相关论文: Regularized Sparse Optimal Discriminant Clustering

Nowadays, data are generated massively and rapidly from scientific fields as bioinformatics, neuroscience and astronomy to business and engineering fields. Cluster analysis, as one of the major data analysis tools, is therefore more…

Sum-of-norms clustering is a clustering formulation based on convex optimization that automatically induces hierarchy. Multiple algorithms have been proposed to solve the optimization problem: subgradient descent by Hocking et al., ADMM and…

Support vector machine is an important and fundamental technique in machine learning. Soft-margin SVM models have stronger generalization performance compared with the hard-margin SVM. Most existing works use the hinge-loss function which…

We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm…

This paper studies high-dimensional sparse clustering, a combinatorial NP-hard problem arising from the bilinear coupling between cluster assignment and feature selection. We analyze semidefinite programming (SDP) relaxations of $K$-means…

Clustering is a fundamental problem in unsupervised learning. Popular methods like K-means, may suffer from poor performance as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as the…

A new model-based procedure is developed for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. The proposed method is…

In this paper, we propose a single-loop stochastic gradient algorithm for solving stochastic nonconvex-concave minimax optimization with nonlinear convex coupled constraints (MCC). The proposed method, SPACO (Stochastic Penalty-based…

This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…

Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not…

The optimization problem of sparse and low-rank matrix recovery is considered, which involves a least squares problem with a rank constraint and a cardinality constraint. To overcome the challenges posed by these constraints, an asymptotic…

We consider the task of classification in the high dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose a heuristic, called sparse…

The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…

Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is…

Evaluating the performance of clustering models is a challenging task where the outcome depends on the definition of what constitutes a cluster. Due to this design, current existing metrics rarely handle multiple clustering models with…

In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and could accelerate optimization algorithms for solving large scale convex optimization problems with…

Unsupervised learning has gained prominence in the big data era, offering a means to extract valuable insights from unlabeled datasets. Deep clustering has emerged as an important unsupervised category, aiming to exploit the non-linear…

Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

We introduce BLOC (Black-box Optimization over Correlation matrices), a general framework for sparse covariance estimation with non-convex penalties. BLOC operates on the manifold of correlation matrices and reparameterizes it via an…