy tensor observations, has gained increasing attention. One extensively studied model for tensor clustering is the tensor block model, which postulates the…

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…

This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must…

Subspace optimization methods have the attractive property of reducing large-scale optimization problems to a sequence of low-dimensional subspace optimization problems. However, existing subspace optimization frameworks adopt a fixed…

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…

Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there…

A new framework for many multiblock component methods (including consensus and hierarchical PCA) is proposed. It is based on the consensus PCA model: a scheme connecting each block of variables to a superblock obtained by concatenation of…

Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…

Insufficient capability of existing subspace clustering methods to handle data coming from nonlinear manifolds, data corruptions, and out-of-sample data hinders their applicability to address real-world clustering and classification…

There are synergies of research interests and industrial efforts in modeling fairness and correcting algorithmic bias in machine learning. In this paper, we present a scalable algorithm for spectral clustering (SC) with group fairness…

An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

Maintaining the pair similarity relationship among originally high-dimensional data into a low-dimensional binary space is a popular strategy to learn binary codes. One simiple and intutive method is to utilize two identical code matrices…

We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…

Minimax problems have recently attracted a lot of research interests. A few efforts have been made to solve decentralized nonconvex strongly-concave (NCSC) minimax-structured optimization; however, all of them focus on smooth problems with…