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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…

In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying…

Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…

Multi-view clustering has attracted broad attention due to its capacity to utilize consistent and complementary information among views. Although tremendous progress has been made recently, most existing methods undergo high complexity,…

Multi-view clustering has become increasingly important due to the multi-source character of real-world data. Among existing multi-view clustering methods, multi-kernel clustering and matrix factorization-based multi-view clustering have…

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

Clustering face images according to their identity has two important applications: (i) grouping a collection of face images when no external labels are associated with images, and (ii) indexing for efficient large scale face retrieval. The…

Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse…

Face clustering is an essential task in computer vision due to the explosion of related applications such as augmented reality or photo album management. The main challenge of this task lies in the imperfectness of similarities among image…

This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…

The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…

Object clustering, aiming at grouping similar objects into one cluster with an unsupervised strategy, has been extensivelystudied among various data-driven applications. However, most existing state-of-the-art object clustering methods…

Self-supervised learning on graphs has made large strides in achieving great performance in various downstream tasks. However, many state-of-the-art methods suffer from a number of impediments, which prevent them from realizing their full…

The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample…

Cluster resource allocation is a multidimensional search problem that finds the best allocation of tasks to servers. Because the search space grows exponentially, modern approaches frame it as a mixed integer program (MIP) or a complex set…

In the era of big data, we are often facing the challenge of data heterogeneity and the lack of label information simultaneously. In the financial domain (e.g., fraud detection), the heterogeneous data may include not only numerical data…

Superpixel decomposition methods are generally used as a pre-processing step to speed up image processing tasks. They group the pixels of an image into homogeneous regions while trying to respect existing contours. For all state-of-the-art…

Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local…