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Cluster analysis organizes data into sensible groupings and is one of fundamental modes of understanding and learning. The widely used K-means and hierarchical clustering methods can be dramatically suboptimal due to local minima. Recently…

Convex-nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while maintaining the convexity of the entire objective function. It has been successfully applied to problems in signal processing,…

We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like online…

Graph based clustering is one of the major clustering methods. Most of it work in three separate steps: similarity graph construction, clustering label relaxing and label discretization with k-means. Such common practice has three…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

Correlation clustering is a widely-used approach for clustering large data sets based only on pairwise similarity information. In recent years, there has been a steady stream of better and better classical algorithms for approximating this…

Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…

Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…

This paper presents a parallel adaptive clustering (PAC) algorithm to automatically classify data while simultaneously choosing a suitable number of classes. Clustering is an important tool for data analysis and understanding in a broad set…

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…

Classification and clustering have been studied separately in machine learning and computer vision. Inspired by the recent success of deep learning models in solving various vision problems (e.g., object recognition, semantic segmentation)…

We propose a novel methodology for feature screening in clustering massive datasets, in which both the number of features and the number of observations can potentially be very large. Taking advantage of a fusion penalization based convex…

There is a growing interest in characterizing circular data found in biological systems. Such data are wide ranging and varied, from signal phase in neural recordings to nucleotide sequences in round genomes. Traditional clustering…

This paper deals with the Stochastic Capacitated Arc Routing Problem (SCARP), obtained by randomizing quantities on the arcs in the CARP. Optimization problems for the SCARP are characterized by decisions that are made without knowing their…

The paper has been withdrawn since more effective experiments should be completed. Auto-encoders (AE) has been widely applied in different fields of machine learning. However, as a deep model, there are a large amount of learnable…

Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…

Visualizations are frequently used as a means to understand trends and gather insights from datasets, but often take a long time to generate. In this paper, we focus on the problem of rapidly generating approximate visualizations while…

This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to…

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…

The parallel alternating direction method of multipliers (ADMM) algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical…