相关论文: Regularized Sparse Optimal Discriminant Clustering

The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found a promising clustering model and can outperform the classical…

Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational…

For the degree corrected stochastic block model in the presence of arbitrary or even adversarial outliers, we develop a convex-optimization-based clustering algorithm that includes a penalization term depending on the positive deviation of…

Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on $U^\top$ to get the…

The stable principal component pursuit (SPCP) is a non-smooth convex optimization problem, the solution of which enables one to reliably recover the low rank and sparse components of a data matrix which is corrupted by a dense noise matrix,…

Spectral Clustering (SC) is one of the most widely used methods for data clustering. It first finds a low-dimensonal embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on…

Clustering, like covariate selection for classification, is an important step to compress and interpret the data. However, clustering of covariates is often performed independently of the classification step, which can lead to undesirable…

Convex clustering is a convex relaxation of the $k$-means and hierarchical clustering. It involves solving a convex optimization problem with the objective function being a squared error loss plus a fusion penalty that encourages the…

Clustering has long been a popular unsupervised learning approach to identify groups of similar objects and discover patterns from unlabeled data in many applications. Yet, coming up with meaningful interpretations of the estimated clusters…

Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering high-dimensional data points lying in a union of low-dimensional subspaces. However, while $\ell_1$ optimization-based SSC algorithms suffer from high…

Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the…

Simultaneous clustering and optimization (SCO) has recently drawn much attention due to its wide range of practical applications. Many methods have been previously proposed to solve this problem and obtain the optimal model. However, when a…

A novel clustering technique based on the projection onto convex set (POCS) method, called POCS-based clustering algorithm, is proposed in this paper. The proposed POCS-based clustering algorithm exploits a parallel projection method of…

This paper aims to investigate the effectiveness of the recently proposed Boosted Difference of Convex functions Algorithm (BDCA) when applied to clustering with constraints and set clustering with constraints problems. This is the first…

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often…

Clustering has been one of the most basic and essential problems in unsupervised learning due to various applications in many critical fields. The recently proposed sum-of-norms (SON) model by Pelckmans et al. (2005), Lindsten et al. (2011)…

Sparse Subspace Clustering (SSC) is one of the most popular methods for clustering data points into their underlying subspaces. However, SSC may suffer from heavy computational burden. Orthogonal Matching Pursuit applied on SSC accelerates…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

This paper investigates quantile regression in the presence of non-convex and non-smooth sparse penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD). The non-smooth and non-convex nature of…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…