Related papers: Laplacian regularized low rank subspace clustering

Recent work has demonstrated that using a carefully designed dictionary instead of a predefined one, can improve the sparsity in jointly representing a class of signals. This has motivated the derivation of learning methods for designing a…

We consider a Canonical Polyadic (CP) decomposition approach to low-rank tensor completion (LRTC) by incorporating external pairwise similarity relations through graph Laplacian regularization on the CP factor matrices. The usage of graph…

Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

Label Smoothing (LS) is widely adopted to reduce overconfidence in neural network predictions and improve generalization. Despite these benefits, recent studies reveal two critical issues with LS. First, LS induces overconfidence in…

Machine learning has become a central research area, with increasing attention devoted to explainable clustering, also known as conceptual clustering, which is a knowledge-driven unsupervised learning paradigm that partitions data into…

We address the multi-focus image fusion problem, where multiple images captured with different focal settings are to be fused into an all-in-focus image of higher quality. Algorithms for this problem necessarily admit the source image…

Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…

Large scale object detection with thousands of classes introduces the problem of many contradicting false positive detections, which have to be suppressed. Class-independent non-maximum suppression has traditionally been used for this step,…

Mixed membership community detection is a challenge problem in network analysis. To estimate the memberships and study the impact of regularized spectral clustering under the mixed membership stochastic block (MMSB) model, this article…

One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…

We study in this paper the problem of jointly clustering and learning representations. As several previous studies have shown, learning representations that are both faithful to the data to be clustered and adapted to the clustering…

Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…

We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data,…

Linear discrimination, from the point of view of numerical linear algebra, can be treated as solving an ill-posed system of linear equations. In order to generate a solution that is robust in the presence of noise, these problems require…

Multi-view subspace learning (MSL) aims to find a low-dimensional subspace of the data obtained from multiple views. Different from single view case, MSL should take both common and specific knowledge among different views into…

Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace…

Spectral clustering is a well-known technique which identifies $k$ clusters in an undirected graph with weight matrix $W\in\mathbb{R}^{n\times n}$ by exploiting its graph Laplacian $L(W)$, whose eigenvalues $0=\lambda_1\leq \lambda_2 \leq…

Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the…

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…